↑

Properties

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

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 62 = 2 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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