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

• Label: 966.2.f
• Level: $966$
• Weight: $2$
• Character orbit: 966.f
• Rep. character: $\chi_{966}(461,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	200	56	144
Cusp forms	184	56	128
Eisenstein series	16	0	16

Trace form

\( 56 q - 56 q^{4} + 8 q^{7} - 8 q^{9} + O(q^{10}) \)

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.f.a	$966$	$2$	966.f	21.c	$2$	$4$	$4$	$7.714$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}-q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
966.2.f.b	$966$	$2$	966.f	21.c	$2$	$24$	$24$	$7.714$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$
966.2.f.c	$966$	$2$	966.f	21.c	$2$	$28$	$28$	$7.714$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)