Space of modular forms of level 912, weight 2, and Character 912.cn

• Label: 912.2.cn
• Level: $912$
• Weight: $2$
• Character orbit: 912.cn
• Rep. character: $\chi_{912}(67,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $960$
• Newform subspaces: $1$
• Sturm bound: $320$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cn (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 304 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(320\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

	Total	New	Old
Modular forms	1968	960	1008
Cusp forms	1872	960	912
Eisenstein series	96	0	96

Trace form

960 * q + 48 * q^10 + 12 * q^16 - 60 * q^32 - 120 * q^34 + 12 * q^36 + 108 * q^38 + 60 * q^40 + 180 * q^46 - 480 * q^49 - 108 * q^50 - 24 * q^51 + 48 * q^52 + 12 * q^54 + 72 * q^68 - 144 * q^69 - 72 * q^70 - 48 * q^76 + 72 * q^78 - 120 * q^80 + 120 * q^82 + 96 * q^85 + 84 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.2.cn.a	$912$	$2$	912.cn	304.ag	$36$	$960$	$80$	$7.282$		None		✓	✓	✓	912.2.cn.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)