Space of modular forms of level 668, weight 2, and Character 668.h

• Label: 668.2.h
• Level: $668$
• Weight: $2$
• Character orbit: 668.h
• Rep. character: $\chi_{668}(15,\cdot)$
• Character field: $\Q(\zeta_{166})$
• Dimension: $6724$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.h (of order \(166\) and degree \(82\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 668 \)
Character field:			\(\Q(\zeta_{166})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(668, [\chi])\).

	Total	New	Old
Modular forms	7052	7052	0
Cusp forms	6724	6724	0
Eisenstein series	328	328	0

Trace form

\( 6724 q - 81 q^{2} - 85 q^{4} - 166 q^{5} - 75 q^{6} - 75 q^{8} - 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(668, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
668.2.h.a	$668$	$2$	668.h	668.h	$166$	$6724$	$82$	$5.334$		None		$4$	$0$	\(-81\)	\(0\)	\(-166\)	\(0\)		$\mathrm{SU}(2)[C_{166}]$