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

• Label: 936.2.dl
• Level: $936$
• Weight: $2$
• Character orbit: 936.dl
• Rep. character: $\chi_{936}(187,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $656$
• 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.dl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 936 \)
Character field:			\(\Q(\zeta_{12})\)
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	688	688	0
Cusp forms	656	656	0
Eisenstein series	32	32	0

Trace form

656 * q - 2 * q^2 - 16 * q^3 - 6 * q^6 - 20 * q^8 - 16 * q^9 - 4 * q^11 - 4 * q^14 - 4 * q^16 + 6 * q^18 - 16 * q^19 + 14 * q^20 - 4 * q^22 - 32 * q^24 - 16 * q^27 + 8 * q^28 - 2 * q^32 + 4 * q^33 + 2 * q^34 - 32 * q^35 - 4 * q^40 - 4 * q^41 - 16 * q^42 + 40 * q^44 + 24 * q^48 - 46 * q^50 + 32 * q^52 - 10 * q^54 - 32 * q^57 + 8 * q^58 + 20 * q^59 - 32 * q^60 - 4 * q^65 - 68 * q^66 - 4 * q^67 + 116 * q^68 - 40 * q^70 - 66 * q^72 - 16 * q^73 + 52 * q^74 + 6 * q^76 - 48 * q^78 + 16 * q^80 - 16 * q^81 - 4 * q^83 - 78 * q^84 - 98 * q^86 - 16 * q^89 - 16 * q^91 + 8 * q^92 + 20 * q^94 - 132 * q^96 - 4 * q^97 + 108 * q^98 - 36 * q^99

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.dl.a	$936$	$2$	936.dl	936.cl	$12$	$656$	$164$	$7.474$		None		✓	✓	✓	936.2.dl.a	$8$	$0$	\(-2\)	\(-16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$