Base field 4.4.11324.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, w^{3} - 4w - 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 6x^{3} + 6x^{2} + 4x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 4w + 1]$ | $-1$ |
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e^{4} - e^{3} - 6e^{2} + 6e + 4$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 7e + 6$ |
| 19 | $[19, 19, -w^{3} + 3w - 1]$ | $\phantom{-}e^{4} - 5e^{2} + 4$ |
| 23 | $[23, 23, -w + 3]$ | $\phantom{-}e^{4} + e^{3} - 5e^{2} - e$ |
| 31 | $[31, 31, -w^{2} - 2w + 1]$ | $\phantom{-}3e^{4} - 17e^{2} + 4e + 6$ |
| 41 | $[41, 41, w^{3} + w^{2} - 5w - 3]$ | $-e^{4} + 2e^{3} + 5e^{2} - 8e$ |
| 43 | $[43, 43, 2w - 1]$ | $\phantom{-}3e^{4} - 15e^{2} + 2e + 6$ |
| 53 | $[53, 53, -w - 3]$ | $\phantom{-}e^{4} + e^{3} - 6e^{2} - 6e + 6$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e^{4} - 3e^{3} - 8e^{2} + 14e + 8$ |
| 61 | $[61, 61, w^{3} - 3w - 5]$ | $\phantom{-}2e^{4} - 3e^{3} - 9e^{2} + 16e + 2$ |
| 67 | $[67, 67, w^{3} + w^{2} - 5w - 1]$ | $-2e^{4} + 12e^{2} + 2e - 4$ |
| 81 | $[81, 3, -3]$ | $-e^{4} + 3e^{2} + 4$ |
| 83 | $[83, 83, -w^{3} + 5w - 3]$ | $-2e^{4} + e^{3} + 13e^{2} - 2e - 12$ |
| 89 | $[89, 89, w^{2} + 1]$ | $\phantom{-}2e^{4} - 9e^{2} + e + 2$ |
| 97 | $[97, 97, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 12$ |
| 97 | $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ | $\phantom{-}2e^{3} + 4e^{2} - 10e - 2$ |
| 97 | $[97, 97, w^{3} - 3w - 3]$ | $-2e^{4} + 9e^{2} - 3e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{3} + 4w + 1]$ | $1$ |
| $5$ | $[5, 5, w + 1]$ | $1$ |