Space of modular forms of level 310, weight 4, and Character 310.b

• Label: 310.4.b
• Level: $310$
• Weight: $4$
• Character orbit: 310.b
• Rep. character: $\chi_{310}(249,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(310, [\chi])\).

	Total	New	Old
Modular forms	148	44	104
Cusp forms	140	44	96
Eisenstein series	8	0	8

Trace form

\( 44 q - 176 q^{4} + 4 q^{5} + 8 q^{6} - 396 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(310, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
310.4.b.a	$310$	$4$	310.b	5.b	$2$	$4$	$4$	$18.291$	\(\Q(i, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-4q^{4}+(3-2\beta _{1}+\cdots)q^{5}+\cdots\)
310.4.b.b	$310$	$4$	310.b	5.b	$2$	$18$	$18$	$18.291$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{10}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{4}q^{3}-4q^{4}-\beta _{11}q^{5}+\cdots\)
310.4.b.c	$310$	$4$	310.b	5.b	$2$	$22$	$22$	$18.291$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(310, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(310, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)