## Defining parameters

 Level: $$N$$ = $$19$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$150$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(19))$$.

Total New Old
Modular forms 69 69 0
Cusp forms 51 51 0
Eisenstein series 18 18 0

## Trace form

 $$51q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} + O(q^{10})$$ $$51q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} - 9q^{10} - 9q^{11} + 855q^{12} - 69q^{13} - 873q^{14} - 1143q^{15} - 2025q^{16} - 306q^{17} + 768q^{19} + 2574q^{20} + 2070q^{21} + 3015q^{22} + 936q^{23} + 2583q^{24} + 117q^{25} - 1737q^{26} + 1215q^{27} + 786q^{28} + 855q^{29} - 4860q^{30} - 2817q^{31} - 8784q^{32} - 10809q^{33} - 7974q^{34} - 4761q^{35} - 6255q^{36} + 4716q^{38} + 7974q^{39} + 13266q^{40} + 4743q^{41} + 26541q^{42} + 14028q^{43} + 30420q^{44} + 20430q^{45} + 7326q^{46} - 4248q^{47} - 33462q^{48} - 17148q^{49} - 51876q^{50} - 29178q^{51} - 23241q^{52} - 10485q^{53} - 10512q^{54} - 3933q^{55} + 5076q^{57} + 8046q^{58} + 14706q^{59} + 72540q^{60} + 48531q^{61} + 54828q^{62} + 29763q^{63} + 28239q^{64} + 3636q^{65} - 10017q^{66} - 37326q^{67} - 44424q^{68} - 54954q^{69} - 90333q^{70} - 51768q^{71} - 100764q^{72} - 30306q^{73} - 10449q^{74} + 13581q^{76} + 47637q^{77} + 97137q^{78} + 65793q^{79} + 73503q^{80} + 64503q^{81} + 100026q^{82} + 16002q^{83} + 11115q^{84} + 21555q^{85} + 4230q^{86} - 37089q^{87} - 69057q^{88} - 34272q^{89} - 102024q^{90} - 75525q^{91} - 106254q^{92} - 87849q^{93} + 91926q^{95} + 172854q^{96} + 50688q^{97} + 94896q^{98} + 60507q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(19))$$

We only show spaces with odd 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
19.5.b $$\chi_{19}(18, \cdot)$$ 19.5.b.a 1 1
19.5.b.b 4
19.5.d $$\chi_{19}(8, \cdot)$$ 19.5.d.a 10 2
19.5.f $$\chi_{19}(2, \cdot)$$ 19.5.f.a 36 6