Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + w + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 15x^{2} + 36x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{7}{2}e - 4$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{9}{2}e - 7$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $\phantom{-}e - 1$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - 5e + 9$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{15}{2}e + 2$ |
| 19 | $[19, 19, -w + 3]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{3}{4}e^{2} - \frac{25}{2}e + 13$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $-e - 3$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 8e + 7$ |
| 25 | $[25, 5, w^{2} - 3]$ | $-e^{2} - e + 8$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{3}{2}e^{3} + e^{2} + \frac{45}{2}e - 25$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{3}{4}e^{2} - \frac{9}{2}e - 2$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 2$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + 6e - 12$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{3}{4}e^{3} - \frac{3}{4}e^{2} + 12e - 4$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{11}{2}e - 13$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 3$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}e^{3} - \frac{1}{2}e^{2} - \frac{35}{2}e + 18$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{3}{4}e^{2} - \frac{23}{2}e + 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + w + 3]$ | $-1$ |