## Defining parameters

 Level: $$N$$ = $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$54$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(18))$$.

Total New Old
Modular forms 26 6 20
Cusp forms 10 6 4
Eisenstein series 16 0 16

## Trace form

 $$6q - 18q^{5} - 12q^{6} - 6q^{7} + 12q^{9} + O(q^{10})$$ $$6q - 18q^{5} - 12q^{6} - 6q^{7} + 12q^{9} + 12q^{10} + 18q^{11} + 12q^{12} + 6q^{13} + 36q^{14} + 18q^{15} - 24q^{18} - 72q^{19} - 36q^{20} - 42q^{21} - 60q^{22} + 18q^{23} + 18q^{25} + 24q^{28} + 18q^{29} + 72q^{30} + 126q^{31} + 54q^{33} + 60q^{34} + 12q^{36} + 60q^{37} - 72q^{38} - 102q^{39} - 24q^{40} - 126q^{41} - 48q^{42} - 126q^{43} - 54q^{45} + 24q^{46} + 54q^{47} + 24q^{48} - 78q^{49} - 72q^{51} - 12q^{52} + 36q^{54} + 36q^{55} + 72q^{56} + 144q^{57} + 12q^{58} + 126q^{59} - 36q^{60} + 162q^{61} + 222q^{63} - 48q^{64} + 90q^{65} - 72q^{66} - 90q^{67} + 72q^{68} + 18q^{69} - 156q^{70} - 96q^{72} - 240q^{73} + 72q^{74} - 12q^{75} + 24q^{76} - 90q^{77} + 144q^{78} - 138q^{79} - 252q^{81} + 12q^{82} - 378q^{83} - 144q^{84} - 108q^{86} - 54q^{87} + 120q^{88} + 348q^{91} + 36q^{92} + 222q^{93} + 324q^{94} + 180q^{95} + 48q^{96} + 366q^{97} + 126q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$

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
18.3.b $$\chi_{18}(17, \cdot)$$ 18.3.b.a 2 1
18.3.d $$\chi_{18}(5, \cdot)$$ 18.3.d.a 4 2

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(18))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(18)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$