Base field 5.5.36497.1
Generator \(w\), with minimal polynomial \(x^5 - 2 x^4 - 3 x^3 + 5 x^2 + x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[32, 2, 2]$ |
| 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:
| \(x^6 - 14 x^4 + 46 x^2 - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^4 - 2 w^3 - 3 w^2 + 4 w + 1]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^3 - 2 w^2 - 2 w + 2]$ | $-\frac{1}{4} e^5 + \frac{5}{2} e^3 - \frac{7}{2} e$ |
| 23 | $[23, 23, 2 w^4 - 3 w^3 - 6 w^2 + 5 w + 1]$ | $\phantom{-}\frac{1}{2} e^4 - 5 e^2 + 7$ |
| 25 | $[25, 5, -w^2 + 2 w + 2]$ | $-e^3 + 7 e$ |
| 29 | $[29, 29, -w^4 + w^3 + 4 w^2 - 3 w - 1]$ | $-\frac{1}{2} e^5 + 7 e^3 - 23 e$ |
| 31 | $[31, 31, w^4 - w^3 - 5 w^2 + 2 w + 4]$ | $\phantom{-}\frac{1}{2} e^5 - 7 e^3 + 23 e$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^4 - 2 w^3 - 2 w^2 + 4 w + 1]$ | $-\frac{1}{2} e^5 + 7 e^3 - 21 e$ |
| 47 | $[47, 47, w^4 - w^3 - 5 w^2 + 2 w + 3]$ | $\phantom{-}\frac{1}{4} e^5 - \frac{5}{2} e^3 + \frac{7}{2} e$ |
| 47 | $[47, 47, 2 w^4 - 3 w^3 - 6 w^2 + 6 w + 2]$ | $\phantom{-}\frac{1}{2} e^4 - 3 e^2 - 1$ |
| 49 | $[49, 7, -w^4 + 2 w^3 + 4 w^2 - 6 w - 2]$ | $-\frac{1}{4} e^5 + \frac{7}{2} e^3 - \frac{21}{2} e$ |
| 53 | $[53, 53, -2 w^4 + 3 w^3 + 7 w^2 - 7 w - 2]$ | $-2 e$ |
| 59 | $[59, 59, -2 w^4 + 3 w^3 + 6 w^2 - 5 w - 2]$ | $-2$ |
| 67 | $[67, 67, -w^4 + 3 w^3 + 2 w^2 - 7 w]$ | $-\frac{1}{2} e^4 + 2 e^2 + 9$ |
| 67 | $[67, 67, -w^4 + 3 w^3 + w^2 - 7 w + 1]$ | $\phantom{-}\frac{1}{2} e^5 - 6 e^3 + 16 e$ |
| 71 | $[71, 71, w^4 - 2 w^3 - 4 w^2 + 3 w + 3]$ | $\phantom{-}e^4 - 8 e^2 + 6$ |
| 71 | $[71, 71, -w^2 + 5]$ | $\phantom{-}\frac{3}{4} e^5 - \frac{19}{2} e^3 + \frac{49}{2} e$ |
| 79 | $[79, 79, 2 w^4 - 3 w^3 - 5 w^2 + 3 w + 1]$ | $-e^4 + 10 e^2 - 10$ |
| 81 | $[81, 3, -w^4 + 3 w^3 + 3 w^2 - 8 w - 2]$ | $\phantom{-}\frac{1}{2} e^5 - 7 e^3 + 20 e$ |
| 83 | $[83, 83, -3 w^4 + 3 w^3 + 10 w^2 - 2 w - 2]$ | $\phantom{-}\frac{1}{2} e^4 - 5 e^2 + 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $32$ | $[32, 2, 2]$ | $-1$ |