Space of modular forms of level 5096, weight 2, and trivial character

• Label: 5096.2.a
• Level: $5096$
• Weight: $2$
• Character orbit: 5096.a
• Rep. character: $\chi_{5096}(1,\cdot)$
• Character field: $\Q$
• Dimension: $123$
• Newform subspaces: $33$
• Sturm bound: $1568$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5096 = 2^{3} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5096.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 33 \)
Sturm bound:			\(1568\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5096))\).

	Total	New	Old
Modular forms	816	123	693
Cusp forms	753	123	630
Eisenstein series	63	0	63

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

\(2\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(14\)
\(+\)	\(+\)	\(-\)	\(-\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)	\(15\)
\(-\)	\(+\)	\(-\)	\(+\)	\(13\)
\(-\)	\(-\)	\(+\)	\(+\)	\(15\)
\(-\)	\(-\)	\(-\)	\(-\)	\(18\)
Plus space			\(+\)	\(54\)
Minus space			\(-\)	\(69\)

Trace form

\( 123 q + 2 q^{3} - 2 q^{5} + 113 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5096))\) 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	7	13
5096.2.a.a	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-3q^{5}+q^{9}+q^{13}+6q^{15}+\cdots\)
5096.2.a.b	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.r.c	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots\)
5096.2.a.c	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				104.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}-2q^{11}+q^{13}+\cdots\)
5096.2.a.d	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.r.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+5q^{11}+q^{13}+\cdots\)
5096.2.a.e	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.r.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{9}-q^{11}-q^{13}+\cdots\)
5096.2.a.f	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+2q^{11}-q^{13}+7q^{19}+\cdots\)
5096.2.a.g	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.r.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{9}-q^{11}+q^{13}+\cdots\)
5096.2.a.h	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.r.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+5q^{11}-q^{13}+\cdots\)
5096.2.a.i	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{9}+3q^{11}+q^{13}-4q^{17}+\cdots\)
5096.2.a.j	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.r.c	$1$	$1$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+q^{13}+\cdots\)
5096.2.a.k	$5096$	$2$	5096.a	1.a	$1$	$1$	$1$	$40.692$	\(\Q\)	None	✓				728.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}+4q^{11}+q^{13}+\cdots\)
5096.2.a.l	$5096$	$2$	5096.a	1.a	$1$	$2$	$2$	$40.692$	\(\Q(\sqrt{7}) \)	None	✓				728.2.r.d	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+(-2+\beta )q^{11}+q^{13}+\cdots\)
5096.2.a.m	$5096$	$2$	5096.a	1.a	$1$	$2$	$2$	$40.692$	\(\Q(\sqrt{17}) \)	None	✓				104.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
5096.2.a.n	$5096$	$2$	5096.a	1.a	$1$	$2$	$2$	$40.692$	\(\Q(\sqrt{17}) \)	None	✓				728.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+(1+\beta )q^{9}+(2+\beta )q^{11}+\cdots\)
5096.2.a.o	$5096$	$2$	5096.a	1.a	$1$	$2$	$2$	$40.692$	\(\Q(\sqrt{3}) \)	None	✓				728.2.a.f	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}+(1+2\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
5096.2.a.p	$5096$	$2$	5096.a	1.a	$1$	$2$	$2$	$40.692$	\(\Q(\sqrt{7}) \)	None	✓				728.2.r.d	$1$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+(-2-\beta )q^{11}-q^{13}+\cdots\)
5096.2.a.q	$5096$	$2$	5096.a	1.a	$1$	$2$	$2$	$40.692$	\(\Q(\sqrt{2}) \)	None	✓				728.2.a.e	$1$	$0$	\(0\)	\(4\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}+(1+\beta )q^{5}+(3+4\beta )q^{9}+\cdots\)
5096.2.a.r	$5096$	$2$	5096.a	1.a	$1$	$4$	$4$	$40.692$	4.4.23252.1	None	✓	✓	✓		5096.2.a.r	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
5096.2.a.s	$5096$	$2$	5096.a	1.a	$1$	$4$	$4$	$40.692$	4.4.64268.1	None	✓				728.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(3+\beta _{1}+\beta _{3})q^{9}+\cdots\)
5096.2.a.t	$5096$	$2$	5096.a	1.a	$1$	$4$	$4$	$40.692$	4.4.183064.1	None	✓				728.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{9}+\beta _{1}q^{11}+\cdots\)
5096.2.a.u	$5096$	$2$	5096.a	1.a	$1$	$4$	$4$	$40.692$	4.4.20308.1	None	✓				728.2.r.e	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
5096.2.a.v	$5096$	$2$	5096.a	1.a	$1$	$4$	$4$	$40.692$	4.4.20308.1	None	✓				728.2.r.e	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
5096.2.a.w	$5096$	$2$	5096.a	1.a	$1$	$4$	$4$	$40.692$	4.4.23252.1	None	✓	✓			5096.2.a.r	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
5096.2.a.x	$5096$	$2$	5096.a	1.a	$1$	$5$	$5$	$40.692$	5.5.2398996.1	None	✓	✓	✓		5096.2.a.x	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{2}-\beta _{3})q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
5096.2.a.y	$5096$	$2$	5096.a	1.a	$1$	$5$	$5$	$40.692$	5.5.2398996.1	None	✓	✓			5096.2.a.x	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{2}-\beta _{3})q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
5096.2.a.z	$5096$	$2$	5096.a	1.a	$1$	$7$	$7$	$40.692$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				728.2.r.f	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.ba	$5096$	$2$	5096.a	1.a	$1$	$7$	$7$	$40.692$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		728.2.r.f	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.bb	$5096$	$2$	5096.a	1.a	$1$	$8$	$8$	$40.692$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		728.2.r.g	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-\beta _{2}-\beta _{4}+\beta _{7})q^{9}+\cdots\)
5096.2.a.bc	$5096$	$2$	5096.a	1.a	$1$	$8$	$8$	$40.692$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		5096.2.a.bc	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.bd	$5096$	$2$	5096.a	1.a	$1$	$8$	$8$	$40.692$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		5096.2.a.bc	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.be	$5096$	$2$	5096.a	1.a	$1$	$8$	$8$	$40.692$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				728.2.r.g	$1$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2-\beta _{2}-\beta _{4}+\beta _{7})q^{9}+\cdots\)
5096.2.a.bf	$5096$	$2$	5096.a	1.a	$1$	$10$	$10$	$40.692$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		5096.2.a.bf	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{9})q^{5}+(2+\beta _{8}-\beta _{9})q^{9}+\cdots\)
5096.2.a.bg	$5096$	$2$	5096.a	1.a	$1$	$10$	$10$	$40.692$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		5096.2.a.bf	$1$	$0$	\(0\)	\(2\)	\(6\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}+(2+\beta _{8}-\beta _{9})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5096))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5096)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1274))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2548))\)\(^{\oplus 2}\)