Space of modular forms of level 35 and weight 8

• Label: 35.8
• Level: 35
• Weight: 8
• Dimension: 280
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 768
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(768\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(35))\).

	Total	New	Old
Modular forms	360	312	48
Cusp forms	312	280	32
Eisenstein series	48	32	16

Trace form

280 * q - 18 * q^2 - 4 * q^3 + 130 * q^4 - 56 * q^5 - 524 * q^6 + 1074 * q^7 - 918 * q^8 - 14612 * q^9 + 5978 * q^10 + 15360 * q^11 + 12496 * q^12 - 4876 * q^13 - 132534 * q^14 - 12400 * q^15 + 237158 * q^16 + 222852 * q^17 + 31874 * q^18 - 145956 * q^19 - 371924 * q^20 - 320736 * q^21 + 245504 * q^22 + 681516 * q^23 + 1286304 * q^24 + 163924 * q^25 - 124920 * q^26 - 1241296 * q^27 - 1834662 * q^28 - 697632 * q^29 - 1115738 * q^30 + 410440 * q^31 - 227706 * q^32 + 2186176 * q^33 + 2905300 * q^34 + 1805950 * q^35 + 2685686 * q^36 - 771680 * q^37 - 3201948 * q^38 - 4660264 * q^39 - 6726052 * q^40 - 2640240 * q^41 + 888936 * q^42 + 2712320 * q^43 - 801780 * q^44 + 3836344 * q^45 + 7171580 * q^46 + 4148208 * q^47 + 4189048 * q^48 + 3697212 * q^49 - 5446194 * q^50 - 6527408 * q^51 - 7022420 * q^52 + 460116 * q^53 - 451520 * q^54 + 284932 * q^55 + 17803866 * q^56 + 59288 * q^57 + 3538120 * q^58 - 409860 * q^59 - 17827112 * q^60 - 13293696 * q^61 - 23450880 * q^62 - 7420278 * q^63 - 99338 * q^64 + 5206940 * q^65 + 3287996 * q^66 + 6857340 * q^67 + 51138156 * q^68 + 11256408 * q^69 + 40402086 * q^70 + 598464 * q^71 + 26522610 * q^72 + 4660148 * q^73 - 8111376 * q^74 - 32296648 * q^75 - 70671788 * q^76 - 22890948 * q^77 - 47889224 * q^78 - 9327140 * q^79 + 25282504 * q^80 + 15608152 * q^81 + 39492616 * q^82 - 13171020 * q^83 + 10278288 * q^84 - 8582632 * q^85 - 49457736 * q^86 + 27065528 * q^87 + 19566516 * q^88 + 31966992 * q^89 + 96151436 * q^90 + 55530636 * q^91 + 77321016 * q^92 + 5401704 * q^93 - 62737232 * q^94 - 76802320 * q^95 - 233581948 * q^96 - 104951708 * q^97 - 153100914 * q^98 - 46137496 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.8.a	\(\chi_{35}(1, \cdot)\)	35.8.a.a	2	1
		35.8.a.b	3
		35.8.a.c	4
		35.8.a.d	5
35.8.b	\(\chi_{35}(29, \cdot)\)	35.8.b.a	22	1
35.8.e	\(\chi_{35}(11, \cdot)\)	35.8.e.a	16	2
		35.8.e.b	20
35.8.f	\(\chi_{35}(13, \cdot)\)	35.8.f.a	52	2
35.8.j	\(\chi_{35}(4, \cdot)\)	35.8.j.a	52	2
35.8.k	\(\chi_{35}(3, \cdot)\)	35.8.k.a	104	4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)