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

• Label: 76.4.k
• Level: $76$
• Weight: $4$
• Character orbit: 76.k
• Rep. character: $\chi_{76}(3,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $168$
• 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.k (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
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	192	192	0
Cusp forms	168	168	0
Eisenstein series	24	24	0

Trace form

\( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} + O(q^{10}) \)

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.k.a	$76$	$4$	76.k	76.k	$18$	$168$	$28$	$4.484$		None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$