Properties

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

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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

\( 280 q - 18 q^{2} - 4 q^{3} + 130 q^{4} - 56 q^{5} - 524 q^{6} + 1074 q^{7} - 918 q^{8} - 14612 q^{9} + O(q^{10}) \) \( 280 q - 18 q^{2} - 4 q^{3} + 130 q^{4} - 56 q^{5} - 524 q^{6} + 1074 q^{7} - 918 q^{8} - 14612 q^{9} + 5978 q^{10} + 15360 q^{11} + 12496 q^{12} - 4876 q^{13} - 132534 q^{14} - 12400 q^{15} + 237158 q^{16} + 222852 q^{17} + 31874 q^{18} - 145956 q^{19} - 371924 q^{20} - 320736 q^{21} + 245504 q^{22} + 681516 q^{23} + 1286304 q^{24} + 163924 q^{25} - 124920 q^{26} - 1241296 q^{27} - 1834662 q^{28} - 697632 q^{29} - 1115738 q^{30} + 410440 q^{31} - 227706 q^{32} + 2186176 q^{33} + 2905300 q^{34} + 1805950 q^{35} + 2685686 q^{36} - 771680 q^{37} - 3201948 q^{38} - 4660264 q^{39} - 6726052 q^{40} - 2640240 q^{41} + 888936 q^{42} + 2712320 q^{43} - 801780 q^{44} + 3836344 q^{45} + 7171580 q^{46} + 4148208 q^{47} + 4189048 q^{48} + 3697212 q^{49} - 5446194 q^{50} - 6527408 q^{51} - 7022420 q^{52} + 460116 q^{53} - 451520 q^{54} + 284932 q^{55} + 17803866 q^{56} + 59288 q^{57} + 3538120 q^{58} - 409860 q^{59} - 17827112 q^{60} - 13293696 q^{61} - 23450880 q^{62} - 7420278 q^{63} - 99338 q^{64} + 5206940 q^{65} + 3287996 q^{66} + 6857340 q^{67} + 51138156 q^{68} + 11256408 q^{69} + 40402086 q^{70} + 598464 q^{71} + 26522610 q^{72} + 4660148 q^{73} - 8111376 q^{74} - 32296648 q^{75} - 70671788 q^{76} - 22890948 q^{77} - 47889224 q^{78} - 9327140 q^{79} + 25282504 q^{80} + 15608152 q^{81} + 39492616 q^{82} - 13171020 q^{83} + 10278288 q^{84} - 8582632 q^{85} - 49457736 q^{86} + 27065528 q^{87} + 19566516 q^{88} + 31966992 q^{89} + 96151436 q^{90} + 55530636 q^{91} + 77321016 q^{92} + 5401704 q^{93} - 62737232 q^{94} - 76802320 q^{95} - 233581948 q^{96} - 104951708 q^{97} - 153100914 q^{98} - 46137496 q^{99} + O(q^{100}) \)

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

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