Space of modular forms of level 304, weight 2, and Character 304.bg

• Label: 304.2.bg
• Level: $304$
• Weight: $2$
• Character orbit: 304.bg
• Rep. character: $\chi_{304}(3,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $456$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.bg (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 304 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

	Total	New	Old
Modular forms	504	504	0
Cusp forms	456	456	0
Eisenstein series	48	48	0

Trace form

\( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.2.bg.a	$304$	$2$	304.bg	304.ag	$36$	$456$	$38$	$2.427$		None		$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(-12\)		$\mathrm{SU}(2)[C_{36}]$