Properties

Label 70.2
Level 70
Weight 2
Dimension 45
Nonzero newspaces 6
Newforms 10
Sturm bound 576
Trace bound 4

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Defining parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 10 \)
Sturm bound: \(576\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(70))\).

Total New Old
Modular forms 192 45 147
Cusp forms 97 45 52
Eisenstein series 95 0 95

Trace form

\(45q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(45q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 5q^{14} \) \(\mathstrut -\mathstrut 20q^{15} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut -\mathstrut 11q^{18} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 15q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 52q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 42q^{34} \) \(\mathstrut +\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 33q^{36} \) \(\mathstrut +\mathstrut 30q^{37} \) \(\mathstrut +\mathstrut 32q^{38} \) \(\mathstrut +\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 40q^{42} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 7q^{45} \) \(\mathstrut -\mathstrut 51q^{49} \) \(\mathstrut -\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 48q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 66q^{53} \) \(\mathstrut -\mathstrut 32q^{54} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut -\mathstrut 24q^{57} \) \(\mathstrut -\mathstrut 42q^{58} \) \(\mathstrut -\mathstrut 20q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 40q^{62} \) \(\mathstrut +\mathstrut 3q^{63} \) \(\mathstrut -\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 48q^{66} \) \(\mathstrut +\mathstrut 36q^{67} \) \(\mathstrut -\mathstrut 30q^{68} \) \(\mathstrut -\mathstrut 35q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 11q^{72} \) \(\mathstrut +\mathstrut 18q^{73} \) \(\mathstrut -\mathstrut 34q^{74} \) \(\mathstrut -\mathstrut 24q^{75} \) \(\mathstrut -\mathstrut 24q^{76} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 48q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 31q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 92q^{95} \) \(\mathstrut +\mathstrut 16q^{96} \) \(\mathstrut +\mathstrut 66q^{97} \) \(\mathstrut +\mathstrut 97q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)

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
70.2.a \(\chi_{70}(1, \cdot)\) 70.2.a.a 1 1
70.2.c \(\chi_{70}(29, \cdot)\) 70.2.c.a 4 1
70.2.e \(\chi_{70}(11, \cdot)\) 70.2.e.a 2 2
70.2.e.b 2
70.2.e.c 2
70.2.e.d 2
70.2.g \(\chi_{70}(13, \cdot)\) 70.2.g.a 8 2
70.2.i \(\chi_{70}(9, \cdot)\) 70.2.i.a 4 2
70.2.i.b 4
70.2.k \(\chi_{70}(3, \cdot)\) 70.2.k.a 16 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(70)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)