Space of modular forms of level 2496, weight 2, and Character 2496.j

• Label: 2496.2.j
• Level: $2496$
• Weight: $2$
• Character orbit: 2496.j
• Rep. character: $\chi_{2496}(287,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $896$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(896\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(19\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2496, [\chi])\).

	Total	New	Old
Modular forms	472	96	376
Cusp forms	424	96	328
Eisenstein series	48	0	48

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(2496, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2496.2.j.a	$2496$	$2$	2496.j	24.f	$2$	$4$	$4$	$19.931$	\(\Q(\zeta_{8})\)	None		$4$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}^{2})q^{3}+\zeta_{8}^{3}q^{5}-4\zeta_{8}q^{7}+\cdots\)
2496.2.j.b	$2496$	$2$	2496.j	24.f	$2$	$4$	$4$	$19.931$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}^{3}q^{5}-4\zeta_{8}q^{7}+\cdots\)
2496.2.j.c	$2496$	$2$	2496.j	24.f	$2$	$12$	$12$	$19.931$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{8}q^{5}+(-\beta _{3}-\beta _{6}+2\beta _{7}+\cdots)q^{7}+\cdots\)
2496.2.j.d	$2496$	$2$	2496.j	24.f	$2$	$12$	$12$	$19.931$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{8}q^{5}+(\beta _{3}+\beta _{6}-2\beta _{7}+\cdots)q^{7}+\cdots\)
2496.2.j.e	$2496$	$2$	2496.j	24.f	$2$	$32$	$32$	$19.931$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2496.2.j.f	$2496$	$2$	2496.j	24.f	$2$	$32$	$32$	$19.931$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2496, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)