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Properties

Label 71.5
Level 71
Weight 5
Dimension 805
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 2100
Trace bound 1

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Defining parameters

Level: \( N \) = \( 71 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(2100\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(71))\).

Total New Old
Modular forms 875 875 0
Cusp forms 805 805 0
Eisenstein series 70 70 0

Trace form

\( 805 q - 35 q^{2} - 35 q^{3} - 35 q^{4} - 35 q^{5} - 35 q^{6} - 35 q^{7} - 35 q^{8} - 35 q^{9} + O(q^{10}) \) \( 805 q - 35 q^{2} - 35 q^{3} - 35 q^{4} - 35 q^{5} - 35 q^{6} - 35 q^{7} - 35 q^{8} - 35 q^{9} - 35 q^{10} - 35 q^{11} - 35 q^{12} - 35 q^{13} - 35 q^{14} - 35 q^{15} - 35 q^{16} - 35 q^{17} - 35 q^{18} - 35 q^{19} - 35 q^{20} - 35 q^{21} - 35 q^{22} - 35 q^{23} - 35 q^{24} - 35 q^{25} - 35 q^{26} - 35 q^{27} - 35 q^{28} - 35 q^{29} - 35 q^{30} - 35 q^{31} - 35 q^{32} - 35 q^{33} - 35 q^{34} - 35 q^{35} - 35 q^{36} - 35 q^{37} - 35 q^{38} - 35 q^{39} - 35 q^{40} - 35 q^{41} - 35 q^{42} - 35 q^{43} - 35 q^{44} - 35 q^{45} - 35 q^{46} - 35 q^{47} - 35 q^{48} - 35 q^{49} - 35 q^{50} - 35 q^{51} - 35 q^{52} - 35 q^{53} - 35 q^{54} - 35 q^{55} + 82285 q^{56} + 75040 q^{57} + 23485 q^{58} + 2275 q^{59} - 56035 q^{60} - 12950 q^{61} - 67235 q^{62} - 75495 q^{63} - 154595 q^{64} - 36785 q^{65} - 129955 q^{66} - 52535 q^{67} - 36995 q^{68} - 24010 q^{69} + 14770 q^{71} + 137130 q^{72} + 43120 q^{73} + 73885 q^{74} + 109340 q^{75} + 97405 q^{76} + 102865 q^{77} + 206045 q^{78} + 48475 q^{79} + 167965 q^{80} + 63105 q^{81} + 33565 q^{82} - 1400 q^{83} - 109795 q^{84} - 57785 q^{85} - 94115 q^{86} - 205310 q^{87} - 186515 q^{88} - 35 q^{89} - 35 q^{90} - 35 q^{91} - 35 q^{92} - 35 q^{93} - 35 q^{94} - 35 q^{95} - 35 q^{96} - 35 q^{97} - 35 q^{98} - 35 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(71))\)

We only show spaces with odd 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
71.5.b \(\chi_{71}(70, \cdot)\) 71.5.b.a 7 1
71.5.b.b 16
71.5.e \(\chi_{71}(14, \cdot)\) 71.5.e.a 92 4
71.5.f \(\chi_{71}(23, \cdot)\) 71.5.f.a 138 6
71.5.h \(\chi_{71}(7, \cdot)\) 71.5.h.a 552 24