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

• Label: 912.2.br
• Level: $912$
• Weight: $2$
• Character orbit: 912.br
• Rep. character: $\chi_{912}(221,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $624$
• 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.br (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 912 \)
Character field:			\(\Q(\zeta_{12})\)
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	656	656	0
Cusp forms	624	624	0
Eisenstein series	32	32	0

Trace form

624 * q - 6 * q^3 - 4 * q^4 - 2 * q^6 - 24 * q^10 - 12 * q^13 - 12 * q^15 + 12 * q^21 - 12 * q^22 + 14 * q^24 + 12 * q^28 - 56 * q^30 - 12 * q^33 - 12 * q^34 - 18 * q^36 - 12 * q^40 + 30 * q^42 - 4 * q^43 + 12 * q^45 - 6 * q^48 - 560 * q^49 - 6 * q^51 + 36 * q^52 + 20 * q^54 - 16 * q^58 - 48 * q^60 + 28 * q^61 + 24 * q^63 - 64 * q^64 + 2 * q^66 - 12 * q^67 + 144 * q^70 + 126 * q^72 + 4 * q^76 - 18 * q^78 - 24 * q^79 - 4 * q^81 + 20 * q^82 - 60 * q^85 - 114 * q^90 + 72 * q^91 + 4 * q^93 + 24 * q^96 - 24 * q^97 - 52 * 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.br.a	$912$	$2$	912.br	912.ar	$12$	$624$	$156$	$7.282$		None		✓	✓	✓	912.2.br.a	$8$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$