Base field 4.4.5725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 5x^{3} - 3x^{2} - 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w + 1]$ | $\phantom{-}e^{3} + 5e^{2} - 3e - 2$ |
| 11 | $[11, 11, w]$ | $\phantom{-}2e^{3} + 11e^{2} - e - 5$ |
| 11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $\phantom{-}e^{2} + 6e$ |
| 11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $-2e^{3} - 11e^{2} + 4$ |
| 11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $\phantom{-}2e^{3} + 10e^{2} - 5e - 4$ |
| 16 | $[16, 2, 2]$ | $-e^{3} - 5e^{2} + 2e + 1$ |
| 25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $-4e^{3} - 20e^{2} + 11e + 7$ |
| 29 | $[29, 29, -w - 3]$ | $-2e^{2} - 10e + 1$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $\phantom{-}2e^{3} + 11e^{2} - 7$ |
| 31 | $[31, 31, w^{3} - 6w + 1]$ | $-4e^{3} - 22e^{2} + e + 8$ |
| 31 | $[31, 31, w^{3} - 6w - 2]$ | $-e^{2} - 7e$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $-e - 10$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $-2e^{3} - 10e^{2} + 3e + 2$ |
| 59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $\phantom{-}2e^{3} + 11e^{2} - 2e - 9$ |
| 59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $-2e^{3} - 10e^{2} + 8e + 2$ |
| 79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $\phantom{-}1$ |
| 79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $-4e^{3} - 21e^{2} + 6e - 2$ |
| 89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $-e^{3} - 7e^{2} - 7e + 4$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $\phantom{-}e^{2} + 7e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $79$ | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $-1$ |