Space of modular forms of level 115, weight 7, and Character 115.d

• Label: 115.7.d
• Level: $115$
• Weight: $7$
• Character orbit: 115.d
• Rep. character: $\chi_{115}(91,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(115, [\chi])\).

	Total	New	Old
Modular forms	74	48	26
Cusp forms	70	48	22
Eisenstein series	4	0	4

Trace form

\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
115.7.d.a	$115$	$7$	115.d	23.b	$2$	$48$	$48$	$26.456$		None		$2$	$0$	\(-20\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)