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

• Label: 666.2.g
• Level: $666$
• Weight: $2$
• Character orbit: 666.g
• Rep. character: $\chi_{666}(211,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $76$
• Newform subspaces: $3$
• Sturm bound: $228$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(228\)
Trace bound:			\(1\)
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	76	160
Cusp forms	220	76	144
Eisenstein series	16	0	16

Trace form

\( 76 q + 2 q^{3} - 38 q^{4} + 4 q^{5} - 4 q^{7} + 2 q^{9} + O(q^{10}) \)

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.g.a	$666$	$2$	666.g	333.g	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
666.2.g.b	$666$	$2$	666.g	333.g	$3$	$36$	$18$	$5.318$		None		$2$	$0$	\(18\)	\(-2\)	\(4\)	\(-8\)		$\mathrm{SU}(2)[C_{3}]$
666.2.g.c	$666$	$2$	666.g	333.g	$3$	$38$	$19$	$5.318$		None		$2$	$0$	\(-19\)	\(1\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$

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

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