Space of modular forms of level 7524, weight 2, and Character 7524.f

• Label: 7524.2.f
• Level: $7524$
• Weight: $2$
• Character orbit: 7524.f
• Rep. character: $\chi_{7524}(4445,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $2880$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7524.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2880\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7524, [\chi])\).

	Total	New	Old
Modular forms	1464	64	1400
Cusp forms	1416	64	1352
Eisenstein series	48	0	48

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7524, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7524.2.f.a	$7524$	$2$	7524.f	57.d	$2$	$64$	$64$	$60.079$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(7524, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7524, [\chi]) \cong \)