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Properties

Label 81.11
Level 81
Weight 11
Dimension 1892
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 5346
Trace bound 1

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Defining parameters

Level: \( N \) = \( 81 = 3^{4} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(5346\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(81))\).

Total New Old
Modular forms 2484 1948 536
Cusp forms 2376 1892 484
Eisenstein series 108 56 52

Trace form

\( 1892 q - 12 q^{2} - 18 q^{3} + 1004 q^{4} + 4947 q^{5} - 18 q^{6} + 18337 q^{7} - 9 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1892 q - 12 q^{2} - 18 q^{3} + 1004 q^{4} + 4947 q^{5} - 18 q^{6} + 18337 q^{7} - 9 q^{8} - 18 q^{9} + 17187 q^{10} + 960 q^{11} - 18 q^{12} - 712181 q^{13} - 2134587 q^{14} - 18 q^{15} + 1956344 q^{16} - 9 q^{17} + 3053934 q^{18} - 3745733 q^{19} - 46393467 q^{20} + 14086557 q^{21} + 33892032 q^{22} - 6931029 q^{23} - 79322130 q^{24} - 27912934 q^{25} - 27 q^{26} + 61523235 q^{27} + 190437367 q^{28} + 25742193 q^{29} - 144526482 q^{30} - 154233893 q^{31} - 317694834 q^{32} + 61477713 q^{33} + 251791974 q^{34} + 520307217 q^{35} - 271411218 q^{36} - 526087535 q^{37} + 120372114 q^{38} - 18 q^{39} + 168528387 q^{40} + 1222884114 q^{41} + 1118151027 q^{42} - 404150522 q^{43} - 4491812889 q^{44} - 194789250 q^{45} + 1589369271 q^{46} + 3661443069 q^{47} + 2041031007 q^{48} - 656783208 q^{49} - 7012404852 q^{50} - 3031812648 q^{51} - 822306851 q^{52} - 27 q^{53} + 4967777412 q^{54} + 3396434883 q^{55} + 12794508285 q^{56} + 1983447846 q^{57} - 802607505 q^{58} - 6678457878 q^{59} - 13162246479 q^{60} - 2018236289 q^{61} - 5573260251 q^{62} + 4406834682 q^{63} + 4132074233 q^{64} + 4795212651 q^{65} - 15147331146 q^{66} - 3871566488 q^{67} + 2194666830 q^{68} + 19837801782 q^{69} + 8759418537 q^{70} - 5512912173 q^{71} - 54775775250 q^{72} - 9027925970 q^{73} - 38195041227 q^{74} + 5449218732 q^{75} - 10312354430 q^{76} + 47299182315 q^{77} + 42944779773 q^{78} - 1384385387 q^{79} - 14741418186 q^{81} - 19175616714 q^{82} - 39122387463 q^{83} - 95272080417 q^{84} + 13829998491 q^{85} + 44980429524 q^{86} + 53793420894 q^{87} - 29339866812 q^{88} + 19001697408 q^{89} + 158245888851 q^{90} + 9984104894 q^{91} - 170203518609 q^{92} - 154074907782 q^{93} - 9413825703 q^{94} - 78776198115 q^{95} + 60611267655 q^{96} + 46328701684 q^{97} + 422764606521 q^{98} + 80391149946 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.11.b \(\chi_{81}(80, \cdot)\) 81.11.b.a 18 1
81.11.b.b 20
81.11.d \(\chi_{81}(26, \cdot)\) 81.11.d.a 2 2
81.11.d.b 2
81.11.d.c 2
81.11.d.d 4
81.11.d.e 8
81.11.d.f 8
81.11.d.g 12
81.11.d.h 40
81.11.f \(\chi_{81}(8, \cdot)\) 81.11.f.a 174 6
81.11.h \(\chi_{81}(2, \cdot)\) 81.11.h.a 1602 18

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)