Space of modular forms of level 87, weight 2, and Character 87.f

• Label: 87.2.f
• Level: $87$
• Weight: $2$
• Character orbit: 87.f
• Rep. character: $\chi_{87}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(87, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	16	16	0
Eisenstein series	8	8	0

Trace form

16 * q - 2 * q^3 - 8 * q^7 - 24 * q^10 - 6 * q^12 + 2 * q^15 + 20 * q^16 + 14 * q^18 - 8 * q^19 - 12 * q^21 + 12 * q^24 - 8 * q^25 - 8 * q^27 - 40 * q^30 + 4 * q^31 + 48 * q^36 - 24 * q^37 + 54 * q^39 + 20 * q^40 + 4 * q^43 - 56 * q^45 - 36 * q^46 + 6 * q^48 + 24 * q^49 + 12 * q^52 + 16 * q^54 + 20 * q^55 + 28 * q^58 - 6 * q^60 + 16 * q^61 + 18 * q^66 - 24 * q^69 + 4 * q^70 - 54 * q^72 - 16 * q^73 + 60 * q^75 - 40 * q^76 - 24 * q^78 + 4 * q^79 + 20 * q^81 + 24 * q^82 - 76 * q^84 - 8 * q^85 - 14 * q^87 + 88 * q^88 - 58 * q^90 - 140 * q^94 - 88 * q^97 - 54 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(87, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
87.2.f.a	$87$	$2$	87.f	87.f	$4$	$4$	$2$	$0.695$	\(\Q(\zeta_{12})\)	None		✓			87.2.f.a	$2$	$0$	\(-2\)	\(0\)	\(8\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
87.2.f.b	$87$	$2$	87.f	87.f	$4$	$4$	$2$	$0.695$	\(\Q(\zeta_{12})\)	None		✓			87.2.f.a	$2$	$0$	\(2\)	\(6\)	\(-8\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
87.2.f.c	$87$	$2$	87.f	87.f	$4$	$8$	$4$	$0.695$	8.0.1871773696.1	None		✓	✓		87.2.f.c	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(2\beta _{3}+\cdots)q^{4}+\cdots\)