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

• Label: 920.2.v
• Level: $920$
• Weight: $2$
• Character orbit: 920.v
• Rep. character: $\chi_{920}(323,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $264$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	296	264	32
Cusp forms	280	264	16
Eisenstein series	16	0	16

Trace form

264 * q - 12 * q^8 + 16 * q^10 - 16 * q^12 - 16 * q^16 + 8 * q^17 - 28 * q^18 - 16 * q^22 - 8 * q^25 - 48 * q^26 - 12 * q^28 - 24 * q^30 + 40 * q^32 - 48 * q^35 + 32 * q^36 + 12 * q^38 + 16 * q^40 + 40 * q^42 - 64 * q^43 - 28 * q^48 - 40 * q^50 + 16 * q^52 - 40 * q^56 - 20 * q^58 - 100 * q^60 - 60 * q^62 - 8 * q^65 - 72 * q^66 + 48 * q^67 + 72 * q^68 - 60 * q^70 + 80 * q^72 - 40 * q^73 + 112 * q^75 + 48 * q^76 + 28 * q^78 - 60 * q^80 - 264 * q^81 + 44 * q^82 + 56 * q^86 - 68 * q^88 + 64 * q^91 + 16 * q^96 - 40 * q^97 + 16 * 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.v.a	$920$	$2$	920.v	40.k	$4$	$264$	$132$	$7.346$		None		✓	✓	✓	920.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)