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Properties

Label 35.10
Level 35
Weight 10
Dimension 364
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 960
Trace bound 2

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(960\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(35))\).

Total New Old
Modular forms 456 396 60
Cusp forms 408 364 44
Eisenstein series 48 32 16

Trace form

\( 364 q + 30 q^{2} - 622 q^{3} + 1538 q^{4} - 4391 q^{5} + 18772 q^{6} - 8684 q^{7} - 76710 q^{8} + 86488 q^{9} + O(q^{10}) \) \( 364 q + 30 q^{2} - 622 q^{3} + 1538 q^{4} - 4391 q^{5} + 18772 q^{6} - 8684 q^{7} - 76710 q^{8} + 86488 q^{9} + 190986 q^{10} - 323682 q^{11} - 617024 q^{12} + 733792 q^{13} + 848202 q^{14} + 281354 q^{15} - 4582874 q^{16} - 3570246 q^{17} + 3924962 q^{18} + 5321658 q^{19} + 6538492 q^{20} - 1825734 q^{21} - 4704208 q^{22} - 7441710 q^{23} - 11370288 q^{24} + 5021635 q^{25} + 13570008 q^{26} + 16379912 q^{27} + 7132234 q^{28} - 5852616 q^{29} + 28778542 q^{30} - 6552242 q^{31} - 30157002 q^{32} + 16428598 q^{33} - 18578508 q^{34} - 16639151 q^{35} + 11849798 q^{36} - 27962862 q^{37} - 132018060 q^{38} + 69035360 q^{39} + 112065316 q^{40} + 201015648 q^{41} + 112304520 q^{42} - 279216380 q^{43} - 433444020 q^{44} - 75745808 q^{45} + 66686140 q^{46} + 32425314 q^{47} + 349845112 q^{48} + 56173524 q^{49} + 425515758 q^{50} - 214755854 q^{51} - 394573428 q^{52} + 25396914 q^{53} - 179721680 q^{54} + 59762962 q^{55} + 361381242 q^{56} + 322080404 q^{57} - 134945624 q^{58} + 445144710 q^{59} - 1027513136 q^{60} - 656029158 q^{61} - 656243328 q^{62} + 879610104 q^{63} + 2673342550 q^{64} + 527099102 q^{65} + 1235799500 q^{66} + 458672174 q^{67} - 3767916372 q^{68} - 4067716140 q^{69} - 3313775658 q^{70} + 1271746536 q^{71} + 4098027090 q^{72} + 2441566138 q^{73} + 212742000 q^{74} + 1189927829 q^{75} + 1799893908 q^{76} - 1398163770 q^{77} - 814049192 q^{78} + 500272486 q^{79} - 4314227816 q^{80} - 2191755854 q^{81} - 3389588936 q^{82} - 1610283732 q^{83} + 2972510160 q^{84} + 3176030298 q^{85} + 8090252040 q^{86} + 2487768272 q^{87} + 4922708916 q^{88} - 1550332854 q^{89} - 3834046756 q^{90} - 6171150844 q^{91} - 9675577128 q^{92} - 6107966586 q^{93} - 7882779648 q^{94} + 2373760595 q^{95} + 14546202020 q^{96} + 8346369924 q^{97} + 17522645310 q^{98} + 15798283616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.10.a \(\chi_{35}(1, \cdot)\) 35.10.a.a 1 1
35.10.a.b 2
35.10.a.c 4
35.10.a.d 5
35.10.a.e 6
35.10.b \(\chi_{35}(29, \cdot)\) 35.10.b.a 26 1
35.10.e \(\chi_{35}(11, \cdot)\) 35.10.e.a 22 2
35.10.e.b 26
35.10.f \(\chi_{35}(13, \cdot)\) 35.10.f.a 68 2
35.10.j \(\chi_{35}(4, \cdot)\) 35.10.j.a 68 2
35.10.k \(\chi_{35}(3, \cdot)\) 35.10.k.a 136 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)