Space of modular forms of level 87 and weight 2

• Label: 87.2
• Level: 87
• Weight: 2
• Dimension: 181
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 1120
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(87))\).

	Total	New	Old
Modular forms	336	237	99
Cusp forms	225	181	44
Eisenstein series	111	56	55

Trace form

181 * q - 3 * q^2 - 15 * q^3 - 35 * q^4 - 6 * q^5 - 17 * q^6 - 36 * q^7 - 15 * q^8 - 15 * q^9 - 46 * q^10 - 12 * q^11 - 21 * q^12 - 42 * q^13 - 24 * q^14 - 20 * q^15 - 59 * q^16 - 18 * q^17 - 17 * q^18 - 48 * q^19 + 6 * q^21 - 8 * q^22 + 4 * q^23 + 55 * q^24 - 3 * q^25 + 28 * q^26 + 27 * q^27 + 56 * q^28 + 27 * q^29 + 38 * q^30 - 4 * q^31 + 49 * q^32 + 16 * q^33 - 12 * q^34 + 8 * q^35 + 63 * q^36 - 38 * q^37 - 4 * q^38 - 76 * q^40 - 42 * q^41 - 38 * q^42 - 72 * q^43 - 56 * q^44 - 6 * q^45 + 40 * q^46 + 8 * q^47 + 67 * q^48 + 27 * q^49 + 103 * q^50 + 24 * q^51 + 98 * q^52 + 72 * q^53 - 17 * q^54 + 124 * q^55 + 76 * q^56 + 36 * q^57 + 221 * q^58 - 4 * q^59 + 140 * q^60 + 22 * q^61 + 100 * q^62 + 6 * q^63 + 97 * q^64 + 42 * q^65 + 62 * q^66 + 16 * q^67 + 70 * q^68 + 18 * q^69 + 52 * q^70 - 16 * q^71 - 85 * q^72 - 32 * q^73 - 86 * q^74 - 115 * q^75 - 168 * q^76 - 96 * q^77 - 168 * q^78 - 108 * q^79 - 186 * q^80 - 127 * q^81 - 154 * q^82 - 84 * q^83 - 196 * q^84 - 136 * q^85 - 132 * q^86 - 113 * q^87 - 236 * q^88 - 90 * q^89 - 172 * q^90 - 140 * q^91 - 168 * q^92 - 102 * q^93 - 172 * q^94 - 120 * q^95 - 231 * q^96 - 28 * q^97 - 31 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
87.2.a	\(\chi_{87}(1, \cdot)\)	87.2.a.a	2	1
		87.2.a.b	3
87.2.c	\(\chi_{87}(28, \cdot)\)	87.2.c.a	4	1
87.2.f	\(\chi_{87}(17, \cdot)\)	87.2.f.a	4	2
		87.2.f.b	4
		87.2.f.c	8
87.2.g	\(\chi_{87}(7, \cdot)\)	87.2.g.a	18	6
		87.2.g.b	18
87.2.i	\(\chi_{87}(4, \cdot)\)	87.2.i.a	24	6
87.2.k	\(\chi_{87}(2, \cdot)\)	87.2.k.a	96	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(87))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(87)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 1}\)