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

• Label: 87.2.i
• Level: $87$
• Weight: $2$
• Character orbit: 87.i
• Rep. character: $\chi_{87}(4,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.i (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	72	24	48
Cusp forms	48	24	24
Eisenstein series	24	0	24

Trace form

24 * q - 2 * q^4 - 4 * q^5 - 2 * q^6 + 8 * q^7 + 4 * q^9 - 28 * q^11 - 10 * q^13 - 14 * q^15 - 22 * q^16 - 20 * q^20 + 4 * q^22 + 18 * q^23 - 18 * q^25 + 28 * q^26 + 8 * q^28 + 28 * q^29 - 40 * q^30 + 28 * q^31 - 14 * q^32 + 34 * q^34 + 2 * q^36 - 28 * q^37 - 4 * q^38 + 14 * q^42 - 14 * q^43 + 14 * q^44 - 10 * q^45 + 56 * q^48 + 20 * q^49 + 42 * q^50 + 2 * q^51 - 68 * q^52 + 6 * q^53 + 2 * q^54 - 14 * q^55 + 32 * q^57 + 50 * q^58 + 28 * q^59 + 42 * q^60 - 8 * q^62 + 6 * q^63 - 20 * q^64 + 18 * q^65 - 28 * q^66 + 8 * q^67 + 14 * q^68 + 28 * q^69 - 42 * q^71 + 14 * q^72 - 84 * q^73 + 10 * q^74 - 14 * q^76 - 70 * q^77 + 2 * q^78 - 14 * q^79 + 36 * q^80 - 4 * q^81 - 50 * q^82 - 32 * q^83 + 14 * q^85 - 128 * q^86 - 44 * q^87 - 20 * q^88 - 14 * q^89 + 34 * q^91 - 58 * q^92 - 20 * q^93 - 44 * q^94 - 52 * q^96 + 56 * q^97 - 42 * q^98

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.i.a	$87$	$2$	87.i	29.e	$14$	$24$	$4$	$0.695$		None		✓	✓	✓	87.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)		$\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{2}^{\mathrm{old}}(87, [\chi])\) into lower level spaces

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