Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, w^{2} - w - 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 27x^{3} + 36x^{2} + 170x - 289\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $-\frac{14}{17}e^{4} - \frac{20}{17}e^{3} + \frac{344}{17}e^{2} + \frac{295}{17}e - 110$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $\phantom{-}\frac{1}{17}e^{4} - \frac{1}{17}e^{3} - \frac{10}{17}e^{2} + \frac{19}{17}e - 2$ |
| 13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-\frac{1}{17}e^{4} + \frac{1}{17}e^{3} + \frac{27}{17}e^{2} - \frac{19}{17}e - 10$ |
| 16 | $[16, 2, 2]$ | $-\frac{23}{17}e^{4} - \frac{28}{17}e^{3} + \frac{553}{17}e^{2} + \frac{413}{17}e - 168$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{22}{17}e^{4} + \frac{29}{17}e^{3} - \frac{526}{17}e^{2} - \frac{432}{17}e + 163$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $-\frac{8}{17}e^{4} - \frac{9}{17}e^{3} + \frac{182}{17}e^{2} + \frac{137}{17}e - 54$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{9}{17}e^{4} + \frac{8}{17}e^{3} - \frac{209}{17}e^{2} - \frac{101}{17}e + 63$ |
| 19 | $[19, 19, w^{2} - w - 2]$ | $-1$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $-\frac{12}{17}e^{4} - \frac{22}{17}e^{3} + \frac{290}{17}e^{2} + \frac{316}{17}e - 90$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{15}{17}e^{4} + \frac{19}{17}e^{3} - \frac{371}{17}e^{2} - \frac{310}{17}e + 121$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{15}{17}e^{4} - \frac{19}{17}e^{3} + \frac{354}{17}e^{2} + \frac{276}{17}e - 108$ |
| 43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $\phantom{-}\frac{6}{17}e^{4} + \frac{11}{17}e^{3} - \frac{162}{17}e^{2} - \frac{175}{17}e + 60$ |
| 47 | $[47, 47, w^{3} - 7w - 4]$ | $-\frac{33}{17}e^{4} - \frac{35}{17}e^{3} + \frac{772}{17}e^{2} + \frac{512}{17}e - 226$ |
| 53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $-\frac{9}{17}e^{4} - \frac{8}{17}e^{3} + \frac{209}{17}e^{2} + \frac{101}{17}e - 61$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{10}{17}e^{4} + \frac{7}{17}e^{3} - \frac{253}{17}e^{2} - \frac{82}{17}e + 77$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{2}{17}e^{4} + \frac{2}{17}e^{3} + \frac{54}{17}e^{2} - \frac{4}{17}e - 22$ |
| 73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}\frac{22}{17}e^{4} + \frac{29}{17}e^{3} - \frac{543}{17}e^{2} - \frac{449}{17}e + 169$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{4} + e^{3} - 22e^{2} - 14e + 98$ |
| 83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $\phantom{-}\frac{8}{17}e^{4} + \frac{9}{17}e^{3} - \frac{199}{17}e^{2} - \frac{154}{17}e + 73$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{2} - w - 2]$ | $1$ |