Space of modular forms of level 85 and weight 6

• Label: 85.6
• Level: 85
• Weight: 6
• Dimension: 1266
• Nonzero newspaces: 10
• Newform subspaces: 14
• Sturm bound: 3456
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(3456\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(85))\).

	Total	New	Old
Modular forms	1504	1358	146
Cusp forms	1376	1266	110
Eisenstein series	128	92	36

Trace form

1266 * q - 20 * q^2 - 8 * q^3 + 88 * q^4 + 106 * q^5 - 560 * q^6 - 400 * q^7 + 224 * q^8 + 1050 * q^9 + 2020 * q^10 - 2024 * q^11 - 8688 * q^12 - 2204 * q^13 - 960 * q^14 + 1880 * q^15 + 18048 * q^16 + 5486 * q^17 + 8812 * q^18 - 2392 * q^19 - 9296 * q^20 - 18192 * q^21 - 18496 * q^22 - 13184 * q^23 + 33296 * q^24 + 2334 * q^25 - 29032 * q^26 - 46544 * q^27 - 55600 * q^28 + 22724 * q^29 + 35080 * q^30 + 16560 * q^31 + 64512 * q^32 + 68512 * q^33 + 129228 * q^34 + 8704 * q^35 + 32248 * q^36 - 10044 * q^37 + 25488 * q^38 - 13344 * q^39 - 109480 * q^40 - 146868 * q^41 - 389104 * q^42 - 114248 * q^43 - 152048 * q^44 + 27006 * q^45 + 298496 * q^46 + 105840 * q^47 + 288160 * q^48 + 51218 * q^49 - 41716 * q^50 + 177432 * q^51 + 284272 * q^52 + 287132 * q^53 + 341712 * q^54 + 37568 * q^55 - 448288 * q^56 - 641168 * q^57 - 688568 * q^58 - 376280 * q^59 - 548720 * q^60 - 313668 * q^61 - 222080 * q^62 + 346016 * q^63 + 604368 * q^64 + 353096 * q^65 + 1037376 * q^66 + 165352 * q^67 + 300632 * q^68 + 306256 * q^69 + 117344 * q^70 + 49376 * q^71 + 669040 * q^72 + 448772 * q^73 + 565944 * q^74 + 373136 * q^75 - 33760 * q^76 - 440304 * q^77 - 1440320 * q^78 - 658864 * q^79 - 1224728 * q^80 - 528646 * q^81 - 585320 * q^82 + 702392 * q^83 + 1385024 * q^84 - 413294 * q^85 - 419168 * q^86 - 1032608 * q^87 - 1824336 * q^88 - 1192540 * q^89 - 1212348 * q^90 - 977072 * q^91 - 658864 * q^92 - 200912 * q^93 + 471712 * q^94 + 950880 * q^95 + 2772480 * q^96 + 1276012 * q^97 + 2525852 * q^98 + 2898360 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(85))\)

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
85.6.a	\(\chi_{85}(1, \cdot)\)	85.6.a.a	5	1
		85.6.a.b	7
		85.6.a.c	8
		85.6.a.d	8
85.6.b	\(\chi_{85}(69, \cdot)\)	85.6.b.a	40	1
85.6.c	\(\chi_{85}(84, \cdot)\)	85.6.c.a	44	1
85.6.d	\(\chi_{85}(16, \cdot)\)	85.6.d.a	2	1
		85.6.d.b	28
85.6.e	\(\chi_{85}(21, \cdot)\)	85.6.e.a	60	2
85.6.j	\(\chi_{85}(4, \cdot)\)	85.6.j.a	88	2
85.6.l	\(\chi_{85}(26, \cdot)\)	85.6.l.a	120	4
85.6.m	\(\chi_{85}(9, \cdot)\)	85.6.m.a	168	4
85.6.o	\(\chi_{85}(3, \cdot)\)	85.6.o.a	344	8
85.6.r	\(\chi_{85}(12, \cdot)\)	85.6.r.a	344	8

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(85))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(85)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)