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

• Label: 37.10.f
• Level: $37$
• Weight: $10$
• Character orbit: 37.f
• Rep. character: $\chi_{37}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $162$
• Newform subspaces: $1$
• Sturm bound: $31$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	174	174	0
Cusp forms	162	162	0
Eisenstein series	12	12	0

Trace form

\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.10.f.a	$37$	$10$	37.f	37.f	$9$	$162$	$27$	$19.056$		None		✓	✓	✓	37.10.f.a	$2$	$0$	\(-57\)	\(-228\)	\(-3420\)	\(5808\)		$\mathrm{SU}(2)[C_{9}]$