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Properties

Label 81.7
Level 81
Weight 7
Dimension 1124
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 3402
Trace bound 1

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Defining parameters

Level: \( N \) = \( 81 = 3^{4} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(3402\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(81))\).

Total New Old
Modular forms 1512 1180 332
Cusp forms 1404 1124 280
Eisenstein series 108 56 52

Trace form

\( 1124 q - 12 q^{2} - 18 q^{3} + 44 q^{4} - 228 q^{5} - 18 q^{6} + 340 q^{7} - 9 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1124 q - 12 q^{2} - 18 q^{3} + 44 q^{4} - 228 q^{5} - 18 q^{6} + 340 q^{7} - 9 q^{8} - 18 q^{9} - 1773 q^{10} + 474 q^{11} - 18 q^{12} + 844 q^{13} + 12165 q^{14} - 18 q^{15} + 3896 q^{16} - 9 q^{17} - 33138 q^{18} + 10591 q^{19} + 102693 q^{20} + 20502 q^{21} - 17712 q^{22} - 82524 q^{23} - 146898 q^{24} - 1099 q^{25} - 27 q^{26} + 56142 q^{27} + 114487 q^{28} + 172032 q^{29} + 223758 q^{30} + 98260 q^{31} + 62766 q^{32} - 151218 q^{33} - 139914 q^{34} - 536553 q^{35} - 184338 q^{36} - 47513 q^{37} + 314994 q^{38} - 18 q^{39} - 29133 q^{40} - 702174 q^{41} + 195507 q^{42} + 542662 q^{43} + 2445543 q^{44} + 582750 q^{45} + 167895 q^{46} - 891336 q^{47} - 1354833 q^{48} - 916653 q^{49} - 3739812 q^{50} - 882396 q^{51} - 670259 q^{52} - 27 q^{53} + 1075140 q^{54} + 1463733 q^{55} + 5993277 q^{56} + 1372662 q^{57} + 1685151 q^{58} + 1456638 q^{59} + 1180161 q^{60} - 604352 q^{61} - 3555099 q^{62} - 1778238 q^{63} - 3812167 q^{64} - 2283564 q^{65} - 3057930 q^{66} + 1274542 q^{67} - 690210 q^{68} - 902898 q^{69} + 2633337 q^{70} - 427689 q^{71} + 2101230 q^{72} + 822535 q^{73} + 3648549 q^{74} + 4499982 q^{75} - 5679038 q^{76} + 1061844 q^{77} + 4895181 q^{78} - 2346176 q^{79} - 1393938 q^{81} + 2770614 q^{82} + 1090248 q^{83} - 16169841 q^{84} + 4499361 q^{85} - 2889660 q^{86} - 8120466 q^{87} - 98172 q^{88} - 13622589 q^{89} - 1601469 q^{90} + 1736321 q^{91} + 26236047 q^{92} + 18596682 q^{93} + 583065 q^{94} + 19557165 q^{95} + 15695127 q^{96} + 532618 q^{97} - 15538887 q^{98} - 18515250 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.7.b \(\chi_{81}(80, \cdot)\) 81.7.b.a 10 1
81.7.b.b 12
81.7.d \(\chi_{81}(26, \cdot)\) 81.7.d.a 2 2
81.7.d.b 4
81.7.d.c 4
81.7.d.d 4
81.7.d.e 8
81.7.d.f 24
81.7.f \(\chi_{81}(8, \cdot)\) 81.7.f.a 102 6
81.7.h \(\chi_{81}(2, \cdot)\) 81.7.h.a 954 18

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 1}\)