Space of modular forms of level 966, weight 2, and Character 966.g

• Label: 966.2.g
• Level: $966$
• Weight: $2$
• Character orbit: 966.g
• Rep. character: $\chi_{966}(643,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(966, [\chi])\).

	Total	New	Old
Modular forms	200	32	168
Cusp forms	184	32	152
Eisenstein series	16	0	16

Trace form

\( 32 q + 32 q^{4} - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(966, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
966.2.g.a	$966$	$2$	966.g	161.c	$2$	$4$	$4$	$7.714$	\(\Q(i, \sqrt{14})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
966.2.g.b	$966$	$2$	966.g	161.c	$2$	$4$	$4$	$7.714$	\(\Q(i, \sqrt{14})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
966.2.g.c	$966$	$2$	966.g	161.c	$2$	$4$	$4$	$7.714$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots\)
966.2.g.d	$966$	$2$	966.g	161.c	$2$	$4$	$4$	$7.714$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
966.2.g.e	$966$	$2$	966.g	161.c	$2$	$16$	$16$	$7.714$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(966, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)