Space of modular forms of level 731, weight 2, and Character 731.bl

• Label: 731.2.bl
• Level: $731$
• Weight: $2$
• Character orbit: 731.bl
• Rep. character: $\chi_{731}(9,\cdot)$
• Character field: $\Q(\zeta_{168})$
• Dimension: $3072$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.bl (of order \(168\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 731 \)
Character field:			\(\Q(\zeta_{168})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

	Total	New	Old
Modular forms	3264	3264	0
Cusp forms	3072	3072	0
Eisenstein series	192	192	0

Trace form

\( 3072 q - 40 q^{2} - 52 q^{3} - 44 q^{5} - 24 q^{6} - 24 q^{7} - 72 q^{8} - 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
731.2.bl.a	$731$	$2$	731.bl	731.al	$168$	$3072$	$64$	$5.837$		None		$4$	$0$	\(-40\)	\(-52\)	\(-44\)	\(-24\)		$\mathrm{SU}(2)[C_{168}]$