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

• Label: 920.2.bo
• Level: $920$
• Weight: $2$
• Character orbit: 920.bo
• Rep. character: $\chi_{920}(37,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $2800$
• 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.bo (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 920 \)
Character field:			\(\Q(\zeta_{44})\)
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	2960	2960	0
Cusp forms	2800	2800	0
Eisenstein series	160	160	0

Trace form

2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * 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.bo.a	$920$	$2$	920.bo	920.ao	$44$	$2800$	$140$	$7.346$		None		✓	✓	✓	920.2.bo.a	$8$	$0$	\(-18\)	\(0\)	\(0\)	\(-44\)		$\mathrm{SU}(2)[C_{44}]$