## Defining parameters

 Level: $$N$$ = $$19$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$3$$ Newform subspaces: $$6$$ Sturm bound: $$180$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(19))$$.

Total New Old
Modular forms 84 82 2
Cusp forms 66 66 0
Eisenstein series 18 16 2

## Trace form

 $$66q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} + O(q^{10})$$ $$66q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} - 9q^{10} - 9q^{11} - 1737q^{12} + 2163q^{13} + 3951q^{14} + 1773q^{15} - 2889q^{16} - 2160q^{17} - 8766q^{18} - 6414q^{19} - 6354q^{20} + 936q^{21} + 8523q^{22} + 5130q^{23} + 25911q^{24} + 11673q^{25} + 3951q^{26} - 32418q^{27} - 43224q^{28} + 11349q^{29} + 69858q^{30} + 19629q^{31} + 33786q^{32} + 12897q^{33} - 14364q^{34} - 29565q^{35} - 107307q^{36} - 24660q^{37} - 83862q^{38} - 57744q^{39} - 38160q^{40} + 549q^{41} + 68481q^{42} + 28128q^{43} - 3042q^{44} + 127080q^{45} + 173160q^{46} + 105606q^{47} + 207576q^{48} + 14970q^{49} - 38718q^{50} - 72315q^{51} - 30633q^{52} - 52533q^{53} - 125532q^{54} - 103005q^{55} - 338706q^{56} - 138564q^{57} - 96642q^{58} - 88614q^{59} - 354654q^{60} - 179835q^{61} + 40320q^{62} + 224595q^{63} + 593967q^{64} + 510246q^{65} + 760671q^{66} + 417090q^{67} + 440172q^{68} + 145278q^{69} - 107325q^{70} - 277020q^{71} - 874008q^{72} - 438675q^{73} - 378657q^{74} - 472518q^{75} - 499419q^{76} - 656127q^{77} - 787383q^{78} - 290967q^{79} + 37071q^{80} + 286182q^{81} + 682110q^{82} + 410400q^{83} + 1613403q^{84} + 843075q^{85} + 759114q^{86} + 871047q^{87} + 640143q^{88} + 273204q^{89} - 245574q^{90} - 401181q^{91} - 1081026q^{92} - 1299591q^{93} - 1980990q^{94} - 1015812q^{95} - 1847898q^{96} - 201690q^{97} + 214938q^{98} + 413604q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(19))$$

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
19.6.a $$\chi_{19}(1, \cdot)$$ 19.6.a.a 1 1
19.6.a.b 1
19.6.a.c 2
19.6.a.d 4
19.6.c $$\chi_{19}(7, \cdot)$$ 19.6.c.a 16 2
19.6.e $$\chi_{19}(4, \cdot)$$ 19.6.e.a 42 6