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

• Label: 2496.2.m
• Level: $2496$
• Weight: $2$
• Character orbit: 2496.m
• Rep. character: $\chi_{2496}(2209,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $896$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(896\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\)

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

\( 56 q - 56 q^{9} - 48 q^{17} + 8 q^{25} - 24 q^{49} + 48 q^{65} + 56 q^{81}+O(q^{100}) \)

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.m.a	$2496$	$2$	2496.m	104.e	$2$	$8$	$8$	$19.931$	8.0.40960000.1	None		✓			2496.2.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}-q^{9}-\beta _{7}q^{11}+(2\beta _{3}+\cdots)q^{13}+\cdots\)
2496.2.m.b	$2496$	$2$	2496.m	104.e	$2$	$8$	$8$	$19.931$	8.0.1871773696.1	None		✓			2496.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+2\beta _{4}q^{7}-q^{9}-\beta _{6}q^{11}+\cdots\)
2496.2.m.c	$2496$	$2$	2496.m	104.e	$2$	$16$	$16$	$19.931$	16.0.\(\cdots\).1	None		✓			2496.2.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{11}q^{5}-\beta _{14}q^{7}-q^{9}+\cdots\)
2496.2.m.d	$2496$	$2$	2496.m	104.e	$2$	$24$	$24$	$19.931$		None		✓	✓		2496.2.m.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)