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

• Label: 667.2.u
• Level: $667$
• Weight: $2$
• Character orbit: 667.u
• Rep. character: $\chi_{667}(4,\cdot)$
• Character field: $\Q(\zeta_{154})$
• Dimension: $3480$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.u (of order \(154\) and degree \(60\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 667 \)
Character field:			\(\Q(\zeta_{154})\)
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	3720	3720	0
Cusp forms	3480	3480	0
Eisenstein series	240	240	0

Trace form

\( 3480 q - 63 q^{2} - 63 q^{3} - 105 q^{4} - 49 q^{5} - 51 q^{6} - 41 q^{7} - 84 q^{8} - 91 q^{9} + O(q^{10}) \)

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.u.a	$667$	$2$	667.u	667.u	$154$	$3480$	$58$	$5.326$		None		$4$	$0$	\(-63\)	\(-63\)	\(-49\)	\(-41\)		$\mathrm{SU}(2)[C_{154}]$