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

• Label: 920.2.bj
• Level: $920$
• Weight: $2$
• Character orbit: 920.bj
• Rep. character: $\chi_{920}(101,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $960$
• 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.bj (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q(\zeta_{22})\)
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	1480	960	520
Cusp forms	1400	960	440
Eisenstein series	80	0	80

Trace form

960 * q + 4 * q^2 - 2 * q^6 + 8 * q^7 + 10 * q^8 + 96 * q^9 - 4 * q^10 - 6 * q^12 - 4 * q^14 - 8 * q^15 - 24 * q^16 - 14 * q^18 + 16 * q^22 - 8 * q^23 - 4 * q^24 + 96 * q^25 + 26 * q^26 + 16 * q^31 + 24 * q^32 + 34 * q^34 - 72 * q^36 + 130 * q^38 - 24 * q^39 - 72 * q^40 - 40 * q^42 - 22 * q^44 + 156 * q^46 - 178 * q^48 - 96 * q^49 + 18 * q^50 - 14 * q^52 + 90 * q^54 - 134 * q^56 + 108 * q^58 - 18 * q^60 - 30 * q^62 - 40 * q^63 + 18 * q^64 + 44 * q^66 - 96 * q^68 + 16 * q^71 - 42 * q^72 - 38 * q^74 - 60 * q^76 - 182 * q^78 + 64 * q^79 + 16 * q^80 - 80 * q^81 - 58 * q^82 - 300 * q^84 - 96 * q^86 + 24 * q^87 - 84 * q^88 - 16 * q^89 + 16 * q^90 - 162 * q^92 - 208 * q^94 - 6 * q^96 - 228 * 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.bj.a	$920$	$2$	920.bj	184.p	$22$	$960$	$96$	$7.346$		None		✓	✓	✓	920.2.bj.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{22}]$

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

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