Space of modular forms of level 966, weight 4, and Character 966.g

• Label: 966.4.g
• Level: $966$
• Weight: $4$
• Character orbit: 966.g
• Rep. character: $\chi_{966}(643,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $768$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(768\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(966, [\chi])\).

	Total	New	Old
Modular forms	584	96	488
Cusp forms	568	96	472
Eisenstein series	16	0	16

Trace form

\( 96 q + 384 q^{4} - 864 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(966, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
966.4.g.a	$966$	$4$	966.g	161.c	$2$	$48$	$48$	$56.996$		None		$4$	$0$	\(-96\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
966.4.g.b	$966$	$4$	966.g	161.c	$2$	$48$	$48$	$56.996$		None		$4$	$0$	\(96\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(966, [\chi])\) into lower level spaces

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