Space of modular forms of level 792, weight 5, and Character 792.j

• Label: 792.5.j
• Level: $792$
• Weight: $5$
• Character orbit: 792.j
• Rep. character: $\chi_{792}(505,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	792.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(792, [\chi])\).

	Total	New	Old
Modular forms	592	60	532
Cusp forms	560	60	500
Eisenstein series	32	0	32

Trace form

\( 60 q + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(792, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
792.5.j.a	$792$	$5$	792.j	11.b	$2$	$12$	$12$	$81.869$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					88.5.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
792.5.j.b	$792$	$5$	792.j	11.b	$2$	$24$	$24$	$81.869$		None					264.5.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
792.5.j.c	$792$	$5$	792.j	11.b	$2$	$24$	$24$	$81.869$		None		✓			792.5.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(792, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(792, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 2}\)