Space of modular forms of level 805, weight 2, and Character 805.bs

• Label: 805.2.bs
• Level: $805$
• Weight: $2$
• Character orbit: 805.bs
• Rep. character: $\chi_{805}(37,\cdot)$
• Character field: $\Q(\zeta_{132})$
• Dimension: $3680$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bs (of order \(132\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 805 \)
Character field:			\(\Q(\zeta_{132})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(805, [\chi])\).

	Total	New	Old
Modular forms	4000	4000	0
Cusp forms	3680	3680	0
Eisenstein series	320	320	0

Trace form

\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(805, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
805.2.bs.a	$805$	$2$	805.bs	805.as	$132$	$3680$	$92$	$6.428$		None		$8$	$0$	\(-18\)	\(-18\)	\(-22\)	\(-44\)		$\mathrm{SU}(2)[C_{132}]$