Space of modular forms of level 287, weight 2, and Character 287.be

• Label: 287.2.be
• Level: $287$
• Weight: $2$
• Character orbit: 287.be
• Rep. character: $\chi_{287}(12,\cdot)$
• Character field: $\Q(\zeta_{120})$
• Dimension: $832$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.be (of order \(120\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 287 \)
Character field:			\(\Q(\zeta_{120})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(287, [\chi])\).

	Total	New	Old
Modular forms	960	960	0
Cusp forms	832	832	0
Eisenstein series	128	128	0

Trace form

\( 832 q - 16 q^{2} - 48 q^{3} - 20 q^{4} - 48 q^{5} - 32 q^{7} - 48 q^{8} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(287, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
287.2.be.a	$287$	$2$	287.be	287.ae	$120$	$832$	$26$	$2.292$		None		$4$	$0$	\(-16\)	\(-48\)	\(-48\)	\(-32\)		$\mathrm{SU}(2)[C_{120}]$