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

• Label: 966.2.i
• Level: $966$
• Weight: $2$
• Character orbit: 966.i
• Rep. character: $\chi_{966}(277,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $14$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)
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	400	56	344
Cusp forms	368	56	312
Eisenstein series	32	0	32

Trace form

\( 56 q - 28 q^{4} + 8 q^{6} - 4 q^{7} - 28 q^{9} + O(q^{10}) \)

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.i.a	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-1\)	\(-4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.b	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.c	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.d	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.e	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.f	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.g	$966$	$2$	966.i	7.c	$3$	$2$	$1$	$7.714$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.h	$966$	$2$	966.i	7.c	$3$	$4$	$2$	$7.714$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-2\)	\(-2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
966.2.i.i	$966$	$2$	966.i	7.c	$3$	$4$	$2$	$7.714$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(2\)	\(-2\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
966.2.i.j	$966$	$2$	966.i	7.c	$3$	$4$	$2$	$7.714$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(2\)	\(-2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
966.2.i.k	$966$	$2$	966.i	7.c	$3$	$6$	$3$	$7.714$	6.0.29428272.1	None		$2$	$0$	\(3\)	\(3\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{2}-\beta _{3}q^{3}+\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
966.2.i.l	$966$	$2$	966.i	7.c	$3$	$8$	$4$	$7.714$	8.0.1768034304.4	None		$2$	$0$	\(-4\)	\(-4\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
966.2.i.m	$966$	$2$	966.i	7.c	$3$	$8$	$4$	$7.714$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-4\)	\(4\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1})q^{2}-\beta _{1}q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{5}+\cdots\)
966.2.i.n	$966$	$2$	966.i	7.c	$3$	$8$	$4$	$7.714$	8.0.\(\cdots\).2	None		$2$	$0$	\(4\)	\(4\)	\(-2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{5})q^{2}-\beta _{5}q^{3}+\beta _{5}q^{4}-\beta _{1}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)