Space of modular forms of level 310, weight 2, and Character 310.b

• Label: 310.2.b
• Level: $310$
• Weight: $2$
• Character orbit: 310.b
• Rep. character: $\chi_{310}(249,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(310, [\chi])\).

	Total	New	Old
Modular forms	52	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

\( 16 q - 16 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(310, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
310.2.b.a	$310$	$2$	310.b	5.b	$2$	$8$	$8$	$2.475$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
310.2.b.b	$310$	$2$	310.b	5.b	$2$	$8$	$8$	$2.475$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{6}q^{3}-q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(310, [\chi])\) into lower level spaces

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