Space of modular forms of level 666, weight 2, and Character 666.x

• Label: 666.2.x
• Level: $666$
• Weight: $2$
• Character orbit: 666.x
• Rep. character: $\chi_{666}(127,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $102$
• Newform subspaces: $9$
• Sturm bound: $228$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.x (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(228\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

	Total	New	Old
Modular forms	732	102	630
Cusp forms	636	102	534
Eisenstein series	96	0	96

Trace form

\( 102 q - 3 q^{5} + 12 q^{7} - 3 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
666.2.x.a	$666$	$2$	666.x	37.f	$9$	$6$	$1$	$5.318$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-9\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(-2+\cdots)q^{5}+\cdots\)
666.2.x.b	$666$	$2$	666.x	37.f	$9$	$6$	$1$	$5.318$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-9\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(-1+\cdots)q^{5}+\cdots\)
666.2.x.c	$666$	$2$	666.x	37.f	$9$	$6$	$1$	$5.318$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(-1+\cdots)q^{5}+\cdots\)
666.2.x.d	$666$	$2$	666.x	37.f	$9$	$6$	$1$	$5.318$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(-2\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
666.2.x.e	$666$	$2$	666.x	37.f	$9$	$6$	$1$	$5.318$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(2\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
666.2.x.f	$666$	$2$	666.x	37.f	$9$	$12$	$2$	$5.318$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-9\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}+\beta _{7})q^{2}+\beta _{4}q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
666.2.x.g	$666$	$2$	666.x	37.f	$9$	$12$	$2$	$5.318$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{7})q^{2}-\beta _{6}q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
666.2.x.h	$666$	$2$	666.x	37.f	$9$	$24$	$4$	$5.318$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
666.2.x.i	$666$	$2$	666.x	37.f	$9$	$24$	$4$	$5.318$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)