Base field 3.3.1436.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 12\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 4, w^{2} - 2w - 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 15x^{6} + 72x^{4} - 112x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$ |
| 9 | $[9, 3, -w^{2} + 3w + 5]$ | $-\frac{1}{4}e^{7} + \frac{11}{4}e^{5} - 9e^{3} + 10e$ |
| 11 | $[11, 11, -w^{2} + w + 11]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{11}{2}e^{4} + 16e^{2} - 8$ |
| 13 | $[13, 13, 2w^{2} - 4w - 13]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{11}{4}e^{5} + 8e^{3} - 3e$ |
| 23 | $[23, 23, -w^{2} + w + 7]$ | $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - 19e$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $-\frac{1}{4}e^{7} + \frac{11}{4}e^{5} - 7e^{3}$ |
| 41 | $[41, 41, -2w^{2} + 2w + 19]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{15}{4}e^{5} + 19e^{3} - 31e$ |
| 41 | $[41, 41, w^{2} - 3w - 7]$ | $\phantom{-}e^{6} - 10e^{4} + 23e^{2}$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{15}{4}e^{5} + 16e^{3} - 18e$ |
| 47 | $[47, 47, 3w^{2} - 7w - 17]$ | $-e^{4} + 5e^{2} + 4$ |
| 53 | $[53, 53, -2w - 1]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{11}{4}e^{5} + 6e^{3} + 7e$ |
| 61 | $[61, 61, -2w + 7]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{15}{4}e^{5} + 15e^{3} - 11e$ |
| 67 | $[67, 67, 3w^{2} - 5w - 23]$ | $-\frac{1}{2}e^{5} + \frac{5}{2}e^{3} + e$ |
| 67 | $[67, 67, 2w^{2} - 4w - 11]$ | $-\frac{1}{2}e^{7} + \frac{15}{2}e^{5} - 34e^{3} + 42e$ |
| 67 | $[67, 67, 3w^{2} - 7w - 13]$ | $\phantom{-}e^{6} - 8e^{4} + 9e^{2} + 12$ |
| 79 | $[79, 79, w^{2} + w - 5]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 9e$ |
| 89 | $[89, 89, 5w^{2} - 7w - 47]$ | $-e^{4} + 9e^{2} - 12$ |
| 97 | $[97, 97, 5w^{2} - 11w - 29]$ | $-\frac{3}{4}e^{7} + \frac{37}{4}e^{5} - 34e^{3} + 38e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 2]$ | $-1$ |