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

• Label: 37.4.e
• Level: $37$
• Weight: $4$
• Character orbit: 37.e
• Rep. character: $\chi_{37}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
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	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

\( 16 q - 6 q^{2} - 3 q^{3} + 18 q^{4} + 18 q^{5} + 23 q^{7} - 53 q^{9} + O(q^{10}) \)

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.e.a	$37$	$4$	37.e	37.e	$6$	$16$	$8$	$2.183$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-6\)	\(-3\)	\(18\)	\(23\)	$2^{12}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(2-\beta _{3}-2\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)