## Defining parameters

 Level: $$N$$ = $$27 = 3^{3}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ 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

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

## 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