Properties

Label 35.2
Level 35
Weight 2
Dimension 25
Nonzero newspaces 6
Newforms 8
Sturm bound 192
Trace bound 2

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(35))\).

Total New Old
Modular forms 72 57 15
Cusp forms 25 25 0
Eisenstein series 47 32 15

Trace form

\(25q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 27q^{18} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 21q^{32} \) \(\mathstrut -\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 53q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 16q^{39} \) \(\mathstrut -\mathstrut 9q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 24q^{44} \) \(\mathstrut +\mathstrut 17q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 40q^{48} \) \(\mathstrut +\mathstrut 37q^{49} \) \(\mathstrut +\mathstrut 51q^{50} \) \(\mathstrut +\mathstrut 48q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 42q^{53} \) \(\mathstrut +\mathstrut 36q^{54} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 18q^{58} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 34q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 17q^{63} \) \(\mathstrut -\mathstrut 41q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut -\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 40q^{67} \) \(\mathstrut -\mathstrut 42q^{68} \) \(\mathstrut -\mathstrut 24q^{69} \) \(\mathstrut -\mathstrut 87q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 21q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 30q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 28q^{76} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 13q^{80} \) \(\mathstrut +\mathstrut 25q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 18q^{85} \) \(\mathstrut +\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut 48q^{87} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 15q^{90} \) \(\mathstrut +\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 36q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut 60q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
35.2.a \(\chi_{35}(1, \cdot)\) 35.2.a.a 1 1
35.2.a.b 2
35.2.b \(\chi_{35}(29, \cdot)\) 35.2.b.a 2 1
35.2.e \(\chi_{35}(11, \cdot)\) 35.2.e.a 4 2
35.2.f \(\chi_{35}(13, \cdot)\) 35.2.f.a 4 2
35.2.j \(\chi_{35}(4, \cdot)\) 35.2.j.a 4 2
35.2.k \(\chi_{35}(3, \cdot)\) 35.2.k.a 4 4
35.2.k.b 4