Space of modular forms of level 37, weight 7, and Character 37.g

• Label: 37.7.g
• Level: $37$
• Weight: $7$
• Character orbit: 37.g
• Rep. character: $\chi_{37}(8,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.g (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(22\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(37, [\chi])\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	72	72	0
Eisenstein series	8	8	0

Trace form

\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.7.g.a	$37$	$7$	37.g	37.g	$12$	$72$	$18$	$8.512$		None		$2$	$0$	\(-2\)	\(-6\)	\(52\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$