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

• Label: 966.2.be
• Level: $966$
• Weight: $2$
• Character orbit: 966.be
• Rep. character: $\chi_{966}(19,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $640$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	4000	640	3360
Cusp forms	3680	640	3040
Eisenstein series	320	0	320

Trace form

\( 640 q + 32 q^{4} - 32 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
966.2.be.a	$966$	$2$	966.be	161.o	$66$	$320$	$16$	$7.714$		None		✓			966.2.be.a	$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{66}]$
966.2.be.b	$966$	$2$	966.be	161.o	$66$	$320$	$16$	$7.714$		None		✓			966.2.be.b	$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{66}]$

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

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