Properties

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

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
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

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

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 the 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