Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, -w^{3} + 2w^{2} + 4w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 7x^{2} - 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}2e^{3} - e^{2} - 12e - 6$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $-1$ |
| 13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-2e^{3} + 16e + 10$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{3} - 8e - 2$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}2e^{3} - 2e^{2} - 13e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $\phantom{-}2e^{3} - 14e - 8$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}4e^{3} - 2e^{2} - 26e - 10$ |
| 19 | $[19, 19, w^{2} - w - 2]$ | $-4e^{3} + 3e^{2} + 24e + 6$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $-3e^{3} + 23e + 12$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-e^{2} + 1$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $-2e^{3} - e^{2} + 14e + 13$ |
| 43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $-2e^{2} + 2e + 10$ |
| 47 | $[47, 47, w^{3} - 7w - 4]$ | $-e^{2} + 2e + 3$ |
| 53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $\phantom{-}2e^{3} - e^{2} - 10e - 7$ |
| 61 | $[61, 61, -w - 3]$ | $-e^{3} + 2e^{2} + 5e + 4$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}4e^{3} - 4e^{2} - 26e - 4$ |
| 73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}5e^{3} - 39e - 22$ |
| 81 | $[81, 3, -3]$ | $-6e^{3} + 4e^{2} + 38e + 20$ |
| 83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $-10e^{3} + 4e^{2} + 66e + 26$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $1$ |