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Properties

Label 239.2
Level 239
Weight 2
Dimension 2262
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 9520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 239 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(9520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(239))\).

Total New Old
Modular forms 2499 2499 0
Cusp forms 2262 2262 0
Eisenstein series 237 237 0

Trace form

\( 2262 q - 116 q^{2} - 115 q^{3} - 112 q^{4} - 113 q^{5} - 107 q^{6} - 111 q^{7} - 104 q^{8} - 106 q^{9} + O(q^{10}) \) \( 2262 q - 116 q^{2} - 115 q^{3} - 112 q^{4} - 113 q^{5} - 107 q^{6} - 111 q^{7} - 104 q^{8} - 106 q^{9} - 101 q^{10} - 107 q^{11} - 91 q^{12} - 105 q^{13} - 95 q^{14} - 95 q^{15} - 88 q^{16} - 101 q^{17} - 80 q^{18} - 99 q^{19} - 77 q^{20} - 87 q^{21} - 83 q^{22} - 95 q^{23} - 59 q^{24} - 88 q^{25} - 77 q^{26} - 79 q^{27} - 63 q^{28} - 89 q^{29} - 47 q^{30} - 87 q^{31} - 56 q^{32} - 71 q^{33} - 65 q^{34} - 71 q^{35} - 28 q^{36} - 81 q^{37} - 59 q^{38} - 63 q^{39} - 29 q^{40} - 77 q^{41} - 23 q^{42} - 75 q^{43} - 35 q^{44} - 41 q^{45} - 47 q^{46} - 71 q^{47} + 5 q^{48} - 62 q^{49} - 26 q^{50} - 47 q^{51} - 21 q^{52} - 65 q^{53} + q^{54} - 47 q^{55} + q^{56} - 39 q^{57} - 29 q^{58} - 59 q^{59} + 49 q^{60} - 57 q^{61} - 23 q^{62} - 15 q^{63} + 8 q^{64} - 35 q^{65} + 25 q^{66} - 51 q^{67} + 7 q^{68} - 23 q^{69} + 25 q^{70} - 47 q^{71} + 76 q^{72} - 45 q^{73} - 5 q^{74} + 5 q^{75} + 21 q^{76} - 23 q^{77} + 49 q^{78} - 39 q^{79} + 67 q^{80} + 2 q^{81} + 7 q^{82} - 35 q^{83} + 105 q^{84} - 11 q^{85} + 13 q^{86} + q^{87} + 61 q^{88} - 29 q^{89} + 115 q^{90} - 7 q^{91} + 49 q^{92} + 9 q^{93} + 25 q^{94} + q^{95} + 133 q^{96} - 21 q^{97} + 52 q^{98} + 37 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(239))\)

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
239.2.a \(\chi_{239}(1, \cdot)\) 239.2.a.a 3 1
239.2.a.b 17
239.2.c \(\chi_{239}(10, \cdot)\) 239.2.c.a 6 6
239.2.c.b 108
239.2.e \(\chi_{239}(6, \cdot)\) 239.2.e.a 304 16
239.2.g \(\chi_{239}(2, \cdot)\) 239.2.g.a 1824 96