Space of modular forms of level 76, weight 4, and Character 76.d

• Label: 76.4.d
• Level: $76$
• Weight: $4$
• Character orbit: 76.d
• Rep. character: $\chi_{76}(75,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(76, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	28	28	0
Eisenstein series	4	4	0

Trace form

\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(76, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.4.d.a	$76$	$4$	76.d	76.d	$2$	$28$	$28$	$4.484$		None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$