Properties

Label 62.2
Level 62
Weight 2
Dimension 39
Nonzero newspaces 4
Newforms 8
Sturm bound 480
Trace bound 3

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Defining parameters

Level: \( N \) = \( 62 = 2 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 8 \)
Sturm bound: \(480\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(62))\).

Total New Old
Modular forms 150 39 111
Cusp forms 91 39 52
Eisenstein series 59 0 59

Trace form

\(39q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(39q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 13q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 18q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 39q^{25} \) \(\mathstrut +\mathstrut 16q^{26} \) \(\mathstrut +\mathstrut 50q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 36q^{30} \) \(\mathstrut +\mathstrut 29q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 42q^{34} \) \(\mathstrut +\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut +\mathstrut 52q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 2q^{42} \) \(\mathstrut -\mathstrut 34q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 78q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 31q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 14q^{52} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 28q^{61} \) \(\mathstrut -\mathstrut 31q^{62} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 48q^{66} \) \(\mathstrut -\mathstrut 38q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 13q^{72} \) \(\mathstrut -\mathstrut 44q^{73} \) \(\mathstrut -\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 24q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut +\mathstrut 126q^{83} \) \(\mathstrut +\mathstrut 28q^{84} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 76q^{86} \) \(\mathstrut +\mathstrut 48q^{88} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut +\mathstrut 102q^{90} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 116q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 120q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut 123q^{98} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)

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
62.2.a \(\chi_{62}(1, \cdot)\) 62.2.a.a 1 1
62.2.a.b 2
62.2.c \(\chi_{62}(5, \cdot)\) 62.2.c.a 2 2
62.2.c.b 2
62.2.d \(\chi_{62}(33, \cdot)\) 62.2.d.a 8 4
62.2.d.b 8
62.2.g \(\chi_{62}(7, \cdot)\) 62.2.g.a 8 8
62.2.g.b 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(62))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(62)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)