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

• Label: 792.2.k
• Level: $792$
• Weight: $2$
• Character orbit: 792.k
• Rep. character: $\chi_{792}(683,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	152	40	112
Cusp forms	136	40	96
Eisenstein series	16	0	16

Trace form

40 * q - 8 * q^4 + 8 * q^10 - 8 * q^16 + 32 * q^19 + 40 * q^25 - 32 * q^28 + 32 * q^34 + 16 * q^40 - 24 * q^46 - 8 * q^49 + 40 * q^52 - 8 * q^58 + 16 * q^64 + 72 * q^70 + 32 * q^73 - 8 * q^76 - 64 * q^82 - 24 * q^88 - 56 * q^94 - 32 * q^97

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.k.a	$792$	$2$	792.k	24.f	$2$	$40$	$40$	$6.324$		None		✓	✓	✓	792.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(792, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)