Base field 4.4.7537.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[27, 27, -w^{3} + w^{2} + 3w]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 2x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 8 | $[8, 2, -w^{3} + 5w + 1]$ | $-e + 3$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 2]$ | $\phantom{-}e - 2$ |
| 19 | $[19, 19, -w^{3} + 4w - 2]$ | $-3$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}2e - 6$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 5w - 4]$ | $-3e + 2$ |
| 31 | $[31, 31, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}e + 5$ |
| 47 | $[47, 47, -w^{2} - w + 5]$ | $\phantom{-}e - 4$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 9w + 10]$ | $\phantom{-}3e - 4$ |
| 59 | $[59, 59, 2w - 1]$ | $-7$ |
| 59 | $[59, 59, w^{3} - 2w - 2]$ | $\phantom{-}7$ |
| 61 | $[61, 61, -w^{2} - 2w + 4]$ | $-e + 8$ |
| 67 | $[67, 67, 2w^{2} - 7]$ | $-8e + 6$ |
| 73 | $[73, 73, 5w^{3} + w^{2} - 23w - 8]$ | $\phantom{-}e + 7$ |
| 79 | $[79, 79, -2w^{3} - w^{2} + 9w + 7]$ | $-3e - 6$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 4w - 1]$ | $-3e + 14$ |
| 79 | $[79, 79, w^{3} - w^{2} - w - 2]$ | $\phantom{-}e + 4$ |
| 79 | $[79, 79, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}5e - 10$ |
| 83 | $[83, 83, w^{3} + w^{2} - 3w - 4]$ | $-9e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |