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Properties

Label 83.2
Level 83
Weight 2
Dimension 247
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 1148
Trace bound 1

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Defining parameters

Level: \( N \) = \( 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(1148\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(83))\).

Total New Old
Modular forms 328 328 0
Cusp forms 247 247 0
Eisenstein series 81 81 0

Trace form

\( 247 q - 38 q^{2} - 37 q^{3} - 34 q^{4} - 35 q^{5} - 29 q^{6} - 33 q^{7} - 26 q^{8} - 28 q^{9} + O(q^{10}) \) \( 247 q - 38 q^{2} - 37 q^{3} - 34 q^{4} - 35 q^{5} - 29 q^{6} - 33 q^{7} - 26 q^{8} - 28 q^{9} - 23 q^{10} - 29 q^{11} - 13 q^{12} - 27 q^{13} - 17 q^{14} - 17 q^{15} - 10 q^{16} - 23 q^{17} - 2 q^{18} - 21 q^{19} + q^{20} - 9 q^{21} - 5 q^{22} - 17 q^{23} + 19 q^{24} - 10 q^{25} + q^{26} - q^{27} + 15 q^{28} - 11 q^{29} + 31 q^{30} - 9 q^{31} + 22 q^{32} + 7 q^{33} + 13 q^{34} + 7 q^{35} + 50 q^{36} - 3 q^{37} + 19 q^{38} + 15 q^{39} + 49 q^{40} + q^{41} + 55 q^{42} + 3 q^{43} + 43 q^{44} + 37 q^{45} + 31 q^{46} + 7 q^{47} + 83 q^{48} + 16 q^{49} + 52 q^{50} + 31 q^{51} + 57 q^{52} + 13 q^{53} + 79 q^{54} + 31 q^{55} + 79 q^{56} + 39 q^{57} + 49 q^{58} + 19 q^{59} + 127 q^{60} + 21 q^{61} + 55 q^{62} + 63 q^{63} + 86 q^{64} + 43 q^{65} + 62 q^{66} - 14 q^{67} - 79 q^{68} - 68 q^{69} - 61 q^{70} - 10 q^{71} - 256 q^{72} - 90 q^{73} - 9 q^{74} - 204 q^{75} - 65 q^{76} - 68 q^{77} - 283 q^{78} - 84 q^{79} - 265 q^{80} - 84 q^{81} - 120 q^{82} - 81 q^{83} - 350 q^{84} - 56 q^{85} - 73 q^{86} - 85 q^{87} - 271 q^{88} - 74 q^{89} - 217 q^{90} - 52 q^{91} - 37 q^{92} - 200 q^{93} + 21 q^{94} - 44 q^{95} - 199 q^{96} + 16 q^{97} - 34 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)

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
83.2.a \(\chi_{83}(1, \cdot)\) 83.2.a.a 1 1
83.2.a.b 6
83.2.c \(\chi_{83}(3, \cdot)\) 83.2.c.a 240 40