Space of modular forms of level 37, weight 4, and Character 37.b

• Label: 37.4.b
• Level: $37$
• Weight: $4$
• Character orbit: 37.b
• Rep. character: $\chi_{37}(36,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	37.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(37, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	8	8	0
Eisenstein series	2	2	0

Trace form

\( 8 q - 6 q^{3} - 36 q^{4} + 4 q^{7} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.4.b.a	$37$	$4$	37.b	37.b	$2$	$8$	$8$	$2.183$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(4\)	$2^{4}\cdot 3^{5}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-1-\beta _{3})q^{3}+(-4+\beta _{5}+\cdots)q^{4}+\cdots\)