## Defining parameters

 Level: $$N$$ = $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(18))$$.

Total New Old
Modular forms 17 2 15
Cusp forms 2 2 0
Eisenstein series 15 0 15

## Trace form

 $$2q - q^{2} - 3q^{3} - q^{4} + 3q^{6} - 2q^{7} + 2q^{8} + 3q^{9} + O(q^{10})$$ $$2q - q^{2} - 3q^{3} - q^{4} + 3q^{6} - 2q^{7} + 2q^{8} + 3q^{9} + 3q^{11} - 2q^{13} - 2q^{14} - q^{16} - 6q^{17} - 6q^{18} - 2q^{19} + 6q^{21} + 3q^{22} + 6q^{23} - 3q^{24} + 5q^{25} + 4q^{26} + 4q^{28} - 6q^{29} + 4q^{31} - q^{32} - 9q^{33} + 3q^{34} + 3q^{36} - 8q^{37} + q^{38} - 9q^{41} + q^{43} - 6q^{44} - 12q^{46} + 6q^{47} + 3q^{48} + 3q^{49} + 5q^{50} + 9q^{51} - 2q^{52} + 24q^{53} + 9q^{54} - 2q^{56} + 3q^{57} - 6q^{58} - 3q^{59} - 8q^{61} - 8q^{62} - 12q^{63} + 2q^{64} - 5q^{67} + 3q^{68} - 24q^{71} + 3q^{72} + 22q^{73} + 4q^{74} - 15q^{75} + q^{76} + 6q^{77} - 6q^{78} + 4q^{79} - 9q^{81} + 18q^{82} - 12q^{83} - 6q^{84} + q^{86} + 18q^{87} + 3q^{88} + 12q^{89} + 8q^{91} + 6q^{92} + 6q^{94} - 5q^{97} - 6q^{98} + 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$

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
18.2.a $$\chi_{18}(1, \cdot)$$ None 0 1
18.2.c $$\chi_{18}(7, \cdot)$$ 18.2.c.a 2 2