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

• Label: 308.2.d
• Level: $308$
• Weight: $2$
• Character orbit: 308.d
• Rep. character: $\chi_{308}(43,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(19\)

Dimensions

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

	Total	New	Old
Modular forms	52	36	16
Cusp forms	44	36	8
Eisenstein series	8	0	8

Trace form

\( 36 q + 2 q^{4} - 44 q^{9} + O(q^{10}) \)

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.d.a	$308$	$2$	308.d	44.c	$2$	$18$	$18$	$2.459$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(18\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots\)
308.2.d.b	$308$	$2$	308.d	44.c	$2$	$18$	$18$	$2.459$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-18\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(308, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)