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

• Label: 287.2.n
• Level: $287$
• Weight: $2$
• Character orbit: 287.n
• Rep. character: $\chi_{287}(64,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.n (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{10})\)
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	120	88	32
Cusp forms	104	88	16
Eisenstein series	16	0	16

Trace form

\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + O(q^{10}) \)

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.n.a	$287$	$2$	287.n	41.f	$10$	$88$	$22$	$2.292$		None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(287, [\chi])\) into lower level spaces

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