## Defining parameters

 Level: $$N$$ = $$19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$90$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(19))$$.

Total New Old
Modular forms 39 39 0
Cusp forms 21 21 0
Eisenstein series 18 18 0

## Trace form

 $$21 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10})$$ $$21 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} + 63 q^{12} + 51 q^{13} + 63 q^{14} + 45 q^{15} + 63 q^{16} - 30 q^{19} - 90 q^{20} - 72 q^{21} - 117 q^{22} - 54 q^{23} - 225 q^{24} - 135 q^{25} - 153 q^{26} - 27 q^{27} + 114 q^{28} + 135 q^{29} + 432 q^{30} + 99 q^{31} + 216 q^{32} + 207 q^{33} + 126 q^{34} + 63 q^{35} + 117 q^{36} - 72 q^{38} - 126 q^{39} - 234 q^{40} - 81 q^{41} - 459 q^{42} - 186 q^{43} - 144 q^{45} - 54 q^{46} + 54 q^{47} - 198 q^{48} - 78 q^{49} + 72 q^{50} + 90 q^{51} + 255 q^{52} + 99 q^{53} + 180 q^{54} + 27 q^{55} - 54 q^{57} - 90 q^{58} - 144 q^{59} - 252 q^{60} + 231 q^{61} + 252 q^{62} + 315 q^{63} + 255 q^{64} + 126 q^{65} - 81 q^{66} + 336 q^{67} - 324 q^{68} + 72 q^{69} + 27 q^{70} - 270 q^{71} + 108 q^{72} + 102 q^{73} + 99 q^{74} - 99 q^{76} - 45 q^{77} + 261 q^{78} - 75 q^{79} + 243 q^{80} - 27 q^{81} - 522 q^{82} + 99 q^{84} - 405 q^{85} - 414 q^{86} - 369 q^{87} - 405 q^{88} - 630 q^{89} - 504 q^{90} - 669 q^{91} - 630 q^{92} - 477 q^{93} + 612 q^{95} + 918 q^{96} + 486 q^{97} + 1188 q^{98} + 513 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$

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
19.3.b $$\chi_{19}(18, \cdot)$$ 19.3.b.a 1 1
19.3.b.b 2
19.3.d $$\chi_{19}(8, \cdot)$$ 19.3.d.a 6 2
19.3.f $$\chi_{19}(2, \cdot)$$ 19.3.f.a 12 6