Space of modular forms of level 37, weight 10, and Character 37.e

• Label: 37.10.e
• Level: $37$
• Weight: $10$
• Character orbit: 37.e
• Rep. character: $\chi_{37}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $31$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(31\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(37, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	56	56	0
Eisenstein series	4	4	0

Trace form

\( 56 q - 54 q^{2} - 75 q^{3} + 7082 q^{4} - 186 q^{5} - 4233 q^{7} - 173645 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.10.e.a	$37$	$10$	37.e	37.e	$6$	$56$	$28$	$19.056$		None		$2$	$0$	\(-54\)	\(-75\)	\(-186\)	\(-4233\)		$\mathrm{SU}(2)[C_{6}]$