## Defining parameters

 Level: $$N$$ = $$19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$60$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(19))$$.

Total New Old
Modular forms 24 24 0
Cusp forms 7 7 0
Eisenstein series 17 17 0

## Trace form

 $$7q - 6q^{2} - 5q^{3} - 2q^{4} - 3q^{5} + 3q^{6} - q^{7} + 6q^{8} + 4q^{9} + O(q^{10})$$ $$7q - 6q^{2} - 5q^{3} - 2q^{4} - 3q^{5} + 3q^{6} - q^{7} + 6q^{8} + 4q^{9} + 9q^{10} + 3q^{11} + 7q^{12} - 7q^{13} - 3q^{14} - 3q^{15} - 14q^{16} - 6q^{18} - 11q^{19} - 12q^{20} + 2q^{21} + 6q^{23} + 15q^{24} + 4q^{25} + 15q^{26} + 10q^{27} + 8q^{28} + 3q^{29} + 5q^{31} + 9q^{32} - 15q^{33} + 3q^{35} - 26q^{36} + 2q^{37} - 15q^{38} - 16q^{39} + 15q^{41} - 3q^{42} - 4q^{43} + 3q^{44} - 12q^{45} - 18q^{46} - 6q^{47} - 11q^{48} + 9q^{49} - 15q^{50} + 9q^{51} + 23q^{52} + 9q^{53} + 30q^{54} + 27q^{55} - 6q^{56} + 22q^{57} + 36q^{58} + 6q^{59} + 6q^{60} - 13q^{61} - 12q^{62} + 11q^{63} - 20q^{64} - 24q^{65} - 9q^{66} - 34q^{67} - 9q^{68} - 12q^{69} - 9q^{70} - 12q^{72} - 19q^{73} + 15q^{74} + 22q^{75} + 34q^{76} - 21q^{77} + 15q^{78} - 31q^{79} + 15q^{80} - 5q^{81} - 54q^{82} + 12q^{83} - q^{84} - 9q^{85} + 24q^{86} - 33q^{87} + 9q^{88} + 18q^{90} + 19q^{91} + 42q^{92} + 17q^{93} + 18q^{94} + 42q^{95} + 18q^{96} + 26q^{97} - 9q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$

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
19.2.a $$\chi_{19}(1, \cdot)$$ 19.2.a.a 1 1
19.2.c $$\chi_{19}(7, \cdot)$$ None 0 2
19.2.e $$\chi_{19}(4, \cdot)$$ 19.2.e.a 6 6