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

• Label: 912.2.bb
• Level: $912$
• Weight: $2$
• Character orbit: 912.bb
• Rep. character: $\chi_{912}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $8$
• Sturm bound: $320$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(320\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(23\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	344	40	304
Cusp forms	296	40	256
Eisenstein series	48	0	48

Trace form

\( 40 q - 20 q^{9} + O(q^{10}) \)

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.bb.a	$912$	$2$	912.bb	76.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(1-2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
912.2.bb.b	$912$	$2$	912.bb	76.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
912.2.bb.c	$912$	$2$	912.bb	76.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{3}+(2-2\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
912.2.bb.d	$912$	$2$	912.bb	76.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{3}+(2-2\beta _{2})q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots\)
912.2.bb.e	$912$	$2$	912.bb	76.f	$6$	$6$	$3$	$7.282$	6.0.954288.1	None		$2$	$0$	\(0\)	\(-3\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.bb.f	$912$	$2$	912.bb	76.f	$6$	$6$	$3$	$7.282$	6.0.954288.1	None		$2$	$0$	\(0\)	\(3\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{3}+(\beta _{3}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.bb.g	$912$	$2$	912.bb	76.f	$6$	$8$	$4$	$7.282$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(-2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{6})q^{3}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
912.2.bb.h	$912$	$2$	912.bb	76.f	$6$	$8$	$4$	$7.282$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(-2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{6})q^{3}+(-\beta _{3}-\beta _{6}+\beta _{7})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)