Space of modular forms of level 7488, weight 2, and Character 7488.j

• Label: 7488.2.j
• Level: $7488$
• Weight: $2$
• Character orbit: 7488.j
• Rep. character: $\chi_{7488}(287,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $2688$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7488.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2688\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7488, [\chi])\).

	Total	New	Old
Modular forms	1392	96	1296
Cusp forms	1296	96	1200
Eisenstein series	96	0	96

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(7488, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7488.2.j.a	$7488$	$2$	7488.j	24.f	$2$	$16$	$16$	$59.792$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			7488.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{11})q^{5}+\beta _{1}q^{7}+(\beta _{8}-\beta _{15})q^{11}+\cdots\)
7488.2.j.b	$7488$	$2$	7488.j	24.f	$2$	$16$	$16$	$59.792$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			7488.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{11})q^{5}+\beta _{1}q^{7}+(\beta _{8}-\beta _{15})q^{11}+\cdots\)
7488.2.j.c	$7488$	$2$	7488.j	24.f	$2$	$32$	$32$	$59.792$		None		✓			7488.2.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
7488.2.j.d	$7488$	$2$	7488.j	24.f	$2$	$32$	$32$	$59.792$		None		✓			7488.2.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(7488, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7488, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2496, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3744, [\chi])\)\(^{\oplus 2}\)