Space of modular forms of level 912, weight 3, and Character 912.o

• Label: 912.3.o
• Level: $912$
• Weight: $3$
• Character orbit: 912.o
• Rep. character: $\chi_{912}(721,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $5$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

	Total	New	Old
Modular forms	332	40	292
Cusp forms	308	40	268
Eisenstein series	24	0	24

Trace form

\( 40 q + 16 q^{7} - 120 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.3.o.a	$912$	$3$	912.o	19.b	$2$	$2$	$2$	$24.850$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(20\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+4q^{5}+10q^{7}-3q^{9}-10q^{11}+\cdots\)
912.3.o.b	$912$	$3$	912.o	19.b	$2$	$4$	$4$	$24.850$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-34\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+(-8-\beta _{2}+\cdots)q^{7}+\cdots\)
912.3.o.c	$912$	$3$	912.o	19.b	$2$	$6$	$6$	$24.850$	6.0.219615408.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-3q^{9}+(4+\cdots)q^{11}+\cdots\)
912.3.o.d	$912$	$3$	912.o	19.b	$2$	$8$	$8$	$24.850$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(12\)	$2^{6}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(1+\beta _{1}-\beta _{4})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
912.3.o.e	$912$	$3$	912.o	19.b	$2$	$20$	$20$	$24.850$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}-\beta _{4}q^{5}+(1+\beta _{3})q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)