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

• Label: 936.2.j
• Level: $936$
• Weight: $2$
• Character orbit: 936.j
• Rep. character: $\chi_{936}(755,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• 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.j (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$24$
Character field:			$\Q$
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	176	48	128
Cusp forms	160	48	112
Eisenstein series	16	0	16

Trace form

48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

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.j.a	$936$	$2$	936.j	24.f	$2$	$48$	$48$	$7.474$		None		✓	✓	✓	936.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{2}^{\mathrm{old}}(936, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(936, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(24, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(72, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(312, [\chi])$$^{\oplus 2}$