Space of modular forms of level 37, weight 2, and Character 37.b

• Label: 37.2.b
• Level: $37$
• Weight: $2$
• Character orbit: 37.b
• Rep. character: $\chi_{37}(36,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(37, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.2.b.a	$37$	$2$	37.b	37.b	$2$	$2$	$2$	$0.295$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-q^{3}-2q^{4}-2iq^{5}-2iq^{6}+\cdots\)