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

• Label: 936.2.ds
• Level: $936$
• Weight: $2$
• Character orbit: 936.ds
• Rep. character: $\chi_{936}(353,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $168$
• 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.ds (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
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	704	168	536
Cusp forms	640	168	472
Eisenstein series	64	0	64

Trace form

168 * q - 8 * q^15 + 16 * q^21 - 12 * q^27 + 24 * q^31 + 4 * q^33 + 36 * q^35 + 40 * q^39 + 36 * q^43 + 12 * q^45 + 36 * q^57 - 36 * q^63 + 36 * q^65 + 36 * q^69 + 72 * q^71 - 72 * q^77 + 48 * q^81 + 60 * q^83 - 24 * q^85 - 16 * q^87 + 12 * q^91 + 68 * q^93 - 24 * q^97 - 28 * 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.ds.a	$936$	$2$	936.ds	117.x	$12$	$168$	$42$	$7.474$		None		✓	✓	✓	936.2.ds.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)