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

• Label: 912.2.cp
• Level: $912$
• Weight: $2$
• Character orbit: 912.cp
• Rep. character: $\chi_{912}(35,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $1872$
• 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.cp (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 912 \)
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	1968	0
Cusp forms	1872	1872	0
Eisenstein series	96	96	0

Trace form

1872 * q - 12 * q^3 - 24 * q^4 - 12 * q^6 - 24 * q^7 - 36 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^19 + 6 * q^21 - 24 * q^22 - 12 * q^24 - 6 * q^27 + 24 * q^28 + 36 * q^30 - 24 * q^33 - 24 * q^34 - 12 * q^36 - 48 * q^37 - 48 * q^39 - 24 * q^40 - 96 * q^42 - 24 * q^43 - 6 * q^45 - 12 * q^46 - 12 * q^48 - 816 * q^49 - 12 * q^51 + 24 * q^52 + 54 * q^54 - 48 * q^55 - 48 * q^58 + 30 * q^60 - 24 * q^61 - 12 * q^64 + 48 * q^66 - 24 * q^67 - 6 * q^69 - 12 * q^70 - 48 * q^72 + 144 * q^75 + 24 * q^76 + 12 * q^78 - 24 * q^81 - 24 * q^82 + 78 * q^84 + 72 * q^85 - 12 * q^87 - 12 * q^88 + 96 * q^90 + 60 * q^91 - 30 * q^93 - 48 * q^94 + 276 * q^96 - 48 * q^97 + 42 * q^99

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.cp.a	$912$	$2$	912.cp	912.bp	$36$	$1872$	$156$	$7.282$		None		✓	✓	✓	912.2.cp.a	$8$	$0$	\(0\)	\(-12\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{36}]$