Space of modular forms of level 31, weight 6, and Character 31.d

• Label: 31.6.d
• Level: $31$
• Weight: $6$
• Character orbit: 31.d
• Rep. character: $\chi_{31}(2,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(31, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	52	52	0
Eisenstein series	8	8	0

Trace form

\( 52 q - 3 q^{2} + 17 q^{3} - 207 q^{4} - 66 q^{5} - 298 q^{6} + 205 q^{7} + 823 q^{8} - 994 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(31, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.6.d.a	$31$	$6$	31.d	31.d	$5$	$52$	$13$	$4.972$		None		$2$	$0$	\(-3\)	\(17\)	\(-66\)	\(205\)		$\mathrm{SU}(2)[C_{5}]$