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

• Label: 287.3.m
• Level: $287$
• Weight: $3$
• Character orbit: 287.m
• Rep. character: $\chi_{287}(85,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $168$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.m (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{8})\)
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	232	168	64
Cusp forms	216	168	48
Eisenstein series	16	0	16

Trace form

\( 168 q + 8 q^{2} - 16 q^{3} + 24 q^{6} - 48 q^{8} - 48 q^{9} + O(q^{10}) \)

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.m.a	$287$	$3$	287.m	41.e	$8$	$168$	$42$	$7.820$		None		$2$	$0$	\(8\)	\(-16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(287, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(287, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)