Base field 3.3.469.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[28, 14, -w^{2} - w + 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 7x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} - w + 3]$ | $-1$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}e^{3} - 6e - 1$ |
| 7 | $[7, 7, -w + 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}e^{3} + e^{2} - 7e - 3$ |
| 17 | $[17, 17, w + 3]$ | $-e^{2} + e + 4$ |
| 19 | $[19, 19, w^{2} - 7]$ | $\phantom{-}e^{3} - 9e$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}e^{3} - 7e + 2$ |
| 43 | $[43, 43, -2w - 5]$ | $\phantom{-}2e^{3} + 2e^{2} - 14e - 6$ |
| 47 | $[47, 47, 2w + 3]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 11$ |
| 53 | $[53, 53, 3w^{2} + 2w - 9]$ | $\phantom{-}e^{3} - 11e$ |
| 59 | $[59, 59, 2w^{2} + w - 5]$ | $-4e^{3} + 23e - 1$ |
| 61 | $[61, 61, 3w - 1]$ | $-3e^{3} - e^{2} + 15e + 7$ |
| 61 | $[61, 61, 2w^{2} + w - 9]$ | $\phantom{-}2e^{3} - e^{2} - 14e - 1$ |
| 61 | $[61, 61, 2w^{2} - w - 7]$ | $\phantom{-}2e - 4$ |
| 67 | $[67, 67, -2w^{2} + 13]$ | $-2e^{3} + 12e + 6$ |
| 67 | $[67, 67, -3w - 7]$ | $-3e^{3} + 2e^{2} + 19e - 6$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $\phantom{-}2e^{3} - 3e^{2} - 13e + 6$ |
| 79 | $[79, 79, w - 5]$ | $-3e^{2} + 7$ |
| 83 | $[83, 83, -2w^{2} + 4w + 3]$ | $-2e^{2} - 3e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} - w + 3]$ | $1$ |
| $7$ | $[7, 7, -w + 3]$ | $-1$ |