Space of modular forms of level 792, weight 2, and Character 792.b

• Label: 792.2.b
• Level: $792$
• Weight: $2$
• Character orbit: 792.b
• Rep. character: $\chi_{792}(593,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(792, [\chi])\).

	Total	New	Old
Modular forms	160	12	148
Cusp forms	128	12	116
Eisenstein series	32	0	32

Trace form

\( 12 q - 52 q^{25} - 24 q^{31} + 24 q^{37} - 28 q^{49} + 32 q^{55} + 64 q^{67} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(792, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
792.2.b.a	$792$	$2$	792.b	33.d	$2$	$6$	$6$	$6.324$	6.0.12781568.1	None		✓			792.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}-\beta _{4})q^{11}+\cdots\)
792.2.b.b	$792$	$2$	792.b	33.d	$2$	$6$	$6$	$6.324$	6.0.12781568.1	None		✓			792.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(792, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(792, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 2}\)