Space of modular forms of level 667, weight 2, and Character 667.x

• Label: 667.2.x
• Level: $667$
• Weight: $2$
• Character orbit: 667.x
• Rep. character: $\chi_{667}(10,\cdot)$
• Character field: $\Q(\zeta_{308})$
• Dimension: $6960$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.x (of order \(308\) and degree \(120\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 667 \)
Character field:			\(\Q(\zeta_{308})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(667, [\chi])\).

	Total	New	Old
Modular forms	7440	7440	0
Cusp forms	6960	6960	0
Eisenstein series	480	480	0

Trace form

\( 6960 q - 112 q^{2} - 108 q^{3} - 126 q^{4} - 154 q^{5} - 126 q^{6} - 110 q^{7} - 102 q^{8} - 126 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(667, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
667.2.x.a	$667$	$2$	667.x	667.x	$308$	$6960$	$58$	$5.326$		None		$4$	$0$	\(-112\)	\(-108\)	\(-154\)	\(-110\)		$\mathrm{SU}(2)[C_{308}]$