Space of modular forms of level 87, weight 3, and Character 87.l

• Label: 87.3.l
• Level: $87$
• Weight: $3$
• Character orbit: 87.l
• Rep. character: $\chi_{87}(10,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	87.l (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(87, [\chi])\).

	Total	New	Old
Modular forms	264	120	144
Cusp forms	216	120	96
Eisenstein series	48	0	48

Trace form

\( 120 q + 8 q^{2} - 60 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(87, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
87.3.l.a	$87$	$3$	87.l	29.f	$28$	$120$	$10$	$2.371$		None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{3}^{\mathrm{old}}(87, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(87, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)