Space of modular forms of level 287, weight 3, and Character 287.bd

• Label: 287.3.bd
• Level: $287$
• Weight: $3$
• Character orbit: 287.bd
• Rep. character: $\chi_{287}(5,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $864$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.bd (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 287 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(287, [\chi])\).

	Total	New	Old
Modular forms	928	928	0
Cusp forms	864	864	0
Eisenstein series	64	64	0

Trace form

\( 864 q - 10 q^{2} - 24 q^{3} - 214 q^{4} - 30 q^{5} - 16 q^{7} - 40 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(287, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
287.3.bd.a	$287$	$3$	287.bd	287.ad	$60$	$864$	$54$	$7.820$		None		$4$	$0$	\(-10\)	\(-24\)	\(-30\)	\(-16\)		$\mathrm{SU}(2)[C_{60}]$