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

• Label: 920.2.f
• Level: $920$
• Weight: $2$
• Character orbit: 920.f
• Rep. character: $\chi_{920}(461,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
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	88	60
Cusp forms	140	88	52
Eisenstein series	8	0	8

Trace form

\( 88 q - 6 q^{6} + 6 q^{8} - 88 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
920.2.f.a	$920$	$2$	920.f	8.b	$2$	$2$	$2$	$7.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+i)q^{2}+2iq^{4}+iq^{5}+(-2+2i)q^{8}+\cdots\)
920.2.f.b	$920$	$2$	920.f	8.b	$2$	$8$	$8$	$7.346$	8.0.1871773696.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(\beta _{1}+\beta _{3})q^{3}-2q^{4}-\beta _{1}q^{5}+\cdots\)
920.2.f.c	$920$	$2$	920.f	8.b	$2$	$30$	$30$	$7.346$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$
920.2.f.d	$920$	$2$	920.f	8.b	$2$	$48$	$48$	$7.346$		None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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