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Properties

Label 59.2
Level 59
Weight 2
Dimension 117
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 580
Trace bound 1

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(580\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(59))\).

Total New Old
Modular forms 174 174 0
Cusp forms 117 117 0
Eisenstein series 57 57 0

Trace form

\( 117 q - 26 q^{2} - 25 q^{3} - 22 q^{4} - 23 q^{5} - 17 q^{6} - 21 q^{7} - 14 q^{8} - 16 q^{9} + O(q^{10}) \) \( 117 q - 26 q^{2} - 25 q^{3} - 22 q^{4} - 23 q^{5} - 17 q^{6} - 21 q^{7} - 14 q^{8} - 16 q^{9} - 11 q^{10} - 17 q^{11} - q^{12} - 15 q^{13} - 5 q^{14} - 5 q^{15} + 2 q^{16} - 11 q^{17} + 10 q^{18} - 9 q^{19} + 13 q^{20} + 3 q^{21} + 7 q^{22} - 5 q^{23} + 31 q^{24} + 2 q^{25} + 13 q^{26} + 11 q^{27} + 27 q^{28} + q^{29} + 43 q^{30} + 3 q^{31} + 34 q^{32} + 19 q^{33} + 25 q^{34} + 19 q^{35} + 62 q^{36} + 9 q^{37} + 31 q^{38} + 27 q^{39} + 61 q^{40} + 13 q^{41} + 67 q^{42} + 15 q^{43} + 55 q^{44} + 20 q^{45} - 15 q^{46} - 10 q^{47} - 79 q^{48} - 30 q^{49} - 52 q^{50} - 73 q^{51} - 47 q^{52} - 33 q^{53} - 112 q^{54} - 44 q^{55} - 141 q^{56} - 94 q^{57} - 26 q^{58} - 28 q^{59} - 238 q^{60} - 25 q^{61} + 9 q^{62} - 70 q^{63} - 134 q^{64} - 32 q^{65} - 88 q^{66} - 19 q^{67} - 19 q^{68} - 49 q^{69} - q^{70} - 15 q^{71} - 8 q^{72} + 16 q^{73} + 27 q^{74} + 66 q^{75} + 111 q^{76} + 67 q^{77} + 139 q^{78} + 51 q^{79} + 157 q^{80} + 92 q^{81} + 97 q^{82} + 55 q^{83} + 195 q^{84} + 79 q^{85} + 103 q^{86} + 91 q^{87} + 151 q^{88} + 61 q^{89} + 205 q^{90} + 83 q^{91} + 139 q^{92} + 99 q^{93} + 115 q^{94} + 91 q^{95} + 223 q^{96} + 69 q^{97} + 55 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)

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
59.2.a \(\chi_{59}(1, \cdot)\) 59.2.a.a 5 1
59.2.c \(\chi_{59}(3, \cdot)\) 59.2.c.a 112 28