Space of modular forms of level 5796, weight 2, and trivial character

• Label: 5796.2.a
• Level: $5796$
• Weight: $2$
• Character orbit: 5796.a
• Rep. character: $\chi_{5796}(1,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $22$
• Sturm bound: $2304$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5796.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(2304\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5796))\).

	Total	New	Old
Modular forms	1176	56	1120
Cusp forms	1129	56	1073
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.

\(2\)	\(3\)	\(7\)	\(23\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(10\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(6\)
Plus space				\(+\)	\(24\)
Minus space				\(-\)	\(32\)

Trace form

\( 56 q + 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5796))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7	23
5796.2.a.a	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+q^{7}+2q^{13}-4q^{17}+4q^{19}+\cdots\)
5796.2.a.b	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+3q^{11}-4q^{13}-8q^{17}+\cdots\)
5796.2.a.c	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+5q^{11}-6q^{13}-4q^{17}+7q^{19}+\cdots\)
5796.2.a.d	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{11}+2q^{13}+5q^{19}+q^{23}+\cdots\)
5796.2.a.e	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+2q^{11}-3q^{13}+q^{23}-5q^{25}+\cdots\)
5796.2.a.f	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+2q^{11}-q^{13}-6q^{19}+\cdots\)
5796.2.a.g	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-3q^{11}-4q^{13}+8q^{17}+\cdots\)
5796.2.a.h	$5796$	$2$	5796.a	1.a	$1$	$1$	$1$	$46.281$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+q^{7}+2q^{13}+4q^{17}+4q^{19}+\cdots\)
5796.2.a.i	$5796$	$2$	5796.a	1.a	$1$	$2$	$2$	$46.281$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-q^{7}+(1+2\beta )q^{11}+(1+\beta )q^{13}+\cdots\)
5796.2.a.j	$5796$	$2$	5796.a	1.a	$1$	$2$	$2$	$46.281$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-3\beta )q^{5}+q^{7}-3q^{11}+(-2+\beta )q^{13}+\cdots\)
5796.2.a.k	$5796$	$2$	5796.a	1.a	$1$	$2$	$2$	$46.281$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+q^{7}+(-1+2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
5796.2.a.l	$5796$	$2$	5796.a	1.a	$1$	$2$	$2$	$46.281$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+3q^{11}+(-1+\beta )q^{13}+\cdots\)
5796.2.a.m	$5796$	$2$	5796.a	1.a	$1$	$2$	$2$	$46.281$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(3-\beta )q^{5}-q^{7}+(-1-2\beta )q^{11}+\cdots\)
5796.2.a.n	$5796$	$2$	5796.a	1.a	$1$	$2$	$2$	$46.281$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(5\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(3-\beta )q^{5}+q^{7}+q^{11}+(2-5\beta )q^{13}+\cdots\)
5796.2.a.o	$5796$	$2$	5796.a	1.a	$1$	$3$	$3$	$46.281$	3.3.1101.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}-q^{7}-q^{11}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)
5796.2.a.p	$5796$	$2$	5796.a	1.a	$1$	$3$	$3$	$46.281$	3.3.1509.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+q^{7}+(-1+2\beta _{1})q^{11}+(1+\cdots)q^{13}+\cdots\)
5796.2.a.q	$5796$	$2$	5796.a	1.a	$1$	$4$	$4$	$46.281$	4.4.140608.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+q^{7}+(-1-\beta _{1})q^{11}+(1+\cdots)q^{13}+\cdots\)
5796.2.a.r	$5796$	$2$	5796.a	1.a	$1$	$4$	$4$	$46.281$	4.4.140608.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+q^{7}+(1+\beta _{1})q^{11}+(1+\beta _{2}+\cdots)q^{13}+\cdots\)
5796.2.a.s	$5796$	$2$	5796.a	1.a	$1$	$5$	$5$	$46.281$	5.5.8580816.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{4})q^{5}+q^{7}+(\beta _{2}+\beta _{4})q^{11}+\cdots\)
5796.2.a.t	$5796$	$2$	5796.a	1.a	$1$	$5$	$5$	$46.281$	5.5.6963152.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
5796.2.a.u	$5796$	$2$	5796.a	1.a	$1$	$6$	$6$	$46.281$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-6\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-q^{7}+(-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
5796.2.a.v	$5796$	$2$	5796.a	1.a	$1$	$6$	$6$	$46.281$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-6\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}-q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5796))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5796)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\)\(^{\oplus 2}\)