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

• Label: 287.3.k
• Level: $287$
• Weight: $3$
• Character orbit: 287.k
• Rep. character: $\chi_{287}(124,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
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	116	108	8
Cusp forms	108	108	0
Eisenstein series	8	0	8

Trace form

\( 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9} + O(q^{10}) \)

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.k.a	$287$	$3$	287.k	7.d	$6$	$108$	$54$	$7.820$		None		$2$	$0$	\(-2\)	\(-6\)	\(-6\)	\(-4\)		$\mathrm{SU}(2)[C_{6}]$