Properties

Label 27.3
Level 27
Weight 3
Dimension 35
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 162
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(162\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(27))\).

Total New Old
Modular forms 69 51 18
Cusp forms 39 35 4
Eisenstein series 30 16 14

Trace form

\( 35 q - 3 q^{2} - 6 q^{3} - 13 q^{4} - 21 q^{5} - 18 q^{6} - 11 q^{7} - 9 q^{8} + O(q^{10}) \) \( 35 q - 3 q^{2} - 6 q^{3} - 13 q^{4} - 21 q^{5} - 18 q^{6} - 11 q^{7} - 9 q^{8} + 3 q^{10} - 3 q^{11} - 15 q^{12} - 23 q^{13} - 21 q^{14} - 9 q^{15} - 13 q^{16} - 9 q^{17} + 63 q^{18} - 2 q^{19} + 219 q^{20} + 132 q^{21} + 51 q^{22} + 168 q^{23} + 144 q^{24} + 29 q^{25} - 90 q^{27} - 110 q^{28} - 246 q^{29} - 243 q^{30} - 41 q^{31} - 387 q^{32} - 207 q^{33} - 81 q^{34} - 252 q^{35} - 360 q^{36} + 16 q^{37} - 51 q^{38} + 15 q^{39} - 21 q^{40} + 249 q^{41} + 486 q^{42} + 43 q^{43} + 639 q^{44} + 477 q^{45} + 165 q^{46} + 483 q^{47} + 453 q^{48} + 39 q^{49} + 264 q^{50} + 36 q^{51} + 91 q^{52} - 54 q^{54} - 114 q^{55} - 363 q^{56} - 192 q^{57} - 129 q^{58} - 561 q^{59} - 846 q^{60} - 191 q^{61} - 900 q^{62} - 585 q^{63} + 53 q^{64} - 435 q^{65} - 423 q^{66} + 256 q^{67} + 126 q^{68} + 99 q^{69} + 591 q^{70} + 315 q^{71} + 720 q^{72} + 97 q^{73} + 219 q^{74} + 255 q^{75} + 451 q^{76} + 195 q^{77} + 180 q^{78} + 151 q^{79} + 36 q^{81} - 330 q^{82} + 51 q^{83} - 588 q^{84} - 207 q^{85} - 75 q^{86} - 279 q^{87} - 717 q^{88} + 72 q^{89} + 288 q^{90} - 7 q^{91} - 51 q^{92} + 591 q^{93} - 741 q^{94} + 615 q^{95} + 270 q^{96} - 470 q^{97} + 882 q^{98} + 513 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.3.b \(\chi_{27}(26, \cdot)\) 27.3.b.a 1 1
27.3.b.b 2
27.3.d \(\chi_{27}(8, \cdot)\) 27.3.d.a 2 2
27.3.f \(\chi_{27}(2, \cdot)\) 27.3.f.a 30 6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

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