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

• Label: 912.3.z
• Level: $912$
• Weight: $3$
• Character orbit: 912.z
• Rep. character: $\chi_{912}(463,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	664	80	584
Cusp forms	616	80	536
Eisenstein series	48	0	48

Trace form

\( 80 q + 120 q^{9} + O(q^{10}) \)

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.z.a	$912$	$3$	912.z	76.g	$6$	$12$	$6$	$24.850$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-18\)	\(-4\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{2})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{11})q^{5}+\cdots\)
912.3.z.b	$912$	$3$	912.z	76.g	$6$	$12$	$6$	$24.850$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-18\)	\(2\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{6})q^{3}+\beta _{11}q^{5}+\beta _{5}q^{7}+\cdots\)
912.3.z.c	$912$	$3$	912.z	76.g	$6$	$12$	$6$	$24.850$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(18\)	\(-4\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{2})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{11})q^{5}+\cdots\)
912.3.z.d	$912$	$3$	912.z	76.g	$6$	$12$	$6$	$24.850$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(18\)	\(2\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{6})q^{3}+\beta _{11}q^{5}-\beta _{5}q^{7}+3\beta _{6}q^{9}+\cdots\)
912.3.z.e	$912$	$3$	912.z	76.g	$6$	$16$	$8$	$24.850$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-24\)	\(2\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{3}-\beta _{6}q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
912.3.z.f	$912$	$3$	912.z	76.g	$6$	$16$	$8$	$24.850$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(24\)	\(2\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{3}-\beta _{6}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)