Properties

Label 139.2
Level 139
Weight 2
Dimension 737
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 3220
Trace bound 1

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Defining parameters

Level: \( N \) = \( 139 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(3220\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(139))\).

Total New Old
Modular forms 874 874 0
Cusp forms 737 737 0
Eisenstein series 137 137 0

Trace form

\( 737 q - 66 q^{2} - 65 q^{3} - 62 q^{4} - 63 q^{5} - 57 q^{6} - 61 q^{7} - 54 q^{8} - 56 q^{9} + O(q^{10}) \) \( 737 q - 66 q^{2} - 65 q^{3} - 62 q^{4} - 63 q^{5} - 57 q^{6} - 61 q^{7} - 54 q^{8} - 56 q^{9} - 51 q^{10} - 57 q^{11} - 41 q^{12} - 55 q^{13} - 45 q^{14} - 45 q^{15} - 38 q^{16} - 51 q^{17} - 30 q^{18} - 49 q^{19} - 27 q^{20} - 37 q^{21} - 33 q^{22} - 45 q^{23} - 9 q^{24} - 38 q^{25} - 27 q^{26} - 29 q^{27} - 13 q^{28} - 39 q^{29} + 3 q^{30} - 37 q^{31} - 6 q^{32} - 21 q^{33} - 15 q^{34} - 21 q^{35} + 22 q^{36} - 31 q^{37} - 9 q^{38} - 13 q^{39} + 21 q^{40} - 27 q^{41} + 27 q^{42} - 25 q^{43} + 15 q^{44} + 9 q^{45} + 3 q^{46} - 21 q^{47} + 55 q^{48} - 12 q^{49} + 24 q^{50} + 3 q^{51} + 29 q^{52} - 15 q^{53} + 51 q^{54} + 3 q^{55} + 51 q^{56} + 11 q^{57} + 21 q^{58} - 9 q^{59} + 99 q^{60} - 7 q^{61} + 27 q^{62} + 35 q^{63} + 58 q^{64} + 15 q^{65} + 75 q^{66} - q^{67} + 57 q^{68} + 27 q^{69} + 75 q^{70} + 3 q^{71} + 126 q^{72} + 5 q^{73} + 45 q^{74} + 55 q^{75} + 71 q^{76} + 27 q^{77} + 99 q^{78} + 11 q^{79} + 117 q^{80} + 52 q^{81} + 57 q^{82} + 15 q^{83} + 155 q^{84} + 39 q^{85} + 63 q^{86} + 51 q^{87} + 111 q^{88} + 21 q^{89} + 165 q^{90} + 43 q^{91} + 99 q^{92} + 59 q^{93} + 75 q^{94} + 51 q^{95} + 183 q^{96} + 29 q^{97} + 102 q^{98} + 87 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(139))\)

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
139.2.a \(\chi_{139}(1, \cdot)\) 139.2.a.a 1 1
139.2.a.b 3
139.2.a.c 7
139.2.c \(\chi_{139}(42, \cdot)\) 139.2.c.a 22 2
139.2.e \(\chi_{139}(6, \cdot)\) 139.2.e.a 220 22
139.2.g \(\chi_{139}(4, \cdot)\) 139.2.g.a 484 44