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

• Label: 666.2.e
• Level: $666$
• Weight: $2$
• Character orbit: 666.e
• Rep. character: $\chi_{666}(223,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $228$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	236	72	164
Cusp forms	220	72	148
Eisenstein series	16	0	16

Trace form

\( 72 q + 2 q^{2} + 2 q^{3} - 36 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{8} - 10 q^{9} + O(q^{10}) \)

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.e.a	$666$	$2$	666.e	9.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.b	$666$	$2$	666.e	9.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
666.2.e.c	$666$	$2$	666.e	9.c	$3$	$12$	$6$	$5.318$	12.0.\(\cdots\).1	None		$2$	$0$	\(-6\)	\(2\)	\(5\)	\(5\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{11})q^{3}+\cdots\)
666.2.e.d	$666$	$2$	666.e	9.c	$3$	$14$	$7$	$5.318$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(7\)	\(-1\)	\(-3\)	\(3\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{10})q^{2}+\beta _{2}q^{3}+\beta _{10}q^{4}-\beta _{12}q^{5}+\cdots\)
666.2.e.e	$666$	$2$	666.e	9.c	$3$	$20$	$10$	$5.318$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-10\)	\(2\)	\(-1\)	\(-1\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{11}q^{2}+\beta _{7}q^{3}+(-1+\beta _{11})q^{4}+\cdots\)
666.2.e.f	$666$	$2$	666.e	9.c	$3$	$22$	$11$	$5.318$		None		$2$	$0$	\(11\)	\(-4\)	\(1\)	\(-5\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)