Space of modular forms of level 792, weight 2, and trivial character

• Label: 792.2.a
• Level: $792$
• Weight: $2$
• Character orbit: 792.a
• Rep. character: $\chi_{792}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $10$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(792))\).

	Total	New	Old
Modular forms	160	13	147
Cusp forms	129	13	116
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(18\)	\(1\)	\(17\)		\(15\)	\(1\)	\(14\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(20\)	\(2\)	\(18\)		\(16\)	\(2\)	\(14\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(21\)	\(1\)	\(20\)		\(17\)	\(1\)	\(16\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(19\)	\(2\)	\(17\)		\(15\)	\(2\)	\(13\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(22\)	\(2\)	\(20\)		\(18\)	\(2\)	\(16\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(20\)	\(1\)	\(19\)		\(16\)	\(1\)	\(15\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(19\)	\(1\)	\(18\)		\(15\)	\(1\)	\(14\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(21\)	\(3\)	\(18\)		\(17\)	\(3\)	\(14\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(76\)	\(5\)	\(71\)		\(61\)	\(5\)	\(56\)		\(15\)	\(0\)	\(15\)
Minus space			\(-\)		\(84\)	\(8\)	\(76\)		\(68\)	\(8\)	\(60\)		\(16\)	\(0\)	\(16\)

Trace form

13 * q - 4 * q^5 + 4 * q^7 + 3 * q^11 + 2 * q^13 - 2 * q^17 + 4 * q^19 - 6 * q^23 + 13 * q^25 + 14 * q^29 - 6 * q^31 - 4 * q^35 + 2 * q^41 - 8 * q^43 - 4 * q^47 + 29 * q^49 + 10 * q^53 + 30 * q^59 + 18 * q^61 + 28 * q^65 - 14 * q^67 - 2 * q^71 - 10 * q^73 - 4 * q^77 + 28 * q^79 + 8 * q^83 - 16 * q^89 - 8 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(792))\) 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	11
792.2.a.a	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓				264.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
792.2.a.b	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓		✓	✓	264.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{11}+2q^{13}-6q^{17}-4q^{23}+\cdots\)
792.2.a.c	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓	✓	✓	✓	792.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}-6q^{13}+6q^{17}-2q^{19}+\cdots\)
792.2.a.d	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓	✓	✓	✓	792.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}-6q^{13}-6q^{17}-2q^{19}+\cdots\)
792.2.a.e	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓		✓	✓	264.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}+2q^{17}+8q^{19}+2q^{23}+\cdots\)
792.2.a.f	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓				264.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}+q^{11}+6q^{13}-6q^{17}+\cdots\)
792.2.a.g	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	\(\Q\)	None	✓				88.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
792.2.a.h	$792$	$2$	792.a	1.a	$1$	$2$	$2$	$6.324$	\(\Q(\sqrt{17}) \)	None	✓		✓	✓	88.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+q^{11}+\cdots\)
792.2.a.i	$792$	$2$	792.a	1.a	$1$	$2$	$2$	$6.324$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	792.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots\)
792.2.a.j	$792$	$2$	792.a	1.a	$1$	$2$	$2$	$6.324$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	792.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2+\beta )q^{7}+q^{11}+(2-\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(792))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(792)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 2}\)