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

• Label: 287.3.d
• Level: $287$
• Weight: $3$
• Character orbit: 287.d
• Rep. character: $\chi_{287}(286,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $4$
• Sturm bound: $84$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 287 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(84\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(287, [\chi])\).

	Total	New	Old
Modular forms	58	58	0
Cusp forms	54	54	0
Eisenstein series	4	4	0

Trace form

\( 54 q - 4 q^{2} + 100 q^{4} - 32 q^{8} + 178 q^{9} + O(q^{10}) \)

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.d.a	$287$	$3$	287.d	287.d	$2$	$7$	$7$	$7.820$	7.7.\(\cdots\).1	\(\Q(\sqrt{-287}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-49\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
287.3.d.b	$287$	$3$	287.d	287.d	$2$	$7$	$7$	$7.820$	7.7.\(\cdots\).1	\(\Q(\sqrt{-287}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(49\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
287.3.d.c	$287$	$3$	287.d	287.d	$2$	$8$	$8$	$7.820$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{4}q^{3}-3q^{4}+\beta _{6}q^{5}+\beta _{4}q^{6}+\cdots\)
287.3.d.d	$287$	$3$	287.d	287.d	$2$	$32$	$32$	$7.820$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$