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

• Label: 7524.2.l
• Level: $7524$
• Weight: $2$
• Character orbit: 7524.l
• Rep. character: $\chi_{7524}(2089,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $6$
• Sturm bound: $2880$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7524.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2880\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1464	100	1364
Cusp forms	1416	100	1316
Eisenstein series	48	0	48

Trace form

\( 100 q + 2 q^{5} + O(q^{10}) \)

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.l.a	$7524$	$2$	7524.l	209.d	$2$	$4$	$4$	$60.079$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
7524.2.l.b	$7524$	$2$	7524.l	209.d	$2$	$8$	$8$	$60.079$	8.0.\(\cdots\).6	\(\Q(\sqrt{-627}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots\)
7524.2.l.c	$7524$	$2$	7524.l	209.d	$2$	$8$	$8$	$60.079$	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
7524.2.l.d	$7524$	$2$	7524.l	209.d	$2$	$16$	$16$	$60.079$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots\)
7524.2.l.e	$7524$	$2$	7524.l	209.d	$2$	$24$	$24$	$60.079$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
7524.2.l.f	$7524$	$2$	7524.l	209.d	$2$	$40$	$40$	$60.079$		None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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