Space of modular forms of level 2310, weight 2, and Character 2310.d

• Label: 2310.2.d
• Level: $2310$
• Weight: $2$
• Character orbit: 2310.d
• Rep. character: $\chi_{2310}(769,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $1152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2310.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 385 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1152\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2310, [\chi])\).

	Total	New	Old
Modular forms	592	96	496
Cusp forms	560	96	464
Eisenstein series	32	0	32

Trace form

\( 96 q + 96 q^{4} + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2310, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2310.2.d.a	$2310$	$2$	2310.d	385.h	$2$	$24$	$24$	$18.445$		None		$2$	$0$	\(-24\)	\(-24\)	\(-2\)	\(-2\)		$\mathrm{SU}(2)[C_{2}]$
2310.2.d.b	$2310$	$2$	2310.d	385.h	$2$	$24$	$24$	$18.445$		None		$2$	$0$	\(-24\)	\(24\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{2}]$
2310.2.d.c	$2310$	$2$	2310.d	385.h	$2$	$24$	$24$	$18.445$		None		$2$	$0$	\(24\)	\(-24\)	\(-2\)	\(2\)		$\mathrm{SU}(2)[C_{2}]$
2310.2.d.d	$2310$	$2$	2310.d	385.h	$2$	$24$	$24$	$18.445$		None		$2$	$0$	\(24\)	\(24\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2310, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \)