Space of modular forms of level 670, weight 2, and Character 670.o

• Label: 670.2.o
• Level: $670$
• Weight: $2$
• Character orbit: 670.o
• Rep. character: $\chi_{670}(9,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $340$
• Newform subspaces: $1$
• Sturm bound: $204$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.o (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 335 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(204\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(670, [\chi])\).

	Total	New	Old
Modular forms	1060	340	720
Cusp forms	980	340	640
Eisenstein series	80	0	80

Trace form

\( 340 q + 34 q^{4} + 4 q^{5} - 4 q^{6} + 30 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(670, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
670.2.o.a	$670$	$2$	670.o	335.o	$22$	$340$	$34$	$5.350$		None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(670, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(670, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)