Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 7 x^2 + 10 x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, w^3 + w^2 - 4 w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 - 10 x^4 + 21 x^2 - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^3 + w^2 - 4 w + 1]$ | $-1$ |
| 7 | $[7, 7, -w^3 + 6 w - 2]$ | $\phantom{-}\frac{1}{2} e^5 - \frac{9}{2} e^3 + 8 e$ |
| 8 | $[8, 2, w^3 - 7 w + 3]$ | $-\frac{1}{2} e^3 + \frac{7}{2} e$ |
| 11 | $[11, 11, -w^3 + 6 w - 4]$ | $\phantom{-}\frac{1}{2} e^5 - 5 e^3 + \frac{21}{2} e$ |
| 17 | $[17, 17, w^3 + w^2 - 6 w - 1]$ | $\phantom{-}\frac{1}{2} e^4 - \frac{11}{2} e^2 + 9$ |
| 17 | $[17, 17, -w^2 - w + 3]$ | $-\frac{1}{2} e^5 + \frac{9}{2} e^3 - 6 e$ |
| 31 | $[31, 31, 2 w^3 + w^2 - 13 w + 3]$ | $-e^5 + \frac{19}{2} e^3 - \frac{33}{2} e$ |
| 37 | $[37, 37, -3 w^3 - w^2 + 18 w - 3]$ | $-\frac{3}{2} e^5 + 14 e^3 - \frac{45}{2} e$ |
| 41 | $[41, 41, w^2 + 2 w - 4]$ | $\phantom{-}e^3 - 5 e$ |
| 47 | $[47, 47, 2 w^3 + 2 w^2 - 11 w - 2]$ | $\phantom{-}\frac{3}{2} e^4 - \frac{27}{2} e^2 + 14$ |
| 47 | $[47, 47, -3 w^3 - w^2 + 19 w - 6]$ | $\phantom{-}\frac{1}{2} e^5 - 6 e^3 + \frac{39}{2} e$ |
| 59 | $[59, 59, -2 w^3 + 13 w - 6]$ | $-e^5 + 10 e^3 - 23 e$ |
| 59 | $[59, 59, -w^3 - w^2 + 5 w + 2]$ | $-\frac{3}{2} e^4 + \frac{17}{2} e^2 + 3$ |
| 59 | $[59, 59, w^2 + w - 1]$ | $\phantom{-}\frac{1}{2} e^5 - 3 e^3 + \frac{1}{2} e$ |
| 59 | $[59, 59, w^2 + 2 w - 6]$ | $-2 e^2 + 8$ |
| 61 | $[61, 61, -w^3 + w^2 + 8 w - 7]$ | $\phantom{-}e^5 - 8 e^3 + 7 e$ |
| 67 | $[67, 67, w^3 + 2 w^2 - 4 w - 4]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -2 w^3 - w^2 + 12 w - 4]$ | $-2 e^5 + 16 e^3 - 18 e$ |
| 81 | $[81, 3, -3]$ | $-2 e^2 + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^3 + w^2 - 4 w + 1]$ | $1$ |