Space of modular forms of level 85 and weight 2

• Label: 85.2
• Level: 85
• Weight: 2
• Dimension: 215
• Nonzero newspaces: 10
• Newform subspaces: 14
• Sturm bound: 1152
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1152\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(85))\).

	Total	New	Old
Modular forms	352	307	45
Cusp forms	225	215	10
Eisenstein series	127	92	35

Trace form

215 * q - 19 * q^2 - 20 * q^3 - 23 * q^4 - 25 * q^5 - 60 * q^6 - 24 * q^7 - 31 * q^8 - 29 * q^9 - 23 * q^10 - 44 * q^11 + 4 * q^12 - 14 * q^13 - 8 * q^14 - 4 * q^15 - 7 * q^16 - 17 * q^17 - 7 * q^18 - 20 * q^19 - 3 * q^20 - 32 * q^21 - 20 * q^22 - 24 * q^23 + 4 * q^24 + 3 * q^25 - 18 * q^26 - 8 * q^27 + 24 * q^28 - 6 * q^29 + 28 * q^30 - 16 * q^31 + 33 * q^32 + 16 * q^33 + 61 * q^34 - 24 * q^35 + 21 * q^36 + 10 * q^37 + 20 * q^38 + 24 * q^39 + 57 * q^40 - 2 * q^41 + 80 * q^42 + 20 * q^43 + 92 * q^44 + 15 * q^45 - 24 * q^46 + 16 * q^47 + 68 * q^48 - 9 * q^49 - 3 * q^50 - 52 * q^51 - 2 * q^52 + 18 * q^53 + 104 * q^54 + 28 * q^55 + 72 * q^56 + 96 * q^57 + 70 * q^58 + 52 * q^59 + 116 * q^60 + 18 * q^61 + 96 * q^62 + 120 * q^63 - 47 * q^64 + 38 * q^65 + 64 * q^66 - 4 * q^67 + 17 * q^68 + 32 * q^69 - 40 * q^70 - 88 * q^71 - 59 * q^72 - 50 * q^73 - 106 * q^74 - 28 * q^75 - 204 * q^76 - 80 * q^77 - 104 * q^78 - 96 * q^79 - 199 * q^80 - 153 * q^81 - 198 * q^82 - 68 * q^83 - 288 * q^84 - 141 * q^85 - 132 * q^86 - 136 * q^87 - 260 * q^88 - 58 * q^89 - 107 * q^90 - 128 * q^91 - 120 * q^92 - 80 * q^93 - 96 * q^94 - 60 * q^95 - 28 * q^96 - 114 * q^97 + 13 * q^98 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)

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
85.2.a	\(\chi_{85}(1, \cdot)\)	85.2.a.a	1	1
		85.2.a.b	2
		85.2.a.c	2
85.2.b	\(\chi_{85}(69, \cdot)\)	85.2.b.a	8	1
85.2.c	\(\chi_{85}(84, \cdot)\)	85.2.c.a	8	1
85.2.d	\(\chi_{85}(16, \cdot)\)	85.2.d.a	6	1
85.2.e	\(\chi_{85}(21, \cdot)\)	85.2.e.a	12	2
85.2.j	\(\chi_{85}(4, \cdot)\)	85.2.j.a	2	2
		85.2.j.b	2
		85.2.j.c	12
85.2.l	\(\chi_{85}(26, \cdot)\)	85.2.l.a	24	4
85.2.m	\(\chi_{85}(9, \cdot)\)	85.2.m.a	24	4
85.2.o	\(\chi_{85}(3, \cdot)\)	85.2.o.a	56	8
85.2.r	\(\chi_{85}(12, \cdot)\)	85.2.r.a	56	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(85))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(85)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 1}\)