## 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

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

## 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