## Defining parameters

 Level: $$N$$ = $$22 = 2 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(22))$$.

Total New Old
Modular forms 25 4 21
Cusp forms 6 4 2
Eisenstein series 19 0 19

## Trace form

 $$4q - q^{2} - 4q^{3} - q^{4} - 6q^{5} + q^{6} + 2q^{7} - q^{8} + 7q^{9} + O(q^{10})$$ $$4q - q^{2} - 4q^{3} - q^{4} - 6q^{5} + q^{6} + 2q^{7} - q^{8} + 7q^{9} + 4q^{10} - q^{11} + 6q^{12} - 4q^{13} + 2q^{14} + 6q^{15} - q^{16} + 2q^{17} - 8q^{18} - 5q^{19} - 6q^{20} - 12q^{21} - 11q^{22} - 4q^{23} + q^{24} + 9q^{25} + 6q^{26} + 5q^{27} + 2q^{28} + 10q^{29} + 6q^{30} - 2q^{31} + 4q^{32} + 11q^{33} + 2q^{34} + 12q^{35} - 8q^{36} - 18q^{37} + 10q^{38} - 6q^{39} + 4q^{40} - 2q^{41} - 2q^{42} + 6q^{43} + 4q^{44} - 28q^{45} - 4q^{46} - 8q^{47} - 4q^{48} + 3q^{49} - 11q^{50} - 7q^{51} + 6q^{52} - 4q^{53} + 4q^{55} - 8q^{56} + 5q^{57} + 10q^{58} + 5q^{59} - 4q^{60} + 8q^{61} - 2q^{62} + 16q^{63} - q^{64} + 16q^{65} + 16q^{66} + 22q^{67} + 2q^{68} + 14q^{69} - 8q^{70} + 8q^{71} + 7q^{72} - 14q^{73} - 18q^{74} - 9q^{75} - 10q^{76} - 8q^{77} - 16q^{78} - 30q^{79} + 4q^{80} + 14q^{81} - 7q^{82} - 19q^{83} + 8q^{84} + 2q^{85} + 21q^{86} - 20q^{87} - q^{88} - 10q^{89} + 12q^{90} - 12q^{91} + 6q^{92} + 2q^{93} + 12q^{94} - 10q^{95} - 4q^{96} - 3q^{97} - 12q^{98} - 13q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$

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
22.2.a $$\chi_{22}(1, \cdot)$$ None 0 1
22.2.c $$\chi_{22}(3, \cdot)$$ 22.2.c.a 4 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(22))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(22)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$