Space of modular forms of level 31, weight 3, and Character 31.h

• Label: 31.3.h
• Level: $31$
• Weight: $3$
• Character orbit: 31.h
• Rep. character: $\chi_{31}(3,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(31, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	32	32	0
Eisenstein series	16	16	0

Trace form

\( 32 q - 6 q^{2} - 10 q^{3} - 18 q^{4} - 7 q^{5} - 9 q^{6} - 22 q^{7} + 43 q^{8} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(31, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.3.h.a	$31$	$3$	31.h	31.h	$30$	$32$	$4$	$0.845$		None		✓	✓	✓	31.3.h.a	$2$	$0$	\(-6\)	\(-10\)	\(-7\)	\(-22\)		$\mathrm{SU}(2)[C_{30}]$