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Results (16 matches)

 

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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
419.1.b.a	$419$	$1$	419.b	419.b	$2$	$1$	$1$	$0.209$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-419}) \)	None	✓	✓			419.1.b.a	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(-1\)	$1$		\(q-q^{3}+q^{4}+2q^{5}-q^{7}-q^{12}-q^{13}+\cdots\)
419.1.b.b	$419$	$1$	419.b	419.b	$2$	$3$	$3$	$0.209$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-419}) \)	None	✓	✓	✓		419.1.b.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+q^{4}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
1676.1.d.a	$1676$	$1$	1676.d	419.b	$2$	$9$	$9$	$0.836$	\(\Q(\zeta_{54})^+\)	$D_{27}$	\(\Q(\sqrt{-419}) \)	None	✓	✓	✓	✓	1676.1.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+(\beta _{3}-\beta _{6})q^{5}-\beta _{5}q^{7}+(1+\cdots)q^{9}+\cdots\)
2095.1.d.a	$2095$	$1$	2095.d	2095.d	$2$	$1$	$1$	$1.046$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-419}) \), \(\Q(\sqrt{-2095}) \)	\(\Q(\sqrt{5}) \)	✓	✓			2095.1.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{4}+q^{5}+q^{9}+q^{16}-q^{20}+q^{25}+\cdots\)
2095.1.d.b	$2095$	$1$	2095.d	2095.d	$2$	$2$	$2$	$1.046$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-419}) \)	None		✓			2095.1.d.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}+q^{5}+(-\zeta_{6}+\cdots)q^{7}+\cdots\)
2095.1.d.f	$2095$	$1$	2095.d	2095.d	$2$	$6$	$6$	$1.046$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-419}) \)	None		✓	✓		2095.1.d.f	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+(-\zeta_{18}-\zeta_{18}^{8})q^{3}-q^{4}+\zeta_{18}^{6}q^{5}+\cdots\)
2933.1.g.b	$2933$	$1$	2933.g	2933.g	$6$	$18$	$9$	$1.464$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-419}) \)	None		✓	✓		2933.1.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{3}-\zeta_{54}^{9}q^{4}+\cdots\)
3771.1.c.a	$3771$	$1$	3771.c	419.b	$2$	$1$	$1$	$1.882$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-419}) \)	None	✓				419.1.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)	$1$		\(q+q^{4}-2q^{5}-q^{7}-q^{13}+q^{16}-2q^{20}+\cdots\)
3771.1.c.b	$3771$	$1$	3771.c	419.b	$2$	$3$	$3$	$1.882$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-419}) \)	None	✓				419.1.b.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q+q^{4}+q^{5}-\beta _{1}q^{7}+(\beta _{1}-\beta _{2})q^{13}+\cdots\)
3771.1.g.a	$3771$	$1$	3771.g	3771.g	$6$	$2$	$1$	$1.882$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-419}) \)	None		✓			3771.1.g.a	$4$	$0$	\(0\)	\(-1\)	\(-2\)	\(-2\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
3771.1.g.b	$3771$	$1$	3771.g	3771.g	$6$	$2$	$1$	$1.882$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-419}) \)	None		✓			3771.1.g.b	$4$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)	$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
3771.1.g.c	$3771$	$1$	3771.g	3771.g	$6$	$2$	$1$	$1.882$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-419}) \)	None		✓			3771.1.g.c	$4$	$0$	\(0\)	\(2\)	\(-2\)	\(1\)	$1$		\(q+q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}+\cdots\)
3771.1.g.e	$3771$	$1$	3771.g	3771.g	$6$	$6$	$3$	$1.882$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-419}) \)	None		✓			3771.1.g.e	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}-\zeta_{18}^{6}q^{5}+\cdots\)
3771.1.g.f	$3771$	$1$	3771.g	3771.g	$6$	$6$	$3$	$1.882$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-419}) \)	None		✓			3771.1.g.f	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}-\zeta_{18}^{6}q^{5}+\cdots\)
419.3.b.a	$419$	$3$	419.b	419.b	$2$	$9$	$9$	$11.417$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	$_{}$	\(\Q(\sqrt{-419}) \)	None	✓	✓			419.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+4q^{4}+(-\beta _{3}+\beta _{6})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
1676.3.d.a	$1676$	$3$	1676.d	419.b	$2$	$18$	$18$	$45.668$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	\(\Q(\sqrt{-419}) \)	None	✓	✓			1676.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(-\beta _{13}-\beta _{15})q^{7}+\cdots\)