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

• Label: 671.2.de
• Level: $671$
• Weight: $2$
• Character orbit: 671.de
• Rep. character: $\chi_{671}(18,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $960$
• Newform subspaces: $1$
• Sturm bound: $124$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.de (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 671 \)
Character field:			\(\Q(\zeta_{60})\)
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	1024	1024	0
Cusp forms	960	960	0
Eisenstein series	64	64	0

Trace form

\( 960 q - 20 q^{2} - 20 q^{3} - 18 q^{4} - 8 q^{5} - 60 q^{6} - 40 q^{7} - 40 q^{8} + 220 q^{9} + O(q^{10}) \)

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.de.a	$671$	$2$	671.de	671.ce	$60$	$960$	$60$	$5.358$		None		$2$	$0$	\(-20\)	\(-20\)	\(-8\)	\(-40\)		$\mathrm{SU}(2)[C_{60}]$