Space of modular forms of level 5295, weight 2, and trivial character

• Label: 5295.2.a
• Level: $5295$
• Weight: $2$
• Character orbit: 5295.a
• Rep. character: $\chi_{5295}(1,\cdot)$
• Character field: $\Q$
• Dimension: $235$
• Newform subspaces: $8$
• Sturm bound: $1416$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 5295 = 3 \cdot 5 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5295.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1416\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5295))\).

	Total	New	Old
Modular forms	712	235	477
Cusp forms	705	235	470
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(5\)	\(353\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(24\)
\(+\)	\(+\)	\(-\)	\(-\)	\(34\)
\(+\)	\(-\)	\(+\)	\(-\)	\(34\)
\(+\)	\(-\)	\(-\)	\(+\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)	\(40\)
\(-\)	\(+\)	\(-\)	\(+\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(39\)
Plus space			\(+\)	\(88\)
Minus space			\(-\)	\(147\)

Trace form

\( 235 q + 5 q^{2} + 3 q^{3} + 241 q^{4} - q^{5} - 3 q^{6} + 8 q^{7} + 9 q^{8} + 235 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5295))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	353
5295.2.a.a	$5295$	$2$	5295.a	1.a	$1$	$20$	$20$	$42.281$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	5295.2.a.a	$1$	$1$	\(-6\)	\(20\)	\(20\)	\(-17\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5295.2.a.b	$5295$	$2$	5295.a	1.a	$1$	$20$	$20$	$42.281$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	5295.2.a.b	$1$	$1$	\(-2\)	\(20\)	\(-20\)	\(-11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
5295.2.a.c	$5295$	$2$	5295.a	1.a	$1$	$24$	$24$	$42.281$		None	✓	✓	✓	✓	5295.2.a.c	$1$	$1$	\(-6\)	\(-24\)	\(24\)	\(-5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
5295.2.a.d	$5295$	$2$	5295.a	1.a	$1$	$24$	$24$	$42.281$		None	✓	✓	✓	✓	5295.2.a.d	$1$	$1$	\(-2\)	\(-24\)	\(-24\)	\(9\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
5295.2.a.e	$5295$	$2$	5295.a	1.a	$1$	$34$	$34$	$42.281$		None	✓	✓	✓	✓	5295.2.a.e	$1$	$0$	\(3\)	\(-34\)	\(-34\)	\(-9\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
5295.2.a.f	$5295$	$2$	5295.a	1.a	$1$	$34$	$34$	$42.281$		None	✓	✓	✓	✓	5295.2.a.f	$1$	$0$	\(9\)	\(-34\)	\(34\)	\(5\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
5295.2.a.g	$5295$	$2$	5295.a	1.a	$1$	$39$	$39$	$42.281$		None	✓	✓	✓	✓	5295.2.a.g	$1$	$0$	\(6\)	\(39\)	\(39\)	\(25\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
5295.2.a.h	$5295$	$2$	5295.a	1.a	$1$	$40$	$40$	$42.281$		None	✓	✓	✓	✓	5295.2.a.h	$1$	$0$	\(3\)	\(40\)	\(-40\)	\(11\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5295))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5295)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(353))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1059))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1765))\)\(^{\oplus 2}\)