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

• Label: 667.2.o
• Level: $667$
• Weight: $2$
• Character orbit: 667.o
• Rep. character: $\chi_{667}(68,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $696$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.o (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 667 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	744	744	0
Cusp forms	696	696	0
Eisenstein series	48	48	0

Trace form

\( 696 q - 20 q^{2} - 24 q^{3} - 28 q^{4} - 28 q^{6} - 30 q^{8} - 28 q^{9} + O(q^{10}) \)

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.o.a	$667$	$2$	667.o	667.o	$28$	$72$	$6$	$5.326$		\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{28}]$
667.2.o.b	$667$	$2$	667.o	667.o	$28$	$624$	$52$	$5.326$		None		$4$	$0$	\(-20\)	\(-24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$