Space of modular forms of level 2520, weight 2, and Character 2520.e

• Label: 2520.2.e
• Level: $2520$
• Weight: $2$
• Character orbit: 2520.e
• Rep. character: $\chi_{2520}(1331,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $1152$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1152\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2520, [\chi])\).

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

Trace form

\( 96 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2520, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2520.2.e.a	$2520$	$2$	2520.e	24.f	$2$	$48$	$48$	$20.122$		None		$2$	$0$	\(-4\)	\(0\)	\(48\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2520.2.e.b	$2520$	$2$	2520.e	24.f	$2$	$48$	$48$	$20.122$		None		$2$	$0$	\(4\)	\(0\)	\(-48\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)