Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + 3w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 3x^{5} - 18x^{4} - 20x^{3} + 113x^{2} - 87x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{17}{375}e^{5} + \frac{24}{125}e^{4} - \frac{13}{25}e^{3} - \frac{5}{3}e^{2} + \frac{796}{375}e + \frac{298}{125}$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{89}{375}e^{5} - \frac{133}{125}e^{4} + \frac{71}{25}e^{3} + \frac{26}{3}e^{2} - \frac{6307}{375}e + \frac{359}{125}$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{14}{125}e^{5} + \frac{74}{125}e^{4} - \frac{13}{25}e^{3} - 4e^{2} + \frac{207}{125}e + \frac{398}{125}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{4}{75}e^{5} - \frac{13}{25}e^{4} - \frac{4}{5}e^{3} + \frac{11}{3}e^{2} + \frac{448}{75}e - \frac{101}{25}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{37}{125}e^{5} - \frac{142}{125}e^{4} + \frac{104}{25}e^{3} + 9e^{2} - \frac{2931}{125}e + \frac{966}{125}$ |
| 19 | $[19, 19, w + 3]$ | $-\frac{103}{375}e^{5} - \frac{116}{125}e^{4} + \frac{117}{25}e^{3} + \frac{25}{3}e^{2} - \frac{10139}{375}e + \frac{1018}{125}$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $-\frac{3}{25}e^{5} - \frac{23}{25}e^{4} - \frac{4}{5}e^{3} + 5e^{2} + \frac{111}{25}e - \frac{21}{25}$ |
| 19 | $[19, 19, -w^{2} + 3w + 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $\phantom{-}\frac{9}{25}e^{5} + \frac{44}{25}e^{4} - \frac{13}{5}e^{3} - 11e^{2} + \frac{342}{25}e - \frac{112}{25}$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-\frac{16}{125}e^{5} - \frac{31}{125}e^{4} + \frac{72}{25}e^{3} + 3e^{2} - \frac{1683}{125}e + \frac{438}{125}$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}\frac{208}{375}e^{5} + \frac{301}{125}e^{4} - \frac{162}{25}e^{3} - \frac{55}{3}e^{2} + \frac{14129}{375}e - \frac{898}{125}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $-\frac{32}{125}e^{5} - \frac{187}{125}e^{4} + \frac{19}{25}e^{3} + 10e^{2} - \frac{241}{125}e - \frac{499}{125}$ |
| 43 | $[43, 43, w^{2} - 3w - 3]$ | $\phantom{-}\frac{157}{375}e^{5} + \frac{229}{125}e^{4} - \frac{123}{25}e^{3} - \frac{40}{3}e^{2} + \frac{10991}{375}e - \frac{1417}{125}$ |
| 49 | $[49, 7, w^{2} - 6]$ | $\phantom{-}\frac{436}{375}e^{5} + \frac{667}{125}e^{4} - \frac{304}{25}e^{3} - \frac{121}{3}e^{2} + \frac{25268}{375}e - \frac{1291}{125}$ |
| 53 | $[53, 53, 2w - 5]$ | $-\frac{7}{25}e^{5} - \frac{37}{25}e^{4} + \frac{9}{5}e^{3} + 9e^{2} - \frac{291}{25}e + \frac{226}{25}$ |
| 61 | $[61, 61, 2w^{2} - 2w - 9]$ | $-\frac{16}{75}e^{5} - \frac{27}{25}e^{4} + \frac{4}{5}e^{3} + \frac{14}{3}e^{2} - \frac{383}{75}e + \frac{271}{25}$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}\frac{116}{375}e^{5} + \frac{127}{125}e^{4} - \frac{149}{25}e^{3} - \frac{32}{3}e^{2} + \frac{13108}{375}e - \frac{1496}{125}$ |
| 73 | $[73, 73, 2w^{2} - 5w - 5]$ | $-\frac{97}{125}e^{5} - \frac{477}{125}e^{4} + \frac{149}{25}e^{3} + 25e^{2} - \frac{3961}{125}e + \frac{921}{125}$ |
| 83 | $[83, 83, w^{2} - w - 9]$ | $\phantom{-}\frac{77}{125}e^{5} + \frac{282}{125}e^{4} - \frac{234}{25}e^{3} - 18e^{2} + \frac{6451}{125}e - \frac{2561}{125}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + 3w + 2]$ | $-1$ |