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

• Label: 37.8.b
• Level: $37$
• Weight: $8$
• Character orbit: 37.b
• Rep. character: $\chi_{37}(36,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
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	22	22	0
Cusp forms	20	20	0
Eisenstein series	2	2	0

Trace form

\( 20 q + 78 q^{3} - 844 q^{4} - 1746 q^{7} + 12362 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.8.b.a	$37$	$8$	37.b	37.b	$2$	$20$	$20$	$11.558$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	37.8.b.a	$2$	$0$	\(0\)	\(78\)	\(0\)	\(-1746\)	$2^{19}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(4+\beta _{4})q^{3}+(-42+\beta _{2}+\cdots)q^{4}+\cdots\)