Space of modular forms of level 304, weight 3, and Character 304.y

• Label: 304.3.y
• Level: $304$
• Weight: $3$
• Character orbit: 304.y
• Rep. character: $\chi_{304}(11,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $312$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	304.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 304 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(304, [\chi])\).

	Total	New	Old
Modular forms	328	328	0
Cusp forms	312	312	0
Eisenstein series	16	16	0

Trace form

\( 312 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 16 q^{7} - 20 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(304, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.3.y.a	$304$	$3$	304.y	304.y	$12$	$312$	$78$	$8.283$		None		$4$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-16\)		$\mathrm{SU}(2)[C_{12}]$