Space of modular forms of level 304, weight 7, and Character 304.d

• Label: 304.7.d
• Level: $304$
• Weight: $7$
• Character orbit: 304.d
• Rep. character: $\chi_{304}(191,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $2$
• Sturm bound: $280$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	304.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(280\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(304, [\chi])\).

	Total	New	Old
Modular forms	246	54	192
Cusp forms	234	54	180
Eisenstein series	12	0	12

Trace form

\( 54 q + 132 q^{5} - 13122 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(304, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.7.d.a	$304$	$7$	304.d	4.b	$2$	$18$	$18$	$69.936$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-356\)	\(0\)	$2^{37}\cdot 19^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-20-\beta _{2})q^{5}+(\beta _{1}+\beta _{11}+\cdots)q^{7}+\cdots\)
304.7.d.b	$304$	$7$	304.d	4.b	$2$	$36$	$36$	$69.936$		None		$2$	$0$	\(0\)	\(0\)	\(488\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)