## 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

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

## 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