Properties

Label 27.9
Level 27
Weight 9
Dimension 163
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 486
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(486\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(27))\).

Total New Old
Modular forms 231 179 52
Cusp forms 201 163 38
Eisenstein series 30 16 14

Trace form

\( 163 q - 3 q^{2} - 6 q^{3} - 1013 q^{4} - 885 q^{5} - 774 q^{6} + 2033 q^{7} - 9 q^{8} - 12960 q^{9} + O(q^{10}) \) \( 163 q - 3 q^{2} - 6 q^{3} - 1013 q^{4} - 885 q^{5} - 774 q^{6} + 2033 q^{7} - 9 q^{8} - 12960 q^{9} - 12453 q^{10} + 57345 q^{11} + 77421 q^{12} - 52675 q^{13} - 241941 q^{14} + 105507 q^{15} + 329059 q^{16} - 9 q^{17} - 241317 q^{18} - 177442 q^{19} - 401541 q^{20} + 1164372 q^{21} + 823155 q^{22} + 1068828 q^{23} - 2624256 q^{24} - 840593 q^{25} + 3500568 q^{27} - 2074966 q^{28} - 4741662 q^{29} - 1533627 q^{30} + 1381403 q^{31} + 5456745 q^{32} - 1245285 q^{33} + 7714791 q^{34} + 6225408 q^{35} + 4021128 q^{36} - 13483924 q^{37} - 34684575 q^{38} - 5699685 q^{39} + 8769291 q^{40} + 26933829 q^{41} + 1594134 q^{42} + 19602071 q^{43} + 17341119 q^{44} + 12986721 q^{45} - 32584659 q^{46} - 42490497 q^{47} - 26229183 q^{48} + 15314877 q^{49} + 22900476 q^{50} - 16497396 q^{51} + 45478487 q^{52} + 34106454 q^{54} - 50703990 q^{55} - 64422903 q^{56} + 26766582 q^{57} + 61379655 q^{58} + 159610533 q^{59} - 24031170 q^{60} + 7491869 q^{61} - 223709616 q^{62} - 149069421 q^{63} - 14277131 q^{64} - 48836955 q^{65} + 83336805 q^{66} - 18274048 q^{67} + 179668170 q^{68} + 38038563 q^{69} + 285619155 q^{70} + 125718795 q^{71} + 183269700 q^{72} - 11169475 q^{73} - 56260437 q^{74} - 167459145 q^{75} - 440936209 q^{76} - 399427869 q^{77} - 344470788 q^{78} - 99525565 q^{79} + 151392924 q^{81} + 188410710 q^{82} + 582160659 q^{83} + 836800692 q^{84} + 195550857 q^{85} - 74763939 q^{86} - 145695735 q^{87} - 476974005 q^{88} + 135692730 q^{89} - 821329020 q^{90} - 91011095 q^{91} - 1047793371 q^{92} - 414573177 q^{93} - 40223361 q^{94} + 494286159 q^{95} + 1578184830 q^{96} + 178475174 q^{97} + 1293135102 q^{98} + 228876057 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(27))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
27.9.b \(\chi_{27}(26, \cdot)\) 27.9.b.a 1 1
27.9.b.b 2
27.9.b.c 2
27.9.b.d 6
27.9.d \(\chi_{27}(8, \cdot)\) 27.9.d.a 14 2
27.9.f \(\chi_{27}(2, \cdot)\) 27.9.f.a 138 6

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

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