Space of modular forms of level 304, weight 5, and Character 304.q

• Label: 304.5.q
• Level: $304$
• Weight: $5$
• Character orbit: 304.q
• Rep. character: $\chi_{304}(159,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $200$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(200\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(304, [\chi])\).

	Total	New	Old
Modular forms	332	80	252
Cusp forms	308	80	228
Eisenstein series	24	0	24

Trace form

\( 80 q + 912 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(304, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.5.q.a	$304$	$5$	304.q	76.g	$6$	$24$	$12$	$31.424$		None		$4$	$0$	\(0\)	\(0\)	\(18\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
304.5.q.b	$304$	$5$	304.q	76.g	$6$	$28$	$14$	$31.424$		None		$2$	$0$	\(0\)	\(-18\)	\(-9\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
304.5.q.c	$304$	$5$	304.q	76.g	$6$	$28$	$14$	$31.424$		None		$2$	$0$	\(0\)	\(18\)	\(-9\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{5}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)