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Properties

Label 81.5
Level 81
Weight 5
Dimension 740
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 2430
Trace bound 1

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Defining parameters

Level: \( N \) = \( 81 = 3^{4} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(2430\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(81))\).

Total New Old
Modular forms 1026 796 230
Cusp forms 918 740 178
Eisenstein series 108 56 52

Trace form

\( 740 q - 12 q^{2} - 18 q^{3} - 4 q^{4} - 21 q^{5} - 18 q^{6} - 59 q^{7} - 9 q^{8} - 18 q^{9} + O(q^{10}) \) \( 740 q - 12 q^{2} - 18 q^{3} - 4 q^{4} - 21 q^{5} - 18 q^{6} - 59 q^{7} - 9 q^{8} - 18 q^{9} + 195 q^{10} + 474 q^{11} - 18 q^{12} - 245 q^{13} - 1155 q^{14} - 18 q^{15} - 760 q^{16} - 9 q^{17} - 2034 q^{18} - 545 q^{19} + 3333 q^{20} + 2277 q^{21} + 3504 q^{22} + 5703 q^{23} + 4734 q^{24} + 962 q^{25} - 27 q^{26} - 1449 q^{27} - 6089 q^{28} - 9003 q^{29} - 9522 q^{30} - 6113 q^{31} - 19314 q^{32} - 3231 q^{33} - 90 q^{34} + 5337 q^{35} + 10062 q^{36} + 7645 q^{37} + 13890 q^{38} - 18 q^{39} - 2229 q^{40} - 19164 q^{41} - 18333 q^{42} - 1868 q^{43} + 9063 q^{44} + 11214 q^{45} + 19959 q^{46} + 27933 q^{47} + 35127 q^{48} + 18504 q^{49} + 66900 q^{50} + 12330 q^{51} + 11125 q^{52} - 27 q^{53} - 13500 q^{54} - 19893 q^{55} - 78051 q^{56} - 21186 q^{57} - 34305 q^{58} - 55776 q^{59} - 58167 q^{60} - 24557 q^{61} - 76635 q^{62} - 14058 q^{63} - 12103 q^{64} + 36627 q^{65} + 99126 q^{66} + 2230 q^{67} + 115686 q^{68} + 20502 q^{69} + 40665 q^{70} - 19773 q^{71} - 138258 q^{72} + 16906 q^{73} - 21939 q^{74} - 56268 q^{75} + 55522 q^{76} - 28749 q^{77} - 44523 q^{78} + 7501 q^{79} + 11574 q^{81} - 11658 q^{82} + 15081 q^{83} + 153927 q^{84} - 52641 q^{85} + 21012 q^{86} + 125982 q^{87} - 133356 q^{88} - 102636 q^{89} - 1557 q^{90} - 62278 q^{91} - 25233 q^{92} + 3294 q^{93} + 33105 q^{94} + 86961 q^{95} - 37665 q^{96} + 119038 q^{97} + 271017 q^{98} + 4266 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.5.b \(\chi_{81}(80, \cdot)\) 81.5.b.a 6 1
81.5.b.b 8
81.5.d \(\chi_{81}(26, \cdot)\) 81.5.d.a 2 2
81.5.d.b 4
81.5.d.c 4
81.5.d.d 4
81.5.d.e 16
81.5.f \(\chi_{81}(8, \cdot)\) 81.5.f.a 66 6
81.5.h \(\chi_{81}(2, \cdot)\) 81.5.h.a 630 18

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)