Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14, 14, w^{3} - 2w^{2} - 4w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 5x^{3} - 6x^{2} + 7x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w - 1]$ | $-1$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}e^{4} + 3e^{3} - 3e^{2} - 9e + 2$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-e^{3} - e^{2} + e - 1$ |
| 29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $-3e^{4} - 9e^{3} + 11e^{2} + 28e - 15$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}2e^{4} + 5e^{3} - 6e^{2} - 12e + 5$ |
| 41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 13e + 5$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $-e^{4} - 4e^{3} + e^{2} + 9e + 1$ |
| 47 | $[47, 47, w^{2} - 3w - 3]$ | $-2e^{4} - 3e^{3} + 9e^{2} + 10e - 8$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}3e^{4} + 7e^{3} - 14e^{2} - 22e + 10$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $-2e^{4} - 3e^{3} + 11e^{2} + 13e - 11$ |
| 61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $\phantom{-}2e^{4} + 5e^{3} - 5e^{2} - 12e + 2$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $\phantom{-}e^{3} + 2e^{2} - 4e - 1$ |
| 67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $\phantom{-}6e^{4} + 11e^{3} - 26e^{2} - 34e + 17$ |
| 67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $-2e^{4} - 7e^{3} + 10e^{2} + 28e - 15$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $\phantom{-}e^{3} + 3e^{2} - 5e - 11$ |
| 71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $-e^{4} - e^{3} + e^{2} - 4e + 11$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $-3e^{4} - 9e^{3} + 10e^{2} + 26e - 6$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $\phantom{-}2e^{3} + 4e^{2} - 9e - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 1]$ | $1$ |
| $7$ | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $-1$ |