Space of modular forms of level 92, weight 3, and Character 92.g

• Label: 92.3.g
• Level: $92$
• Weight: $3$
• Character orbit: 92.g
• Rep. character: $\chi_{92}(3,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $220$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(92, [\chi])\).

	Total	New	Old
Modular forms	260	260	0
Cusp forms	220	220	0
Eisenstein series	40	40	0

Trace form

\( 220 q - 11 q^{2} - 11 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{8} + 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(92, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
92.3.g.a	$92$	$3$	92.g	92.g	$22$	$220$	$22$	$2.507$		None		$4$	$0$	\(-11\)	\(0\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$