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Properties

Label 179.2
Level 179
Weight 2
Dimension 1247
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 5340
Trace bound 1

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Defining parameters

Level: \( N \) = \( 179 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(5340\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(179))\).

Total New Old
Modular forms 1424 1424 0
Cusp forms 1247 1247 0
Eisenstein series 177 177 0

Trace form

\( 1247 q - 86 q^{2} - 85 q^{3} - 82 q^{4} - 83 q^{5} - 77 q^{6} - 81 q^{7} - 74 q^{8} - 76 q^{9} + O(q^{10}) \) \( 1247 q - 86 q^{2} - 85 q^{3} - 82 q^{4} - 83 q^{5} - 77 q^{6} - 81 q^{7} - 74 q^{8} - 76 q^{9} - 71 q^{10} - 77 q^{11} - 61 q^{12} - 75 q^{13} - 65 q^{14} - 65 q^{15} - 58 q^{16} - 71 q^{17} - 50 q^{18} - 69 q^{19} - 47 q^{20} - 57 q^{21} - 53 q^{22} - 65 q^{23} - 29 q^{24} - 58 q^{25} - 47 q^{26} - 49 q^{27} - 33 q^{28} - 59 q^{29} - 17 q^{30} - 57 q^{31} - 26 q^{32} - 41 q^{33} - 35 q^{34} - 41 q^{35} + 2 q^{36} - 51 q^{37} - 29 q^{38} - 33 q^{39} + q^{40} - 47 q^{41} + 7 q^{42} - 45 q^{43} - 5 q^{44} - 11 q^{45} - 17 q^{46} - 41 q^{47} + 35 q^{48} - 32 q^{49} + 4 q^{50} - 17 q^{51} + 9 q^{52} - 35 q^{53} + 31 q^{54} - 17 q^{55} + 31 q^{56} - 9 q^{57} + q^{58} - 29 q^{59} + 79 q^{60} - 27 q^{61} + 7 q^{62} + 15 q^{63} + 38 q^{64} - 5 q^{65} + 55 q^{66} - 21 q^{67} + 37 q^{68} + 7 q^{69} + 55 q^{70} - 17 q^{71} + 106 q^{72} - 15 q^{73} + 25 q^{74} + 35 q^{75} + 51 q^{76} + 7 q^{77} + 79 q^{78} - 9 q^{79} + 97 q^{80} + 32 q^{81} + 37 q^{82} - 5 q^{83} + 135 q^{84} + 19 q^{85} + 43 q^{86} + 31 q^{87} + 91 q^{88} + q^{89} + 145 q^{90} + 23 q^{91} + 79 q^{92} + 39 q^{93} + 55 q^{94} + 31 q^{95} + 163 q^{96} + 9 q^{97} + 82 q^{98} + 67 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(179))\)

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
179.2.a \(\chi_{179}(1, \cdot)\) 179.2.a.a 1 1
179.2.a.b 3
179.2.a.c 11
179.2.c \(\chi_{179}(3, \cdot)\) 179.2.c.a 1232 88