Space of modular forms of level 37, weight 7, and Character 37.d

• Label: 37.7.d
• Level: $37$
• Weight: $7$
• Character orbit: 37.d
• Rep. character: $\chi_{37}(6,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(22\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(37, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	36	36	0
Eisenstein series	4	4	0

Trace form

\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.7.d.a	$37$	$7$	37.d	37.d	$4$	$36$	$18$	$8.512$		None		$2$	$0$	\(-4\)	\(0\)	\(-256\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$