Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 6 x^2 + 8 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w + 1]$ |
| Dimension: | $3$ |
| 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:
| \(x^3 - 5 x^2 - 6 x + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, w^3 - 5 w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^3 - 5 w + 2]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{5}{3} e$ |
| 13 | $[13, 13, w + 1]$ | $-1$ |
| 13 | $[13, 13, w^3 - 6 w + 4]$ | $\phantom{-}\frac{1}{3} e^2 + \frac{1}{3} e - 6$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{5}{3} e - 5$ |
| 17 | $[17, 17, w^2 + w - 2]$ | $\phantom{-}e + 1$ |
| 17 | $[17, 17, w^2 + w - 5]$ | $-\frac{2}{3} e^2 + \frac{4}{3} e + 6$ |
| 23 | $[23, 23, w^3 - w^2 - 6 w + 6]$ | $-e^2 + 4 e + 4$ |
| 23 | $[23, 23, w^3 + w^2 - 4 w - 1]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{5}{3} e$ |
| 25 | $[25, 5, -w^2 + 3]$ | $\phantom{-}e^2 - 4 e - 4$ |
| 25 | $[25, 5, -w^3 - w^2 + 5 w + 1]$ | $-\frac{1}{3} e^2 + \frac{5}{3} e$ |
| 29 | $[29, 29, -w^2 - 2 w + 3]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{2}{3} e + 3$ |
| 29 | $[29, 29, -w^3 + w^2 + 7 w - 7]$ | $-\frac{2}{3} e^2 + \frac{4}{3} e + 5$ |
| 43 | $[43, 43, 2 w^3 + w^2 - 10 w + 3]$ | $\phantom{-}\frac{2}{3} e^2 - \frac{7}{3} e - 5$ |
| 43 | $[43, 43, -w^3 + w^2 + 5 w - 7]$ | $-e^2 + 2 e + 7$ |
| 53 | $[53, 53, w^3 - w^2 - 7 w + 5]$ | $-2 e + 8$ |
| 53 | $[53, 53, w^2 + 2 w - 5]$ | $\phantom{-}e^2 - 3 e - 10$ |
| 61 | $[61, 61, 2 w^3 + w^2 - 10 w]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{2}{3} e + 1$ |
| 61 | $[61, 61, w^3 - 7 w + 3]$ | $-e + 3$ |
| 61 | $[61, 61, 2 w^3 + w^2 - 9 w + 3]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{2}{3} e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w + 1]$ | $1$ |