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

• Label: 666.2.k
• Level: $666$
• Weight: $2$
• Character orbit: 666.k
• Rep. character: $\chi_{666}(175,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $228$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(228\)
Trace bound:			\(0\)

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

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

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.k.a	$666$	$2$	666.k	333.k	$6$	$76$	$38$	$5.318$		None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$

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

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