Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^6 - 2 x^5 - 4 x^4 + 8 x^3 + 2 x^2 - 5 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, 2 w^5 - 3 w^4 - 9 w^3 + 11 w^2 + 9 w - 4]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 2 x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^2 + 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^3 + 4 w]$ | $\phantom{-}6$ |
| 19 | $[19, 19, w^3 - 3 w - 1]$ | $\phantom{-}\frac{1}{2} e - 1$ |
| 29 | $[29, 29, w^5 - w^4 - 6 w^3 + 4 w^2 + 8 w - 3]$ | $\phantom{-}\frac{5}{2} e + 1$ |
| 29 | $[29, 29, w^4 - w^3 - 4 w^2 + 2 w + 2]$ | $-e$ |
| 31 | $[31, 31, -w^4 + 4 w^2 + w - 3]$ | $\phantom{-}\frac{3}{2} e - 6$ |
| 41 | $[41, 41, 2 w^5 - 2 w^4 - 10 w^3 + 7 w^2 + 11 w - 4]$ | $-4 e + 6$ |
| 49 | $[49, 7, -2 w^5 + 3 w^4 + 10 w^3 - 12 w^2 - 11 w + 6]$ | $\phantom{-}2 e + 2$ |
| 59 | $[59, 59, w^5 - 2 w^4 - 5 w^3 + 8 w^2 + 7 w - 5]$ | $-4 e + 4$ |
| 59 | $[59, 59, w^5 - w^4 - 4 w^3 + 3 w^2 + 3 w - 3]$ | $-\frac{1}{2} e$ |
| 59 | $[59, 59, 2 w^5 - 3 w^4 - 9 w^3 + 11 w^2 + 9 w - 4]$ | $-1$ |
| 61 | $[61, 61, -w^5 + w^4 + 5 w^3 - 3 w^2 - 7 w + 1]$ | $\phantom{-}\frac{11}{2} e - 4$ |
| 64 | $[64, 2, -2]$ | $-1$ |
| 71 | $[71, 71, -2 w^5 + 2 w^4 + 10 w^3 - 8 w^2 - 11 w + 6]$ | $-3 e + 6$ |
| 79 | $[79, 79, -3 w^5 + 4 w^4 + 13 w^3 - 14 w^2 - 9 w + 5]$ | $-2 e + 2$ |
| 79 | $[79, 79, -w^4 - w^3 + 5 w^2 + 4 w - 3]$ | $\phantom{-}e - 4$ |
| 79 | $[79, 79, -2 w^5 + 2 w^4 + 9 w^3 - 7 w^2 - 8 w + 4]$ | $-10$ |
| 81 | $[81, 3, 3 w^5 - 5 w^4 - 14 w^3 + 19 w^2 + 13 w - 8]$ | $\phantom{-}\frac{3}{2} e + 11$ |
| 89 | $[89, 89, 2 w^5 - 2 w^4 - 9 w^3 + 6 w^2 + 8 w - 1]$ | $\phantom{-}\frac{3}{2} e - 8$ |
| 101 | $[101, 101, -w^4 - w^3 + 5 w^2 + 3 w - 3]$ | $\phantom{-}3 e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, 2 w^5 - 3 w^4 - 9 w^3 + 11 w^2 + 9 w - 4]$ | $1$ |