Base field 3.3.1509.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, w + 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 11x^{6} + 36x^{4} - 38x^{2} + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w^{2} + w + 15]$ | $\phantom{-}e^{6} - 9e^{4} + 18e^{2} - 4$ |
| 3 | $[3, 3, w - 1]$ | $-e^{7} + 9e^{5} - 19e^{3} + 8e$ |
| 4 | $[4, 2, -w^{2} + 3w - 1]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 3]$ | $-1$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}2e^{7} - 19e^{5} + 46e^{3} - 28e$ |
| 23 | $[23, 23, -2w^{2} + 2w + 17]$ | $\phantom{-}e^{4} - 7e^{2} + 6$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $\phantom{-}e^{5} - 9e^{3} + 15e$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $\phantom{-}e^{5} - 8e^{3} + 10e$ |
| 43 | $[43, 43, 5w^{2} - 2w - 35]$ | $\phantom{-}e^{5} - 7e^{3} + 10e$ |
| 43 | $[43, 43, 3w - 1]$ | $\phantom{-}2e^{6} - 16e^{4} + 25e^{2} - 5$ |
| 43 | $[43, 43, 2w - 3]$ | $-3e^{7} + 28e^{5} - 64e^{3} + 34e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{7} - 10e^{5} + 26e^{3} - 17e$ |
| 59 | $[59, 59, -3w^{2} + 2w + 21]$ | $\phantom{-}3e^{6} - 25e^{4} + 40e^{2} + 6$ |
| 71 | $[71, 71, 2w + 3]$ | $-3e^{6} + 27e^{4} - 55e^{2} + 9$ |
| 71 | $[71, 71, 3w^{2} - 19]$ | $\phantom{-}3e^{7} - 28e^{5} + 64e^{3} - 30e$ |
| 71 | $[71, 71, 4w^{2} - 13w + 5]$ | $-3e^{7} + 25e^{5} - 40e^{3} - 6e$ |
| 83 | $[83, 83, 2w^{2} - 15]$ | $\phantom{-}2e^{7} - 16e^{5} + 23e^{3} + 3e$ |
| 89 | $[89, 89, -w^{2} - 1]$ | $\phantom{-}2e^{6} - 19e^{4} + 42e^{2} - 18$ |
| 89 | $[89, 89, 2w^{2} - 4w + 1]$ | $\phantom{-}5e^{7} - 43e^{5} + 75e^{3} - e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w + 3]$ | $1$ |