Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + 3w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{3} - 4x^{2} + 16x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 3e + 4$ |
| 5 | $[5, 5, w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - 2e + 1$ |
| 5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 4e + 4$ |
| 8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{2}e^{2} + 5$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 2$ |
| 17 | $[17, 17, -w^{2} + 3w + 1]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{2} - 3]$ | $-e^{3} + 3e^{2} + 6e - 8$ |
| 25 | $[25, 5, -w^{2} + 2w + 1]$ | $-\frac{3}{4}e^{3} + \frac{5}{2}e^{2} + 4e - 7$ |
| 37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $-e^{3} + \frac{7}{2}e^{2} + 5e - 10$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}3e^{3} - 9e^{2} - 18e + 24$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $-\frac{5}{4}e^{3} + 5e^{2} + 5e - 15$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}2e^{3} - \frac{11}{2}e^{2} - 13e + 14$ |
| 59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{9}{2}e^{2} - 12e + 15$ |
| 67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 4e + 3$ |
| 71 | $[71, 71, 2w - 3]$ | $-\frac{5}{4}e^{3} + 3e^{2} + 9e - 7$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $-\frac{7}{2}e^{3} + \frac{21}{2}e^{2} + 28e - 36$ |
| 79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + e - 8$ |
| 79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $-\frac{3}{2}e^{3} + \frac{7}{2}e^{2} + 11e - 8$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{3} - 3e^{2} - 8e + 15$ |
| 83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $-\frac{11}{4}e^{3} + 9e^{2} + 15e - 25$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + 3w + 1]$ | $-1$ |