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: | $[28, 14, w^{2} + w - 7]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 10x^{3} + 2x^{2} + 22x - 13\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} - w + 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 1]$ | $-1$ |
| 7 | $[7, 7, -w + 3]$ | $-e^{3} + e^{2} + 6e - 4$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}e^{4} - 8e^{2} - e + 10$ |
| 17 | $[17, 17, w + 3]$ | $-e^{4} - 2e^{3} + 10e^{2} + 13e - 20$ |
| 19 | $[19, 19, w^{2} - 7]$ | $-e^{3} - e^{2} + 6e + 2$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}2e - 2$ |
| 43 | $[43, 43, -2w - 5]$ | $\phantom{-}2e^{3} - 12e + 2$ |
| 47 | $[47, 47, 2w + 3]$ | $-2e^{4} - e^{3} + 15e^{2} + 6e - 16$ |
| 53 | $[53, 53, 3w^{2} + 2w - 9]$ | $\phantom{-}2e^{4} + 2e^{3} - 18e^{2} - 16e + 32$ |
| 59 | $[59, 59, 2w^{2} + w - 5]$ | $\phantom{-}2e^{4} + 2e^{3} - 16e^{2} - 14e + 22$ |
| 61 | $[61, 61, 3w - 1]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 12$ |
| 61 | $[61, 61, 2w^{2} + w - 9]$ | $\phantom{-}2e^{3} - 10e + 6$ |
| 61 | $[61, 61, 2w^{2} - w - 7]$ | $-e^{4} - 2e^{3} + 8e^{2} + 9e - 10$ |
| 67 | $[67, 67, -2w^{2} + 13]$ | $\phantom{-}e^{3} - e^{2} - 6e + 8$ |
| 67 | $[67, 67, -3w - 7]$ | $\phantom{-}e^{4} - 6e^{2} - e + 8$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $\phantom{-}2e^{4} + 2e^{3} - 16e^{2} - 12e + 22$ |
| 79 | $[79, 79, w - 5]$ | $\phantom{-}2e^{4} + 2e^{3} - 18e^{2} - 10e + 32$ |
| 83 | $[83, 83, -2w^{2} + 4w + 3]$ | $\phantom{-}2e^{3} - 6e^{2} - 14e + 30$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} - w + 3]$ | $-1$ |
| $7$ | $[7, 7, w + 1]$ | $1$ |