## 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

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

## 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