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

• Label: 920.2.b
• Level: $920$
• Weight: $2$
• Character orbit: 920.b
• Rep. character: $\chi_{920}(459,\cdot)$
• Character field: $\Q$
• Dimension: $140$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

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

Trace form

140 * q + 8 * q^6 - 140 * q^9 - 8 * q^16 + 4 * q^24 - 4 * q^25 + 8 * q^26 + 16 * q^35 - 24 * q^36 - 8 * q^41 - 8 * q^46 - 124 * q^49 + 4 * q^50 - 76 * q^54 - 8 * q^59 + 36 * q^64 - 8 * q^70 + 8 * q^75 + 108 * q^81 + 44 * q^94 + 16 * 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.b.a	$920$	$2$	920.b	920.b	$2$	$4$	$4$	$7.346$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		✓			920.2.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+2q^{4}-\beta _{3}q^{5}-2\beta _{3}q^{7}+\cdots\)
920.2.b.b	$920$	$2$	920.b	920.b	$2$	$136$	$136$	$7.346$		None		✓	✓		920.2.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$