Space of modular forms of level 92, weight 2, and Character 92.e

• Label: 92.2.e
• Level: $92$
• Weight: $2$
• Character orbit: 92.e
• Rep. character: $\chi_{92}(9,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(92, [\chi])\).

	Total	New	Old
Modular forms	150	20	130
Cusp forms	90	20	70
Eisenstein series	60	0	60

Trace form

\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(92, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
92.2.e.a	$92$	$2$	92.e	23.c	$11$	$20$	$2$	$0.735$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\beta _{6}+\beta _{8}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(92, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(92, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)