Space of modular forms of level 37, weight 6, and Character 37.e

• Label: 37.6.e
• Level: $37$
• Weight: $6$
• Character orbit: 37.e
• Rep. character: $\chi_{37}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $19$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(19\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(37, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	32	32	0
Eisenstein series	4	4	0

Trace form

\( 32 q - 6 q^{2} + 18 q^{3} + 298 q^{4} + 144 q^{5} - 52 q^{7} - 1490 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.6.e.a	$37$	$6$	37.e	37.e	$6$	$32$	$16$	$5.934$		None		$2$	$0$	\(-6\)	\(18\)	\(144\)	\(-52\)		$\mathrm{SU}(2)[C_{6}]$