## Defining parameters

 Level: $$N$$ = $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$12$$ Sturm bound: $$2916$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(162))$$.

Total New Old
Modular forms 837 192 645
Cusp forms 622 192 430
Eisenstein series 215 0 215

## Trace form

 $$192q + 6q^{5} + 6q^{7} + 3q^{8} + O(q^{10})$$ $$192q + 6q^{5} + 6q^{7} + 3q^{8} + 6q^{10} + 15q^{11} + 12q^{13} + 6q^{14} + 12q^{17} - 9q^{18} - 18q^{19} - 30q^{20} - 54q^{21} - 21q^{22} - 78q^{23} - 36q^{25} - 90q^{26} - 54q^{27} - 24q^{28} - 84q^{29} - 54q^{30} - 36q^{31} - 54q^{33} - 15q^{34} - 60q^{35} - 18q^{36} - 6q^{37} + 3q^{38} + 6q^{40} - 3q^{41} + 9q^{43} + 6q^{44} - 54q^{45} + 12q^{46} - 54q^{47} - 12q^{49} + 36q^{50} - 63q^{51} + 12q^{52} - 30q^{53} - 36q^{55} + 6q^{56} - 54q^{57} + 24q^{58} - 69q^{59} - 18q^{61} + 24q^{62} - 54q^{63} + 3q^{64} + 12q^{65} + 72q^{66} - 45q^{67} + 30q^{68} + 126q^{69} - 24q^{70} + 120q^{71} + 72q^{72} + 42q^{73} + 114q^{74} + 180q^{75} - 15q^{76} + 246q^{77} + 144q^{78} - 60q^{79} + 24q^{80} + 144q^{81} + 6q^{82} + 144q^{83} + 36q^{84} - 36q^{85} + 117q^{86} + 288q^{87} - 21q^{88} + 174q^{89} + 144q^{90} + 30q^{91} + 66q^{92} + 126q^{93} - 18q^{94} + 84q^{95} + 18q^{96} - 15q^{97} + 87q^{98} + 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$

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
162.2.a $$\chi_{162}(1, \cdot)$$ 162.2.a.a 1 1
162.2.a.b 1
162.2.a.c 1
162.2.a.d 1
162.2.c $$\chi_{162}(55, \cdot)$$ 162.2.c.a 2 2
162.2.c.b 2
162.2.c.c 2
162.2.c.d 2
162.2.e $$\chi_{162}(19, \cdot)$$ 162.2.e.a 6 6
162.2.e.b 12
162.2.g $$\chi_{162}(7, \cdot)$$ 162.2.g.a 72 18
162.2.g.b 90

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(162))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(162)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 2}$$