Space of modular forms of level 920, weight 2, and Character 920.n

• Label: 920.2.n
• Level: $920$
• Weight: $2$
• Character orbit: 920.n
• Rep. character: $\chi_{920}(91,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

	Total	New	Old
Modular forms	148	96	52
Cusp forms	140	96	44
Eisenstein series	8	0	8

Trace form

96 * q - 4 * q^2 + 8 * q^4 - 10 * q^6 + 2 * q^8 + 96 * q^9 - 6 * q^12 + 24 * q^16 - 14 * q^18 - 4 * q^24 + 96 * q^25 - 14 * q^26 - 24 * q^27 + 16 * q^32 + 2 * q^36 - 24 * q^46 + 66 * q^48 + 96 * q^49 - 4 * q^50 + 14 * q^52 - 34 * q^54 - 30 * q^58 + 24 * q^59 - 30 * q^62 + 14 * q^64 - 6 * q^72 - 38 * q^78 + 112 * q^81 - 14 * q^82 - 68 * q^92 - 50 * q^94 - 130 * q^96 + 20 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
920.2.n.a	$920$	$2$	920.n	184.h	$2$	$48$	$48$	$7.346$		None		✓			920.2.n.a	$2$	$0$	\(-2\)	\(0\)	\(-48\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
920.2.n.b	$920$	$2$	920.n	184.h	$2$	$48$	$48$	$7.346$		None		✓			920.2.n.a	$2$	$0$	\(-2\)	\(0\)	\(48\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)