Space of modular forms of level 308, weight 2, and Character 308.bc

• Label: 308.2.bc
• Level: $308$
• Weight: $2$
• Character orbit: 308.bc
• Rep. character: $\chi_{308}(39,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $352$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.bc (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(308, [\chi])\).

	Total	New	Old
Modular forms	416	416	0
Cusp forms	352	352	0
Eisenstein series	64	64	0

Trace form

\( 352 q - 5 q^{2} - 5 q^{4} - 6 q^{5} - 20 q^{6} - 20 q^{8} - 42 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(308, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
308.2.bc.a	$308$	$2$	308.bc	308.ac	$30$	$352$	$44$	$2.459$		None		$8$	$0$	\(-5\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$