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

• Label: 2496.2.c
• Level: $2496$
• Weight: $2$
• Character orbit: 2496.c
• Rep. character: $\chi_{2496}(961,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $18$
• Sturm bound: $896$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(896\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(23\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	472	56	416
Cusp forms	424	56	368
Eisenstein series	48	0	48

Trace form

\( 56 q + 56 q^{9} - 8 q^{13} + 16 q^{17} - 72 q^{25} - 56 q^{49} - 16 q^{61} - 16 q^{65} + 56 q^{81}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2496.2.c.a	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					312.2.c.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2\beta q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2496.2.c.b	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					156.2.b.b	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}-2\beta q^{7}+q^{9}-3\beta q^{11}+\cdots\)
2496.2.c.c	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					312.2.c.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta q^{7}+q^{9}+\beta q^{11}+(-\beta-3)q^{13}+\cdots\)
2496.2.c.d	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None					39.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{7}+q^{9}-\beta q^{11}+(-\beta+1)q^{13}+\cdots\)
2496.2.c.e	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None					156.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(-\beta+1)q^{13}+\cdots\)
2496.2.c.f	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					78.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(-\beta+3)q^{13}+\cdots\)
2496.2.c.g	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					312.2.c.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
2496.2.c.h	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					312.2.c.c	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2\beta q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
2496.2.c.i	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					156.2.b.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}+3\beta q^{11}+\cdots\)
2496.2.c.j	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					312.2.c.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{7}+q^{9}-\beta q^{11}+(-\beta-3)q^{13}+\cdots\)
2496.2.c.k	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None					39.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{7}+q^{9}-\beta q^{11}+(\beta+1)q^{13}+\cdots\)
2496.2.c.l	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-3}) \)	None					156.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(-\beta+1)q^{13}+\cdots\)
2496.2.c.m	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					78.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+(-\beta+3)q^{13}+\cdots\)
2496.2.c.n	$2496$	$2$	2496.c	13.b	$2$	$2$	$2$	$19.931$	\(\Q(\sqrt{-1}) \)	None					312.2.c.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
2496.2.c.o	$2496$	$2$	2496.c	13.b	$2$	$6$	$6$	$19.931$	6.0.153664.1	None					1248.2.c.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
2496.2.c.p	$2496$	$2$	2496.c	13.b	$2$	$6$	$6$	$19.931$	6.0.153664.1	None					1248.2.c.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
2496.2.c.q	$2496$	$2$	2496.c	13.b	$2$	$8$	$8$	$19.931$	8.0.134560000.4	None					1248.2.c.c	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
2496.2.c.r	$2496$	$2$	2496.c	13.b	$2$	$8$	$8$	$19.931$	8.0.134560000.4	None					1248.2.c.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)