Space of modular forms of level 76, weight 7, and Character 76.b

• Label: 76.7.b
• Level: $76$
• Weight: $7$
• Character orbit: 76.b
• Rep. character: $\chi_{76}(39,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $1$
• Sturm bound: $70$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(70\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(76, [\chi])\).

	Total	New	Old
Modular forms	62	54	8
Cusp forms	58	54	4
Eisenstein series	4	0	4

Trace form

\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(76, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.7.b.a	$76$	$7$	76.b	4.b	$2$	$54$	$54$	$17.484$		None		$2$	$0$	\(-10\)	\(0\)	\(-44\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)