Space of modular forms of level 37, weight 8, and Character 37.f

• Label: 37.8.f
• Level: $37$
• Weight: $8$
• Character orbit: 37.f
• Rep. character: $\chi_{37}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $132$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(25\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(37, [\chi])\).

	Total	New	Old
Modular forms	144	144	0
Cusp forms	132	132	0
Eisenstein series	12	12	0

Trace form

\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(37, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.8.f.a	$37$	$8$	37.f	37.f	$9$	$132$	$22$	$11.558$		None		$2$	$0$	\(15\)	\(33\)	\(576\)	\(-597\)		$\mathrm{SU}(2)[C_{9}]$