Properties

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

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 6 \)
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

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

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 the 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

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