## Defining parameters

 Level: $$N$$ = $$19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$120$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(19))$$.

Total New Old
Modular forms 54 52 2
Cusp forms 36 36 0
Eisenstein series 18 16 2

## Trace form

 $$36 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10})$$ $$36 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} - 297 q^{12} - 153 q^{13} - 45 q^{14} + 99 q^{15} + 423 q^{16} + 135 q^{17} + 468 q^{18} + 369 q^{19} + 558 q^{20} + 243 q^{21} + 153 q^{22} - 27 q^{23} - 441 q^{24} - 441 q^{25} - 693 q^{26} - 1314 q^{27} - 2304 q^{28} - 639 q^{29} - 1206 q^{30} - 99 q^{31} + 306 q^{32} + 909 q^{33} + 1116 q^{34} + 1107 q^{35} + 3069 q^{36} + 648 q^{37} + 2322 q^{38} + 1872 q^{39} + 1872 q^{40} + 441 q^{41} + 1521 q^{42} - 135 q^{43} - 2934 q^{44} - 3087 q^{45} - 3528 q^{46} - 1881 q^{47} - 5616 q^{48} - 1719 q^{49} - 2214 q^{50} - 144 q^{51} + 2367 q^{52} + 1575 q^{53} + 2448 q^{54} + 1935 q^{55} + 6030 q^{56} + 2511 q^{57} + 1926 q^{58} + 2241 q^{59} + 1530 q^{60} - 2763 q^{61} - 3420 q^{62} - 3393 q^{63} - 4113 q^{64} - 2619 q^{65} - 3537 q^{66} - 927 q^{67} - 3600 q^{68} - 333 q^{69} + 315 q^{70} - 2187 q^{71} + 2952 q^{72} + 4932 q^{73} + 5175 q^{74} + 6282 q^{75} + 6741 q^{76} + 4644 q^{77} - 279 q^{78} + 2655 q^{79} - 2889 q^{80} + 468 q^{81} + 2214 q^{82} - 351 q^{83} - 1413 q^{84} - 945 q^{85} - 1422 q^{86} - 1377 q^{87} - 1161 q^{88} - 4059 q^{89} - 4194 q^{90} - 4977 q^{91} - 2538 q^{92} - 315 q^{93} - 2862 q^{94} - 5715 q^{95} - 666 q^{96} - 3357 q^{97} - 6678 q^{98} - 792 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(19))$$

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
19.4.a $$\chi_{19}(1, \cdot)$$ 19.4.a.a 1 1
19.4.a.b 3
19.4.c $$\chi_{19}(7, \cdot)$$ 19.4.c.a 4 2
19.4.c.b 4
19.4.e $$\chi_{19}(4, \cdot)$$ 19.4.e.a 24 6