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

• Label: 668.2.b
• Level: $668$
• Weight: $2$
• Character orbit: 668.b
• Rep. character: $\chi_{668}(667,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 668 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	86	86	0
Cusp forms	82	82	0
Eisenstein series	4	4	0

Trace form

\( 82 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 82 q^{9} + O(q^{10}) \)

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.b.a	$668$	$2$	668.b	668.b	$2$	$22$	$22$	$5.334$		\(\Q(\sqrt{-167}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{2}]$
668.2.b.b	$668$	$2$	668.b	668.b	$2$	$60$	$60$	$5.334$		None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$