Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 6 x^2 - 2 x + 1\); 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:
| \(x^5 - x^4 - 27 x^3 + 36 x^2 + 170 x - 289\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^3 + 2 w^2 + 3 w]$ | $\phantom{-}e$ |
| 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 | $[11, 11, -w^3 + 2 w^2 + 4 w]$ | $\phantom{-}\frac{1}{17} e^4 - \frac{1}{17} e^3 - \frac{10}{17} e^2 + \frac{19}{17} e - 2$ |
| 13 | $[13, 13, -2 w^3 + 3 w^2 + 10 w - 2]$ | $-\frac{1}{17} e^4 + \frac{1}{17} e^3 + \frac{27}{17} e^2 - \frac{19}{17} e - 10$ |
| 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 | $[17, 17, -w^3 + 2 w^2 + 5 w - 3]$ | $\phantom{-}\frac{22}{17} e^4 + \frac{29}{17} e^3 - \frac{526}{17} e^2 - \frac{432}{17} e + 163$ |
| 17 | $[17, 17, -w^3 + w^2 + 5 w]$ | $-\frac{8}{17} e^4 - \frac{9}{17} e^3 + \frac{182}{17} e^2 + \frac{137}{17} e - 54$ |
| 17 | $[17, 17, -w^2 + 2 w + 1]$ | $\phantom{-}\frac{9}{17} e^4 + \frac{8}{17} e^3 - \frac{209}{17} e^2 - \frac{101}{17} e + 63$ |
| 19 | $[19, 19, w^2 - w - 2]$ | $-1$ |
| 29 | $[29, 29, w^3 - 2 w^2 - 5 w]$ | $-\frac{12}{17} e^4 - \frac{22}{17} e^3 + \frac{290}{17} e^2 + \frac{316}{17} e - 90$ |
| 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 | $[31, 31, -w^3 + 2 w^2 + 3 w - 2]$ | $-\frac{15}{17} e^4 - \frac{19}{17} e^3 + \frac{354}{17} e^2 + \frac{276}{17} e - 108$ |
| 43 | $[43, 43, 2 w^3 - 3 w^2 - 11 w]$ | $\phantom{-}\frac{6}{17} e^4 + \frac{11}{17} e^3 - \frac{162}{17} e^2 - \frac{175}{17} e + 60$ |
| 47 | $[47, 47, w^3 - 7 w - 4]$ | $-\frac{33}{17} e^4 - \frac{35}{17} e^3 + \frac{772}{17} e^2 + \frac{512}{17} e - 226$ |
| 53 | $[53, 53, -2 w^3 + 3 w^2 + 9 w - 1]$ | $-\frac{9}{17} e^4 - \frac{8}{17} e^3 + \frac{209}{17} e^2 + \frac{101}{17} e - 61$ |
| 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 | $[73, 73, -w^3 + 2 w^2 + 3 w - 3]$ | $-\frac{2}{17} e^4 + \frac{2}{17} e^3 + \frac{54}{17} e^2 - \frac{4}{17} e - 22$ |
| 73 | $[73, 73, w^3 - w^2 - 7 w - 1]$ | $\phantom{-}\frac{22}{17} e^4 + \frac{29}{17} e^3 - \frac{543}{17} e^2 - \frac{449}{17} e + 169$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^4 + e^3 - 22 e^2 - 14 e + 98$ |
| 83 | $[83, 83, -2 w^3 + 3 w^2 + 9 w + 1]$ | $\phantom{-}\frac{8}{17} e^4 + \frac{9}{17} e^3 - \frac{199}{17} e^2 - \frac{154}{17} e + 73$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^2 - w - 2]$ | $1$ |