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

• Label: 308.2.c
• Level: $308$
• Weight: $2$
• Character orbit: 308.c
• Rep. character: $\chi_{308}(153,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	54	8	46
Cusp forms	42	8	34
Eisenstein series	12	0	12

Trace form

\( 8 q - 4 q^{9} + O(q^{10}) \)

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.c.a	$308$	$2$	308.c	77.b	$2$	$4$	$4$	$2.459$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots\)
308.2.c.b	$308$	$2$	308.c	77.b	$2$	$4$	$4$	$2.459$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)

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

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