Space of modular forms of level 936, weight 2, and Character 936.db

• Label: 936.2.db
• Level: $936$
• Weight: $2$
• Character orbit: 936.db
• Rep. character: $\chi_{936}(61,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $328$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$936 = 2^{3} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	936.db (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$936$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$336$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(936, [\chi])$.

	Total	New	Old
Modular forms	344	344	0
Cusp forms	328	328	0
Eisenstein series	16	16	0

Trace form

328 * q + q^2 + q^4 + q^6 - 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 + 4 * q^15 + q^16 - 4 * q^17 - 12 * q^18 - 18 * q^20 - 7 * q^22 + 44 * q^23 - 6 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 5 * q^30 - 4 * q^31 + q^32 - 14 * q^33 - 13 * q^36 + 6 * q^38 + 20 * q^39 + 8 * q^40 - 4 * q^41 - 46 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 - 46 * q^48 + 276 * q^49 + 68 * q^50 + 40 * q^54 - 14 * q^55 - 56 * q^56 - 20 * q^57 - 25 * q^58 - 41 * q^60 + 3 * q^62 - 58 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 - 64 * q^68 - 17 * q^70 - 4 * q^71 - 7 * q^72 - 16 * q^73 - 38 * q^74 - 18 * q^76 - q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 6 * q^84 + 36 * q^86 - 2 * q^87 + 5 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 - 6 * q^94 + 56 * q^95 - 113 * q^96 - 4 * q^97 + 39 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(936, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
936.2.db.a	$936$	$2$	936.db	936.cb	$6$	$328$	$164$	$7.474$		None		✓	✓	✓	936.2.cj.a	$4$	$0$	$1$	$0$	$0$	$-4$		$\mathrm{SU}(2)[C_{6}]$