Space of modular forms of level 2496, weight 2, and trivial character

• Label: 2496.2.a
• Level: $2496$
• Weight: $2$
• Character orbit: 2496.a
• Rep. character: $\chi_{2496}(1,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $38$
• Sturm bound: $896$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 38 \)
Sturm bound:			\(896\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2496))\).

	Total	New	Old
Modular forms	472	48	424
Cusp forms	425	48	377
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(54\)	\(6\)	\(48\)		\(49\)	\(6\)	\(43\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(62\)	\(6\)	\(56\)		\(56\)	\(6\)	\(50\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(64\)	\(8\)	\(56\)		\(58\)	\(8\)	\(50\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(56\)	\(4\)	\(52\)		\(50\)	\(4\)	\(46\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(60\)	\(6\)	\(54\)		\(54\)	\(6\)	\(48\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(60\)	\(6\)	\(54\)		\(54\)	\(6\)	\(48\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(58\)	\(4\)	\(54\)		\(52\)	\(4\)	\(48\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(58\)	\(8\)	\(50\)		\(52\)	\(8\)	\(44\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(228\)	\(20\)	\(208\)		\(205\)	\(20\)	\(185\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(244\)	\(28\)	\(216\)		\(220\)	\(28\)	\(192\)		\(24\)	\(0\)	\(24\)

Trace form

\( 48 q + 48 q^{9} + 48 q^{25} + 32 q^{29} + 32 q^{37} + 48 q^{49} + 32 q^{53} + 32 q^{61} + 32 q^{69} - 64 q^{77} + 48 q^{81} - 64 q^{85} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	13
2496.2.a.a	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
2496.2.a.b	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				78.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.c	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-q^{13}+2q^{15}+\cdots\)
2496.2.a.d	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.e	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				39.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.f	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
2496.2.a.g	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-6q^{11}+q^{13}+2q^{17}+\cdots\)
2496.2.a.h	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				156.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{13}-6q^{17}+\cdots\)
2496.2.a.i	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{13}+2q^{17}+\cdots\)
2496.2.a.j	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
2496.2.a.k	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
2496.2.a.l	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}-q^{13}+\cdots\)
2496.2.a.m	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
2496.2.a.n	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.o	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				156.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.p	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
2496.2.a.q	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				39.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.r	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.s	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.f	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-q^{13}-2q^{15}+\cdots\)
2496.2.a.t	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				78.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.u	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
2496.2.a.v	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				156.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-q^{13}-6q^{17}+\cdots\)
2496.2.a.w	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-q^{13}+2q^{17}+\cdots\)
2496.2.a.x	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+6q^{11}+q^{13}+2q^{17}+\cdots\)
2496.2.a.y	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
2496.2.a.z	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
2496.2.a.ba	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				1248.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}-q^{13}+\cdots\)
2496.2.a.bb	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
2496.2.a.bc	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				156.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.bd	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	\(\Q\)	None	✓				312.2.a.d	$1$	$0$	\(0\)	\(1\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.be	$2496$	$2$	2496.a	1.a	$1$	$2$	$2$	$19.931$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.l	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
2496.2.a.bf	$2496$	$2$	2496.a	1.a	$1$	$2$	$2$	$19.931$	\(\Q(\sqrt{2}) \)	None	✓		✓		39.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.bg	$2496$	$2$	2496.a	1.a	$1$	$2$	$2$	$19.931$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.k	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-6\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-3+\beta )q^{7}+q^{9}+\cdots\)
2496.2.a.bh	$2496$	$2$	2496.a	1.a	$1$	$2$	$2$	$19.931$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.l	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
2496.2.a.bi	$2496$	$2$	2496.a	1.a	$1$	$2$	$2$	$19.931$	\(\Q(\sqrt{2}) \)	None	✓				39.2.a.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.bj	$2496$	$2$	2496.a	1.a	$1$	$2$	$2$	$19.931$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.k	$1$	$0$	\(0\)	\(2\)	\(2\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots\)
2496.2.a.bk	$2496$	$2$	2496.a	1.a	$1$	$3$	$3$	$19.931$	3.3.148.1	None	✓		✓		1248.2.a.o	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
2496.2.a.bl	$2496$	$2$	2496.a	1.a	$1$	$3$	$3$	$19.931$	3.3.148.1	None	✓		✓		1248.2.a.o	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2496)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)