Base field 4.4.11348.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14, 14, w^{2} - 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 9x^{3} + 16x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}e^{4} - 7e^{2} + 2e + 6$ |
| 19 | $[19, 19, -2w + 1]$ | $\phantom{-}e^{4} - 7e^{2} + 6$ |
| 29 | $[29, 29, -w^{3} + w^{2} + 2w - 1]$ | $-e^{3} + e^{2} + 6e - 4$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $\phantom{-}e^{4} + e^{3} - 6e^{2} - 4e$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 5]$ | $-e^{3} - e^{2} + 6e + 6$ |
| 43 | $[43, 43, -2w^{3} + 2w^{2} + 8w + 3]$ | $-e^{4} - e^{3} + 8e^{2} + 4e - 6$ |
| 43 | $[43, 43, -w^{2} + 3w + 1]$ | $\phantom{-}e^{3} + e^{2} - 6e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}4$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 4e + 10$ |
| 59 | $[59, 59, 2w^{3} - 2w^{2} - 10w + 3]$ | $-e^{4} + 7e^{2} - 2e - 4$ |
| 61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}e^{4} - 2e^{3} - 9e^{2} + 14e + 14$ |
| 61 | $[61, 61, w^{2} + w - 3]$ | $\phantom{-}e^{4} - 2e^{3} - 9e^{2} + 14e + 14$ |
| 71 | $[71, 71, -w^{3} + 5w + 1]$ | $\phantom{-}e^{4} + 2e^{3} - 9e^{2} - 8e + 14$ |
| 71 | $[71, 71, w^{3} - w^{2} - 4w - 3]$ | $-e^{4} - e^{3} + 6e^{2} + 4e - 4$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{4} - 3e^{2} + 2e - 10$ |
| 83 | $[83, 83, -3w^{3} + 5w^{2} + 12w - 9]$ | $\phantom{-}e^{4} - 3e^{3} - 10e^{2} + 16e + 16$ |
| 83 | $[83, 83, -3w^{3} + 6w^{2} + 13w - 13]$ | $-2e^{3} - 2e^{2} + 12e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |
| $7$ | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $1$ |