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

• Label: 920.2.bf
• Level: $920$
• Weight: $2$
• Character orbit: 920.bf
• Rep. character: $\chi_{920}(29,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $1400$
• 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.bf (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 920 \)
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	1480	0
Cusp forms	1400	1400	0
Eisenstein series	80	80	0

Trace form

1400 * q - 14 * q^4 - 14 * q^6 - 168 * q^9 - 5 * q^10 - 26 * q^14 - 6 * q^15 - 14 * q^16 - 27 * q^20 - 32 * q^24 - 18 * q^25 - 30 * q^26 - q^30 - 52 * q^31 + 40 * q^34 + 26 * q^36 - 12 * q^39 + 15 * q^40 - 36 * q^41 - 142 * q^44 - 10 * q^46 + 80 * q^49 - 47 * q^50 + 46 * q^54 - 38 * q^55 + 14 * q^56 + 21 * q^60 - 26 * q^64 + 2 * q^65 - 104 * q^66 - 26 * q^70 - 36 * q^71 - 18 * q^74 - 96 * q^76 - 12 * q^79 + 82 * q^80 - 136 * q^81 - 82 * q^84 - 198 * q^86 - 52 * q^89 + 164 * q^90 - 38 * q^94 + 2 * q^95 - 432 * q^96

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.bf.a	$920$	$2$	920.bf	920.af	$22$	$1400$	$140$	$7.346$		None		✓	✓	✓	920.2.bf.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$