Space of modular forms of level 1287, weight 2, and Character 1287.f

• Label: 1287.2.f
• Level: $1287$
• Weight: $2$
• Character orbit: 1287.f
• Rep. character: $\chi_{1287}(989,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1287.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1287, [\chi])\).

	Total	New	Old
Modular forms	176	48	128
Cusp forms	160	48	112
Eisenstein series	16	0	16

Trace form

\( 48 q + 48 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1287, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1287.2.f.a	$1287$	$2$	1287.f	33.d	$2$	$48$	$48$	$10.277$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \)