Base field 5.5.24217.1
Generator \(w\), with minimal polynomial \(x^5 - 5 x^3 - x^2 + 3 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[85, 85, 3 w^4 - w^3 - 14 w^2 + 3 w + 5]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 - 4 x^2 - 41 x + 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2 w^4 + w^3 + 9 w^2 - 2 w - 3]$ | $-1$ |
| 17 | $[17, 17, -2 w^4 + w^3 + 9 w^2 - 3 w - 5]$ | $\phantom{-}2$ |
| 17 | $[17, 17, w^2 - 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^3 - 3 w]$ | $\phantom{-}e$ |
| 29 | $[29, 29, 2 w^4 - w^3 - 10 w^2 + 2 w + 4]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{2}{3} e - 10$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{3} e^2 + \frac{1}{3} e - 11$ |
| 37 | $[37, 37, -w^4 + w^3 + 4 w^2 - 2 w]$ | $\phantom{-}e - 2$ |
| 41 | $[41, 41, -3 w^4 + 2 w^3 + 14 w^2 - 5 w - 7]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{2}{3} e - 6$ |
| 43 | $[43, 43, -3 w^4 + w^3 + 14 w^2 - 3 w - 6]$ | $\phantom{-}4$ |
| 47 | $[47, 47, -3 w^4 + 2 w^3 + 14 w^2 - 7 w - 6]$ | $-\frac{1}{3} e^2 + \frac{2}{3} e + 12$ |
| 53 | $[53, 53, 2 w^4 - w^3 - 8 w^2 + 2 w + 1]$ | $-\frac{1}{3} e^2 - \frac{4}{3} e + 14$ |
| 53 | $[53, 53, -2 w^4 + w^3 + 10 w^2 - 4 w - 6]$ | $-e - 2$ |
| 59 | $[59, 59, -w^4 + 4 w^2 + 1]$ | $\phantom{-}\frac{1}{3} e^2 + \frac{4}{3} e - 12$ |
| 59 | $[59, 59, -3 w^4 + 2 w^3 + 14 w^2 - 6 w - 8]$ | $\phantom{-}\frac{2}{3} e^2 - \frac{1}{3} e - 20$ |
| 61 | $[61, 61, 4 w^4 - 2 w^3 - 18 w^2 + 5 w + 7]$ | $-e + 2$ |
| 61 | $[61, 61, 3 w^4 - w^3 - 15 w^2 + 2 w + 7]$ | $-\frac{2}{3} e^2 - \frac{2}{3} e + 22$ |
| 73 | $[73, 73, -4 w^4 + 2 w^3 + 18 w^2 - 7 w - 6]$ | $-\frac{2}{3} e^2 - \frac{2}{3} e + 26$ |
| 83 | $[83, 83, -2 w^4 + 9 w^2 + 2 w - 4]$ | $-8$ |
| 83 | $[83, 83, -2 w^4 + 2 w^3 + 10 w^2 - 7 w - 6]$ | $-\frac{1}{3} e^2 + \frac{2}{3} e + 12$ |
| 97 | $[97, 97, -2 w^4 + w^3 + 8 w^2 - 3 w + 1]$ | $\phantom{-}\frac{2}{3} e^2 - \frac{1}{3} e - 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -2 w^4 + w^3 + 9 w^2 - 2 w - 3]$ | $1$ |
| $17$ | $[17, 17, w^2 - 2]$ | $-1$ |