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

• Label: 2496.2.d
• Level: $2496$
• Weight: $2$
• Character orbit: 2496.d
• Rep. character: $\chi_{2496}(1535,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $17$
• Sturm bound: $896$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(896\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(23\)

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.d.a	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2496.2.d.b	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
2496.2.d.c	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}+\beta q^{5}-\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
2496.2.d.d	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}+2\zeta_{6}q^{7}-3q^{9}+\cdots\)
2496.2.d.e	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{6}q^{3}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots\)
2496.2.d.f	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1-2\beta )q^{9}+\cdots\)
2496.2.d.g	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
2496.2.d.h	$2496$	$2$	2496.d	12.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(1-2\zeta_{6})q^{7}+\cdots\)
2496.2.d.i	$2496$	$2$	2496.d	12.b	$2$	$4$	$4$	$19.931$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2496.2.d.j	$2496$	$2$	2496.d	12.b	$2$	$4$	$4$	$19.931$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+(1-\zeta_{8}^{3})q^{9}+\cdots\)
2496.2.d.k	$2496$	$2$	2496.d	12.b	$2$	$4$	$4$	$19.931$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+3q^{9}-2\beta _{2}q^{11}+\cdots\)
2496.2.d.l	$2496$	$2$	2496.d	12.b	$2$	$4$	$4$	$19.931$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2496.2.d.m	$2496$	$2$	2496.d	12.b	$2$	$8$	$8$	$19.931$	8.0.121550625.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
2496.2.d.n	$2496$	$2$	2496.d	12.b	$2$	$8$	$8$	$19.931$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{2}q^{3}-\zeta_{24}q^{5}-\zeta_{24}^{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
2496.2.d.o	$2496$	$2$	2496.d	12.b	$2$	$12$	$12$	$19.931$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{9}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{9}+\cdots)q^{9}+\cdots\)
2496.2.d.p	$2496$	$2$	2496.d	12.b	$2$	$16$	$16$	$19.931$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
2496.2.d.q	$2496$	$2$	2496.d	12.b	$2$	$20$	$20$	$19.931$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{23}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{13}q^{3}+\beta _{12}q^{5}+\beta _{6}q^{7}+\beta _{8}q^{9}+\cdots\)

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

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