Space of modular forms of level 671, weight 2, and Character 671.o

• Label: 671.2.o
• Level: $671$
• Weight: $2$
• Character orbit: 671.o
• Rep. character: $\chi_{671}(353,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $100$
• Newform subspaces: $1$
• Sturm bound: $124$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 61 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(124\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(671, [\chi])\).

	Total	New	Old
Modular forms	128	100	28
Cusp forms	120	100	20
Eisenstein series	8	0	8

Trace form

\( 100 q + 4 q^{3} + 38 q^{4} - 6 q^{5} + 12 q^{6} + 6 q^{7} + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(671, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
671.2.o.a	$671$	$2$	671.o	61.f	$6$	$100$	$50$	$5.358$		None		$2$	$0$	\(0\)	\(4\)	\(-6\)	\(6\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(671, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(671, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)