LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
329.1.f.b	$329$	$1$	329.f	329.f	$6$	$8$	$4$	$0.164$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		✓	✓		329.1.f.b	$4$	$0$	$-1$	$2$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}^{11}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
423.1.f.b	$423$	$1$	423.f	423.f	$6$	$8$	$4$	$0.211$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		✓	✓		423.1.f.b	$4$	$0$	$2$	$-2$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+\zeta_{30}^{12}q^{3}+\cdots$
36.2.h.a	$36$	$2$	36.h	36.h	$6$	$8$	$4$	$0.287$	8.0.170772624.1	$_{}$	None	None		✓	✓	✓	36.2.h.a	$4$	$0$	$-3$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
684.1.q.a	$684$	$1$	684.q	76.g	$6$	$8$	$4$	$0.341$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	684.1.q.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots$
693.1.bp.a	$693$	$1$	693.bp	231.r	$10$	$16$	$4$	$0.346$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	693.1.bp.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{2}+\zeta_{40}^{8}+\cdots)q^{4}+\cdots$
44.2.g.a	$44$	$2$	44.g	44.g	$10$	$16$	$4$	$0.351$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	44.2.g.a	$4$	$0$	$-5$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots$
715.1.bb.a	$715$	$1$	715.bb	715.ab	$6$	$8$	$4$	$0.357$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		✓	✓	✓	715.1.bb.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
45.2.j.a	$45$	$2$	45.j	45.j	$6$	$8$	$4$	$0.359$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓	✓	45.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{6}q^{2}+(\zeta_{24}^{5}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{3}q^{4}+\cdots$
721.1.p.b	$721$	$1$	721.p	721.p	$6$	$8$	$4$	$0.360$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-103}) $	None		✓	✓		721.1.p.b	$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
728.1.bl.a	$728$	$1$	728.bl	728.al	$6$	$8$	$4$	$0.363$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-14}) $	None		✓	✓	✓	728.1.bl.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
777.1.w.d	$777$	$1$	777.w	777.w	$6$	$8$	$4$	$0.388$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-111}) $	None		✓	✓		777.1.w.d	$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{4}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
799.1.h.b	$799$	$1$	799.h	799.h	$8$	$16$	$4$	$0.399$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-47}) $	None		✓	✓		799.1.h.b	$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+(\zeta_{40}^{11}-\zeta_{40}^{19})q^{2}+(-\zeta_{40}^{7}+\zeta_{40}^{8}+\cdots)q^{3}+\cdots$
855.1.u.a	$855$	$1$	855.u	285.n	$6$	$8$	$4$	$0.427$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	855.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{24}^{5}-\zeta_{24}^{11})q^{2}-\zeta_{24}^{4}q^{4}+\cdots$
855.1.z.d	$855$	$1$	855.z	855.z	$6$	$8$	$4$	$0.427$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-95}) $	None		✓	✓		855.1.z.d	$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
55.2.j.a	$55$	$2$	55.j	55.j	$10$	$16$	$4$	$0.439$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	55.2.j.a	$4$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots$
884.1.x.a	$884$	$1$	884.x	884.x	$6$	$8$	$4$	$0.441$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-17}) $	None		✓	✓	✓	884.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots$
57.2.f.a	$57$	$2$	57.f	57.f	$6$	$8$	$4$	$0.455$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓	✓	57.2.f.a	$4$	$0$	$0$	$0$	$0$	$-16$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots$
917.1.h.b	$917$	$1$	917.h	917.h	$6$	$8$	$4$	$0.458$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		✓	✓		917.1.h.b	$4$	$0$	$0$	$-1$	$-1$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{3}+\zeta_{30}^{10}q^{4}+\cdots$
935.1.y.a	$935$	$1$	935.y	935.y	$8$	$16$	$4$	$0.467$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-55}) $	None		✓	✓	✓	935.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{32}^{11}-\zeta_{32}^{13})q^{2}+(-\zeta_{32}^{6}+\zeta_{32}^{8}+\cdots)q^{4}+\cdots$
945.1.y.a	$945$	$1$	945.y	105.o	$6$	$8$	$4$	$0.472$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	945.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}+\zeta_{24}^{7})q^{2}+\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$
969.1.q.c	$969$	$1$	969.q	969.q	$6$	$8$	$4$	$0.484$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓		969.1.q.c	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{5}-\zeta_{24}^{11})q^{2}+\zeta_{24}^{2}q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
975.1.bi.a	$975$	$1$	975.bi	975.ai	$10$	$16$	$4$	$0.487$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-39}) $	None		✓	✓	✓	975.1.bi.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}^{9}-\zeta_{40}^{15})q^{2}-\zeta_{40}^{14}q^{3}+\cdots$
61.2.f.b	$61$	$2$	61.f	61.f	$6$	$8$	$4$	$0.487$	8.0.542936601.2	$_{}$	None	None		✓	✓		61.2.f.b	$2$	$0$	$0$	$-2$	$6$	$-3$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{6})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
61.2.g.a	$61$	$2$	61.g	61.g	$10$	$16$	$4$	$0.487$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	61.2.g.a	$2$	$0$	$-5$	$-1$	$0$	$10$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1}+\beta _{2}-2\beta _{4}-2\beta _{5}+\cdots)q^{3}+\cdots$
980.1.p.c	$980$	$1$	980.p	140.p	$6$	$8$	$4$	$0.489$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓		980.1.f.e	$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$
