Properties

Label 30.2
Level 30
Weight 2
Dimension 7
Nonzero newspaces 3
Newforms 3
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(30))\).

Total New Old
Modular forms 40 7 33
Cusp forms 9 7 2
Eisenstein series 31 0 31

Trace form

\(7q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 9q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 14q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 11q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 5q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 7q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 18q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 21q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 10q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut +\mathstrut 14q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 5q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.2.a \(\chi_{30}(1, \cdot)\) 30.2.a.a 1 1
30.2.c \(\chi_{30}(19, \cdot)\) 30.2.c.a 2 1
30.2.e \(\chi_{30}(17, \cdot)\) 30.2.e.a 4 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(30)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)