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

• Label: 912.2.bh
• Level: $912$
• Weight: $2$
• Character orbit: 912.bh
• Rep. character: $\chi_{912}(239,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $7$
• Sturm bound: $320$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bh (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 228 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(320\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	344	80	264
Cusp forms	296	80	216
Eisenstein series	48	0	48

Trace form

\( 80 q - 6 q^{9} + O(q^{10}) \)

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.bh.a	$912$	$2$	912.bh	228.m	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+\zeta_{6})q^{3}+(3-6\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
912.2.bh.b	$912$	$2$	912.bh	228.m	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
912.2.bh.c	$912$	$2$	912.bh	228.m	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-\zeta_{6})q^{3}+(-3+6\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
912.2.bh.d	$912$	$2$	912.bh	228.m	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
912.2.bh.e	$912$	$2$	912.bh	228.m	$6$	$24$	$12$	$7.282$		None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
912.2.bh.f	$912$	$2$	912.bh	228.m	$6$	$24$	$12$	$7.282$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
912.2.bh.g	$912$	$2$	912.bh	228.m	$6$	$24$	$12$	$7.282$		None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)