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Properties

Label 79.2
Level 79
Weight 2
Dimension 222
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 1040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(1040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(79))\).

Total New Old
Modular forms 299 299 0
Cusp forms 222 222 0
Eisenstein series 77 77 0

Trace form

\( 222 q - 36 q^{2} - 35 q^{3} - 32 q^{4} - 33 q^{5} - 27 q^{6} - 31 q^{7} - 24 q^{8} - 26 q^{9} + O(q^{10}) \) \( 222 q - 36 q^{2} - 35 q^{3} - 32 q^{4} - 33 q^{5} - 27 q^{6} - 31 q^{7} - 24 q^{8} - 26 q^{9} - 21 q^{10} - 27 q^{11} - 11 q^{12} - 25 q^{13} - 15 q^{14} - 15 q^{15} - 8 q^{16} - 21 q^{17} - 19 q^{19} + 3 q^{20} - 7 q^{21} - 3 q^{22} - 15 q^{23} + 21 q^{24} - 8 q^{25} + 3 q^{26} + q^{27} + 17 q^{28} - 9 q^{29} + 33 q^{30} - 7 q^{31} + 24 q^{32} + 9 q^{33} + 15 q^{34} + 9 q^{35} + 52 q^{36} - q^{37} + 21 q^{38} + 17 q^{39} + 51 q^{40} + 3 q^{41} + 57 q^{42} + 5 q^{43} + 45 q^{44} + 39 q^{45} + 33 q^{46} + 9 q^{47} + 85 q^{48} + 18 q^{49} + 54 q^{50} + 33 q^{51} + 59 q^{52} + 15 q^{53} + 81 q^{54} + 33 q^{55} + 81 q^{56} + 41 q^{57} + 51 q^{58} + 21 q^{59} + 129 q^{60} + 23 q^{61} + 57 q^{62} + 13 q^{63} - 68 q^{64} - 33 q^{65} - 51 q^{66} - 62 q^{67} - 69 q^{68} - 99 q^{69} - 207 q^{70} - 45 q^{71} - 234 q^{72} - 43 q^{73} - 81 q^{74} - 71 q^{75} - 263 q^{76} - 60 q^{77} - 66 q^{78} - 194 q^{79} - 282 q^{80} - 152 q^{81} - 69 q^{82} - 72 q^{83} - 179 q^{84} - 87 q^{85} - 63 q^{86} + 3 q^{87} - 249 q^{88} - 27 q^{89} - 117 q^{90} - 83 q^{91} - 27 q^{92} - 2 q^{93} - 51 q^{94} + 3 q^{95} + 57 q^{96} + 7 q^{97} + 132 q^{98} + 117 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)

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
79.2.a \(\chi_{79}(1, \cdot)\) 79.2.a.a 1 1
79.2.a.b 5
79.2.c \(\chi_{79}(23, \cdot)\) 79.2.c.a 12 2
79.2.e \(\chi_{79}(8, \cdot)\) 79.2.e.a 60 12
79.2.g \(\chi_{79}(2, \cdot)\) 79.2.g.a 144 24