## Defining parameters

 Level: $$N$$ = $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(20))$$.

Total New Old
Modular forms 22 11 11
Cusp forms 3 3 0
Eisenstein series 19 8 11

## Trace form

 $$3q - 2q^{2} - 2q^{3} - 5q^{5} + 2q^{7} + 4q^{8} + q^{9} + O(q^{10})$$ $$3q - 2q^{2} - 2q^{3} - 5q^{5} + 2q^{7} + 4q^{8} + q^{9} + 6q^{10} + 2q^{15} - 8q^{16} - 6q^{18} - 4q^{19} - 4q^{20} - 4q^{21} + 6q^{23} + 7q^{25} + 4q^{26} + 4q^{27} + 6q^{29} - 4q^{31} + 8q^{32} - 2q^{35} + 12q^{36} - 12q^{37} - 4q^{39} - 4q^{40} - 10q^{41} - 10q^{43} + 5q^{45} - 6q^{47} - 3q^{49} - 14q^{50} + 12q^{51} - 4q^{52} + 12q^{53} + 8q^{57} + 8q^{58} + 12q^{59} + 26q^{61} + 2q^{63} + 2q^{67} - 12q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 20q^{73} - 2q^{75} + 8q^{79} + 16q^{80} - 29q^{81} + 16q^{82} + 6q^{83} - 12q^{85} - 12q^{87} - 6q^{89} + 6q^{90} + 4q^{91} + 8q^{93} + 4q^{95} + 28q^{97} + 14q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$

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
20.2.a $$\chi_{20}(1, \cdot)$$ 20.2.a.a 1 1
20.2.c $$\chi_{20}(9, \cdot)$$ None 0 1
20.2.e $$\chi_{20}(3, \cdot)$$ 20.2.e.a 2 2