Base field 4.4.15188.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 9x^{6} + 24x^{4} - 19x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{1}{2}e^{7} + \frac{9}{2}e^{5} - 11e^{3} + \frac{9}{2}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 6w + 1]$ | $-e^{3} + 2e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}e^{7} - 10e^{5} + 29e^{3} - 20e$ |
| 19 | $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ | $-2e^{7} + 16e^{5} - 33e^{3} + 12e$ |
| 23 | $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ | $-e^{6} + 9e^{4} - 22e^{2} + 4$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}4e^{7} - 32e^{5} + 68e^{3} - 27e$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-e^{7} + 9e^{5} - 25e^{3} + 19e$ |
| 43 | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $-e^{7} + 10e^{5} - 26e^{3} + 9e$ |
| 67 | $[67, 67, w^{2} - w - 5]$ | $\phantom{-}3e^{6} - 23e^{4} + 42e^{2} - 12$ |
| 67 | $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ | $-2e^{7} + 17e^{5} - 40e^{3} + 20e$ |
| 73 | $[73, 73, w^{2} + w + 1]$ | $-4e^{6} + 30e^{4} - 55e^{2} + 14$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ | $\phantom{-}6e^{6} - 49e^{4} + 108e^{2} - 48$ |
| 81 | $[81, 3, -3]$ | $-5e^{6} + 45e^{4} - 110e^{2} + 46$ |
| 83 | $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ | $-2e^{7} + 17e^{5} - 42e^{3} + 27e$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}e^{4} - 6e^{2} - 4$ |
| 89 | $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ | $-5e^{7} + 45e^{5} - 111e^{3} + 56e$ |
| 89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ | $\phantom{-}9e^{7} - 76e^{5} + 174e^{3} - 77e$ |
| 97 | $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ | $\phantom{-}5e^{6} - 44e^{4} + 104e^{2} - 42$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $-1$ |