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

\( 960 q + 4 q^{2} - 2 q^{6} + 8 q^{7} + 10 q^{8} + 96 q^{9} + O(q^{10}) \)

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.bj.a	$920$	$2$	920.bj	184.p	$22$	$960$	$96$	$7.346$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{22}]$

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

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