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 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
92.2.e.a	$92$	$2$	92.e	23.c	$11$	$20$	$2$	$0.735$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	92.2.e.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\beta _{6}+\beta _{8}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)

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

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