Properties

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

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
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

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

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

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