Space of modular forms of level 37, weight 2, and Character 37.b

• Label: 37.2.b
• Level: $37$
• Weight: $2$
• Character orbit: 37.b
• Rep. character: $\chi_{37}(36,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(37, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

2 * q - 2 * q^3 - 4 * q^4 + 6 * q^7 - 4 * q^9 + 8 * q^10 - 6 * q^11 + 4 * q^12 - 8 * q^16 - 6 * q^21 + 2 * q^25 + 24 * q^26 + 10 * q^27 - 12 * q^28 - 8 * q^30 + 6 * q^33 - 8 * q^34 + 8 * q^36 - 2 * q^37 - 24 * q^38 - 6 * q^41 + 12 * q^44 - 16 * q^46 + 6 * q^47 + 8 * q^48 + 4 * q^49 + 18 * q^53 + 16 * q^58 - 12 * q^63 + 16 * q^64 - 24 * q^65 - 24 * q^67 + 24 * q^70 - 6 * q^71 + 18 * q^73 - 24 * q^74 - 2 * q^75 - 18 * q^77 - 24 * q^78 + 2 * q^81 + 18 * q^83 + 12 * q^84 + 8 * q^85 + 24 * q^86 - 16 * q^90 + 24 * q^95 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(37, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.2.b.a	$37$	$2$	37.b	37.b	$2$	$2$	$2$	$0.295$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	37.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-q^{3}-2 q^{4}-\beta q^{5}-\beta q^{6}+\cdots\)