987.1.o.c	$987$	$1$	987.o	987.o	$6$	$8$	$4$	$0.493$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		✓			987.1.o.c	$4$	$0$	$-3$	$1$	$0$	$-1$	$1$		$q+(\zeta_{30}-\zeta_{30}^{9})q^{2}-\zeta_{30}^{7}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
987.1.o.d	$987$	$1$	987.o	987.o	$6$	$8$	$4$	$0.493$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		✓			987.1.o.c	$4$	$0$	$3$	$-1$	$0$	$-1$	$1$		$q+(\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+\zeta_{30}^{7}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots$
1001.1.y.c	$1001$	$1$	1001.y	1001.y	$6$	$8$	$4$	$0.500$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-143}) $	None		✓			1001.1.y.c	$4$	$0$	$-1$	$-1$	$0$	$1$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1001.1.y.d	$1001$	$1$	1001.y	1001.y	$6$	$8$	$4$	$0.500$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-143}) $	None		✓			1001.1.y.c	$4$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1027.1.o.b	$1027$	$1$	1027.o	1027.o	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		✓	✓		1027.1.o.b	$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{8}+\zeta_{30}^{10}+\cdots)q^{4}+\cdots$
1027.1.s.b	$1027$	$1$	1027.s	1027.s	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-79}) $	None		✓	✓		1027.1.s.b	$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}+\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
65.2.l.a	$65$	$2$	65.l	65.l	$6$	$8$	$4$	$0.519$	8.0.49787136.1	$_{}$	None	None		✓	✓	✓	65.2.l.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
65.2.m.a	$65$	$2$	65.m	13.e	$6$	$8$	$4$	$0.519$	8.0.22581504.2	$_{}$	None	None		✓	✓	✓	65.2.m.a	$2$	$0$	$0$	$2$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{2}+(\beta _{2}+\cdots)q^{3}+\cdots$
1045.1.w.f	$1045$	$1$	1045.w	1045.w	$10$	$16$	$4$	$0.522$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-95}) $	None		✓	✓		1045.1.w.f	$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots$
1064.1.br.c	$1064$	$1$	1064.br	1064.ar	$6$	$8$	$4$	$0.531$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓		1064.1.br.c	$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{24}^{5}q^{2}+(-\zeta_{24}-\zeta_{24}^{7})q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
1071.1.x.c	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		✓			1071.1.x.c	$4$	$0$	$-1$	$-1$	$1$	$4$	$1$		$q+(-\zeta_{30}-\zeta_{30}^{9})q^{2}+\zeta_{30}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
1071.1.x.d	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		✓			1071.1.x.c	$4$	$0$	$-1$	$1$	$-1$	$-4$	$1$		$q+(-\zeta_{30}^{3}-\zeta_{30}^{7})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
1113.1.n.c	$1113$	$1$	1113.n	1113.n	$6$	$8$	$4$	$0.555$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-159}) $	None		✓			1113.1.n.c	$4$	$0$	$-1$	$-4$	$-1$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}-\zeta_{30}^{5}q^{3}+(-\zeta_{30}+\cdots)q^{4}+\cdots$
1113.1.n.d	$1113$	$1$	1113.n	1113.n	$6$	$8$	$4$	$0.555$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-159}) $	None		✓			1113.1.n.c	$4$	$0$	$1$	$4$	$1$	$1$	$1$		$q+(-\zeta_{30}^{6}-\zeta_{30}^{14})q^{2}+\zeta_{30}^{5}q^{3}+\cdots$
1120.1.br.a	$1120$	$1$	1120.br	35.i	$6$	$8$	$4$	$0.559$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	1120.1.br.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}+\zeta_{24}^{10}q^{5}+\zeta_{24}^{11}q^{7}+\cdots$
1127.1.f.f	$1127$	$1$	1127.f	161.f	$6$	$8$	$4$	$0.562$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		✓	✓		1127.1.d.e	$8$	$0$	$0$	$0$	$0$	$0$	$3^{2}$		$q+(\zeta_{24}^{6}+\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11}+\cdots)q^{3}+\cdots$
1140.1.bb.a	$1140$	$1$	1140.bb	285.n	$6$	$8$	$4$	$0.569$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1140.1.bb.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{5}+(-\zeta_{24}^{3}-\zeta_{24}^{9}+\cdots)q^{7}+\cdots$
1148.1.o.d	$1148$	$1$	1148.o	1148.o	$6$	$8$	$4$	$0.573$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-41}) $	None		✓	✓		1148.1.o.d	$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{8}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots$
1161.1.i.c	$1161$	$1$	1161.i	129.f	$6$	$8$	$4$	$0.579$	8.0.12960000.1	$A_{5}$	None	None		✓	✓		1161.1.i.c	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
73.2.e.a	$73$	$2$	73.e	73.e	$6$	$8$	$4$	$0.583$	$\Q(\zeta_{15})$	$_{}$	None	None		✓	✓	✓	73.2.e.a	$2$	$0$	$-1$	$-2$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{3}+\zeta_{15}^{4}+\cdots)q^{2}+\cdots$
1176.1.s.c	$1176$	$1$	1176.s	168.s	$6$	$8$	$4$	$0.587$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		✓	✓		1176.1.n.e	$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots$
1179.1.h.c	$1179$	$1$	1179.h	1179.h	$6$	$8$	$4$	$0.588$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		✓	✓		1179.1.h.c	$4$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q-\zeta_{30}^{11}q^{3}+\zeta_{30}^{10}q^{4}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{5}+\cdots$
1197.1.bt.a	$1197$	$1$	1197.bt	399.s	$6$	$8$	$4$	$0.597$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	1197.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{8}q^{4}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{5}+\cdots$
75.2.i.a	$75$	$2$	75.i	25.e	$10$	$16$	$4$	$0.599$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	75.2.i.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{2}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{2}+\cdots$
77.2.l.b	$77$	$2$	77.l	77.l	$10$	$16$	$4$	$0.615$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		77.2.l.b	$4$	$0$	$-10$	$0$	$0$	$-10$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.