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

• Label: 671.2.bf
• Level: $671$
• Weight: $2$
• Character orbit: 671.bf
• Rep. character: $\chi_{671}(3,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $124$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.bf (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 671 \)
Character field:			\(\Q(\zeta_{10})\)
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	256	256	0
Cusp forms	240	240	0
Eisenstein series	16	16	0

Trace form

\( 240 q - 5 q^{2} - 6 q^{3} + 57 q^{4} - 5 q^{5} - 5 q^{6} - 15 q^{8} + 218 q^{9} + O(q^{10}) \)

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.bf.a	$671$	$2$	671.bf	671.af	$10$	$240$	$60$	$5.358$		None		$2$	$0$	\(-5\)	\(-6\)	\(-5\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$