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

• Label: 966.2.r
• Level: $966$
• Weight: $2$
• Character orbit: 966.r
• Rep. character: $\chi_{966}(113,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.r (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	2000	480	1520
Cusp forms	1840	480	1360
Eisenstein series	160	0	160

Trace form

\( 480 q - 8 q^{3} + 48 q^{4} + 8 q^{9} + O(q^{10}) \)

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.r.a	$966$	$2$	966.r	69.g	$22$	$240$	$24$	$7.714$		None		$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
966.2.r.b	$966$	$2$	966.r	69.g	$22$	$240$	$24$	$7.714$		None		$2$	$0$	\(0\)	\(-4\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)