Space of modular forms of level 317, weight 2, and Character 317.d

• Label: 317.2.d
• Level: $317$
• Weight: $2$
• Character orbit: 317.d
• Rep. character: $\chi_{317}(10,\cdot)$
• Character field: $\Q(\zeta_{79})$
• Dimension: $1950$
• Newform subspaces: $1$
• Sturm bound: $53$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	317.d (of order \(79\) and degree \(78\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 317 \)
Character field:			\(\Q(\zeta_{79})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(53\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(317, [\chi])\).

	Total	New	Old
Modular forms	2106	2106	0
Cusp forms	1950	1950	0
Eisenstein series	156	156	0

Trace form

\( 1950 q - 74 q^{2} - 75 q^{3} - 94 q^{4} - 71 q^{5} - 61 q^{6} - 71 q^{7} - 52 q^{8} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(317, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
317.2.d.a	$317$	$2$	317.d	317.d	$79$	$1950$	$25$	$2.531$		None		$2$	$0$	\(-74\)	\(-75\)	\(-71\)	\(-71\)		$\mathrm{SU}(2)[C_{79}]$