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

• Label: 37.2.e
• Level: $37$
• Weight: $2$
• Character orbit: 37.e
• Rep. character: $\chi_{37}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
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	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

4 * q + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^9 - 8 * q^10 - 12 * q^11 + 2 * q^12 + 12 * q^13 + 6 * q^15 + 2 * q^16 + 6 * q^17 + 12 * q^18 - 6 * q^19 + 6 * q^20 + 12 * q^21 + 6 * q^22 - 18 * q^24 + 4 * q^25 - 16 * q^27 + 2 * q^30 - 12 * q^33 - 4 * q^34 - 24 * q^35 + 4 * q^36 + 2 * q^37 - 12 * q^38 + 12 * q^39 + 12 * q^40 - 6 * q^41 - 12 * q^42 + 6 * q^44 - 2 * q^46 + 12 * q^47 + 4 * q^48 - 10 * q^49 + 24 * q^50 - 12 * q^52 + 12 * q^53 + 6 * q^55 + 36 * q^56 + 12 * q^57 - 4 * q^58 - 12 * q^59 - 6 * q^61 + 6 * q^62 + 48 * q^63 - 28 * q^64 - 12 * q^65 + 18 * q^67 - 12 * q^70 - 12 * q^71 - 36 * q^72 - 40 * q^75 + 6 * q^76 + 12 * q^77 - 12 * q^78 - 18 * q^79 - 2 * q^81 + 6 * q^83 - 24 * q^84 + 4 * q^85 + 6 * q^87 + 18 * q^89 - 8 * q^90 + 6 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^95 + 30 * q^96 + 18 * 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.e.a	$37$	$2$	37.e	37.e	$6$	$4$	$2$	$0.295$	\(\Q(\zeta_{12})\)	None		✓	✓	✓	37.2.e.a	$2$	$0$	\(0\)	\(2\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)