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

• Label: 912.2.bv
• Level: $912$
• Weight: $2$
• Character orbit: 912.bv
• Rep. character: $\chi_{912}(11,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $624$
• Newform subspaces: $3$
• Sturm bound: $320$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 912 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(320\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

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

\( 624 q - 2 q^{3} - 4 q^{4} - 2 q^{6} - 32 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.2.bv.a	$912$	$2$	912.bv	912.av	$12$	$8$	$2$	$7.282$	8.0.303595776.1	None		$4$	$1$	\(-4\)	\(0\)	\(-8\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{4}-\beta _{5})q^{2}+\beta _{1}q^{3}-2\beta _{3}q^{4}+(2\beta _{4}+\cdots)q^{5}+\cdots\)
912.2.bv.b	$912$	$2$	912.bv	912.av	$12$	$8$	$2$	$7.282$	8.0.303595776.1	None		$4$	$0$	\(4\)	\(-2\)	\(8\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{4}-\beta _{5})q^{2}+(-\beta _{2}+\beta _{4})q^{3}+\cdots\)
912.2.bv.c	$912$	$2$	912.bv	912.av	$12$	$608$	$152$	$7.282$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$