Properties

Label 27.2
Level 27
Weight 2
Dimension 13
Nonzero newspaces 2
Newforms 2
Sturm bound 108
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(27))\).

Total New Old
Modular forms 42 29 13
Cusp forms 13 13 0
Eisenstein series 29 16 13

Trace form

\(13q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 15q^{14} \) \(\mathstrut +\mathstrut 9q^{15} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 30q^{26} \) \(\mathstrut -\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 9q^{30} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut +\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 18q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 42q^{38} \) \(\mathstrut +\mathstrut 33q^{39} \) \(\mathstrut +\mathstrut 21q^{40} \) \(\mathstrut +\mathstrut 15q^{41} \) \(\mathstrut +\mathstrut 18q^{42} \) \(\mathstrut +\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut 9q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut -\mathstrut 15q^{48} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 33q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 54q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut -\mathstrut 3q^{57} \) \(\mathstrut +\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 11q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 10q^{67} \) \(\mathstrut +\mathstrut 9q^{68} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 27q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut +\mathstrut 33q^{74} \) \(\mathstrut +\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 18q^{78} \) \(\mathstrut -\mathstrut 25q^{79} \) \(\mathstrut +\mathstrut 42q^{80} \) \(\mathstrut +\mathstrut 36q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 39q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 51q^{86} \) \(\mathstrut +\mathstrut 9q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut +\mathstrut 18q^{90} \) \(\mathstrut +\mathstrut q^{91} \) \(\mathstrut -\mathstrut 39q^{92} \) \(\mathstrut -\mathstrut 39q^{93} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut -\mathstrut 45q^{98} \) \(\mathstrut -\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.2.a \(\chi_{27}(1, \cdot)\) 27.2.a.a 1 1
27.2.c \(\chi_{27}(10, \cdot)\) None 0 2
27.2.e \(\chi_{27}(4, \cdot)\) 27.2.e.a 12 6