Properties

Label 35.4
Level 35
Weight 4
Dimension 112
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 384
Trace bound 2

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(384\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(35))\).

Total New Old
Modular forms 168 144 24
Cusp forms 120 112 8
Eisenstein series 48 32 16

Trace form

\( 112 q + 2 q^{2} + 2 q^{3} - 22 q^{4} - 11 q^{5} - 68 q^{6} - 60 q^{7} + 42 q^{8} + 124 q^{9} + O(q^{10}) \) \( 112 q + 2 q^{2} + 2 q^{3} - 22 q^{4} - 11 q^{5} - 68 q^{6} - 60 q^{7} + 42 q^{8} + 124 q^{9} - 22 q^{10} - 82 q^{11} - 128 q^{12} + 64 q^{13} - 30 q^{14} - 70 q^{15} - 10 q^{16} - 214 q^{17} - 154 q^{18} + 106 q^{19} + 236 q^{20} + 426 q^{21} + 256 q^{22} - 270 q^{23} - 1056 q^{24} - 941 q^{25} - 1240 q^{26} - 664 q^{27} - 822 q^{28} + 160 q^{29} + 982 q^{30} + 990 q^{31} + 2134 q^{32} + 1678 q^{33} + 2092 q^{34} + 1305 q^{35} + 3422 q^{36} + 1394 q^{37} + 1820 q^{38} + 896 q^{39} - 132 q^{40} - 2024 q^{41} - 2304 q^{42} - 1580 q^{43} - 3284 q^{44} - 2456 q^{45} - 3540 q^{46} - 46 q^{47} - 1736 q^{48} + 344 q^{49} + 986 q^{50} - 206 q^{51} + 332 q^{52} + 914 q^{53} - 3344 q^{54} - 2878 q^{55} - 3894 q^{56} - 6412 q^{57} - 6448 q^{58} - 4810 q^{59} - 2792 q^{60} + 946 q^{61} - 624 q^{62} + 2088 q^{63} + 5158 q^{64} + 2590 q^{65} + 8588 q^{66} + 6126 q^{67} + 9244 q^{68} + 11556 q^{69} + 12666 q^{70} + 5608 q^{71} + 10866 q^{72} + 6394 q^{73} + 8968 q^{74} + 2237 q^{75} + 1508 q^{76} + 270 q^{77} - 392 q^{78} - 4314 q^{79} - 6616 q^{80} - 7922 q^{81} - 8512 q^{82} - 7764 q^{83} - 15648 q^{84} - 8542 q^{85} - 12184 q^{86} - 12400 q^{87} - 17772 q^{88} - 9990 q^{89} - 12844 q^{90} - 2364 q^{91} - 8136 q^{92} + 174 q^{93} - 1952 q^{94} + 4435 q^{95} + 5924 q^{96} + 5612 q^{97} + 4258 q^{98} + 8624 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.4.a \(\chi_{35}(1, \cdot)\) 35.4.a.a 1 1
35.4.a.b 2
35.4.a.c 3
35.4.b \(\chi_{35}(29, \cdot)\) 35.4.b.a 10 1
35.4.e \(\chi_{35}(11, \cdot)\) 35.4.e.a 2 2
35.4.e.b 4
35.4.e.c 10
35.4.f \(\chi_{35}(13, \cdot)\) 35.4.f.a 4 2
35.4.f.b 16
35.4.j \(\chi_{35}(4, \cdot)\) 35.4.j.a 20 2
35.4.k \(\chi_{35}(3, \cdot)\) 35.4.k.a 40 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

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