↑

Properties

Label 71.2
Level 71
Weight 2
Dimension 176
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 840
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 71 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(71))\).

Total New Old
Modular forms 245 245 0
Cusp forms 176 176 0
Eisenstein series 69 69 0

Trace form

\( 176 q - 32 q^{2} - 31 q^{3} - 28 q^{4} - 29 q^{5} - 23 q^{6} - 27 q^{7} - 20 q^{8} - 22 q^{9} + O(q^{10}) \) \( 176 q - 32 q^{2} - 31 q^{3} - 28 q^{4} - 29 q^{5} - 23 q^{6} - 27 q^{7} - 20 q^{8} - 22 q^{9} - 17 q^{10} - 23 q^{11} - 7 q^{12} - 21 q^{13} - 11 q^{14} - 11 q^{15} - 4 q^{16} - 17 q^{17} + 4 q^{18} - 15 q^{19} + 7 q^{20} - 3 q^{21} + q^{22} - 11 q^{23} + 25 q^{24} - 4 q^{25} + 7 q^{26} + 5 q^{27} + 21 q^{28} - 5 q^{29} + 37 q^{30} - 3 q^{31} + 28 q^{32} + 13 q^{33} + 19 q^{34} + 13 q^{35} + 56 q^{36} + 3 q^{37} + 25 q^{38} + 21 q^{39} + 55 q^{40} + 7 q^{41} + 61 q^{42} + 9 q^{43} + 49 q^{44} + 43 q^{45} + 37 q^{46} + 13 q^{47} + 89 q^{48} + 22 q^{49} + 58 q^{50} + 37 q^{51} + 63 q^{52} + 19 q^{53} + 85 q^{54} + 37 q^{55} + 15 q^{56} - 60 q^{57} - 15 q^{58} - 45 q^{59} - 147 q^{60} - 8 q^{61} - 79 q^{62} - 71 q^{63} - 188 q^{64} - 21 q^{65} - 171 q^{66} - 107 q^{67} - 49 q^{68} - 114 q^{69} - 66 q^{70} - 69 q^{71} - 365 q^{72} - 66 q^{73} - 61 q^{74} - 86 q^{75} - 35 q^{76} - 79 q^{77} - 147 q^{78} - 25 q^{79} - 129 q^{80} - 54 q^{81} - 49 q^{82} + 14 q^{83} - 91 q^{84} + 3 q^{85} + 27 q^{86} - 20 q^{87} + 75 q^{88} + 55 q^{89} + 199 q^{90} + 77 q^{91} + 133 q^{92} + 93 q^{93} + 109 q^{94} + 85 q^{95} + 217 q^{96} + 63 q^{97} + 136 q^{98} + 121 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(71))\)

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
71.2.a \(\chi_{71}(1, \cdot)\) 71.2.a.a 3 1
71.2.a.b 3
71.2.c \(\chi_{71}(5, \cdot)\) 71.2.c.a 20 4
71.2.d \(\chi_{71}(20, \cdot)\) 71.2.d.a 30 6
71.2.g \(\chi_{71}(2, \cdot)\) 71.2.g.a 120 24