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Properties

Label 27.6
Level 27
Weight 6
Dimension 99
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 324
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(324\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(27))\).

Total New Old
Modular forms 150 115 35
Cusp forms 120 99 21
Eisenstein series 30 16 14

Trace form

\( 99 q - 9 q^{2} - 6 q^{3} + 63 q^{4} - 171 q^{5} - 126 q^{6} + 129 q^{7} + 1323 q^{8} + 324 q^{9} + O(q^{10}) \) \( 99 q - 9 q^{2} - 6 q^{3} + 63 q^{4} - 171 q^{5} - 126 q^{6} + 129 q^{7} + 1323 q^{8} + 324 q^{9} + 39 q^{10} - 333 q^{11} - 2769 q^{12} - 2841 q^{13} - 3033 q^{14} + 1989 q^{15} + 6051 q^{16} + 7821 q^{17} - 99 q^{18} + 1134 q^{19} + 3303 q^{20} + 5424 q^{21} - 13269 q^{22} - 16560 q^{23} - 18486 q^{24} + 8820 q^{25} + 17082 q^{26} - 8109 q^{27} - 12726 q^{28} - 32436 q^{29} - 6453 q^{30} - 10977 q^{31} + 42489 q^{32} + 50634 q^{33} + 28971 q^{34} + 52092 q^{35} - 3600 q^{36} + 19170 q^{37} - 32931 q^{38} - 13971 q^{39} - 12477 q^{40} - 80325 q^{41} - 64422 q^{42} - 17133 q^{43} + 61227 q^{44} + 92493 q^{45} + 4089 q^{46} + 103617 q^{47} + 134049 q^{48} + 46860 q^{49} - 48456 q^{50} - 124866 q^{51} - 85881 q^{52} - 227358 q^{53} - 350946 q^{54} - 39444 q^{55} - 86067 q^{56} + 67767 q^{57} + 141963 q^{58} + 114408 q^{59} + 241290 q^{60} - 154869 q^{61} + 4302 q^{62} + 135981 q^{63} - 50607 q^{64} - 6669 q^{65} - 32931 q^{66} + 107814 q^{67} + 75024 q^{68} + 25263 q^{69} + 442059 q^{70} + 351387 q^{71} + 441684 q^{72} + 122679 q^{73} + 394011 q^{74} + 18399 q^{75} - 217737 q^{76} - 384669 q^{77} - 520974 q^{78} - 531033 q^{79} - 1048626 q^{80} - 428616 q^{81} - 360582 q^{82} - 488097 q^{83} - 522390 q^{84} - 235647 q^{85} + 132597 q^{86} + 304173 q^{87} + 750459 q^{88} + 606555 q^{89} + 327366 q^{90} + 309345 q^{91} + 1145025 q^{92} + 890079 q^{93} + 376791 q^{94} + 792783 q^{95} + 1165698 q^{96} - 189258 q^{97} + 405756 q^{98} - 28323 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)

We only show spaces with even 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
27.6.a \(\chi_{27}(1, \cdot)\) 27.6.a.a 1 1
27.6.a.b 2
27.6.a.c 2
27.6.a.d 2
27.6.c \(\chi_{27}(10, \cdot)\) 27.6.c.a 8 2
27.6.e \(\chi_{27}(4, \cdot)\) 27.6.e.a 84 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)