Base field 4.4.12725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, w^{2} - 2w - 5]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w - 1]$ | $\phantom{-}\frac{1}{2}e - \frac{5}{2}$ |
| 11 | $[11, 11, w^{2} - 5]$ | $\phantom{-}\frac{1}{2}e + \frac{1}{2}$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 2]$ | $-\frac{3}{2}e - \frac{1}{2}$ |
| 16 | $[16, 2, 2]$ | $-\frac{3}{2}e - \frac{3}{2}$ |
| 19 | $[19, 19, w^{2} - 2w - 5]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}\frac{3}{2}e - \frac{5}{2}$ |
| 25 | $[25, 5, -2w^{2} + 2w + 11]$ | $-\frac{3}{2}e - \frac{9}{2}$ |
| 29 | $[29, 29, w]$ | $\phantom{-}\frac{5}{2}e - \frac{7}{2}$ |
| 29 | $[29, 29, 2w^{2} - w - 10]$ | $-\frac{5}{2}e + \frac{5}{2}$ |
| 29 | $[29, 29, -2w^{2} + 3w + 9]$ | $\phantom{-}e$ |
| 29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{5}{2}e + \frac{1}{2}$ |
| 31 | $[31, 31, w^{3} - 6w - 6]$ | $-\frac{7}{2}e + \frac{5}{2}$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ | $\phantom{-}\frac{1}{2}e - \frac{11}{2}$ |
| 41 | $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ | $\phantom{-}\frac{3}{2}e + \frac{15}{2}$ |
| 41 | $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ | $\phantom{-}e + 3$ |
| 59 | $[59, 59, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}2e + 1$ |
| 59 | $[59, 59, 2w^{2} - w - 13]$ | $-3e - 2$ |
| 61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $-e - 4$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $-2e + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{2} - 2w - 5]$ | $-1$ |