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

• Label: 304.2.x
• Level: $304$
• Weight: $2$
• Character orbit: 304.x
• Rep. character: $\chi_{304}(27,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $152$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 304 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	168	168	0
Cusp forms	152	152	0
Eisenstein series	16	16	0

Trace form

\( 152 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 16 q^{7} + O(q^{10}) \)

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.x.a	$304$	$2$	304.x	304.x	$12$	$4$	$1$	$2.427$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b	$304$	$2$	304.x	304.x	$12$	$4$	$1$	$2.427$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(4\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c	$304$	$2$	304.x	304.x	$12$	$144$	$36$	$2.427$		None		$4$	$0$	\(-6\)	\(-12\)	\(2\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$