Base field 4.4.725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 3x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 2x^{2} - 20x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $-\frac{1}{2}e + 1$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{4}e^{2} - \frac{3}{2}e + 3$ |
| 19 | $[19, 19, -w^{3} + 2w + 2]$ | $-\frac{1}{4}e^{2} + 5$ |
| 19 | $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ | $-\frac{1}{8}e^{2} - \frac{1}{2}e + \frac{3}{2}$ |
| 25 | $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}\frac{3}{4}e^{2} + e - 9$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{4}e^{2} + e - 1$ |
| 31 | $[31, 31, w^{3} - 4w + 1]$ | $-\frac{1}{8}e^{2} + \frac{1}{2}e + \frac{3}{2}$ |
| 31 | $[31, 31, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{2} - 6$ |
| 41 | $[41, 41, 2w^{2} - w - 3]$ | $-\frac{1}{4}e^{2} - e + 5$ |
| 41 | $[41, 41, -w^{3} + 3w^{2} + w - 4]$ | $-\frac{7}{8}e^{2} - \frac{1}{2}e + \frac{25}{2}$ |
| 49 | $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ | $\phantom{-}\frac{1}{8}e^{2} + \frac{1}{2}e + \frac{1}{2}$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}\frac{1}{8}e^{2} - \frac{3}{2}e - \frac{19}{2}$ |
| 61 | $[61, 61, 2w^{3} - 3w^{2} - 4w]$ | $\phantom{-}\frac{7}{8}e^{2} + \frac{7}{2}e - \frac{25}{2}$ |
| 61 | $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ | $-\frac{1}{8}e^{2} + \frac{1}{2}e - \frac{5}{2}$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 15$ |
| 79 | $[79, 79, w^{3} + w^{2} - 3w - 5]$ | $\phantom{-}\frac{1}{4}e^{2} + 2e + 3$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{4}e^{2} + \frac{3}{2}e - 6$ |
| 89 | $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ | $-e^{2} + e + 18$ |
| 89 | $[89, 89, 3w^{3} - 2w^{2} - 7w]$ | $-\frac{1}{4}e^{2} - \frac{1}{2}e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $169$ | $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$ | $1$ |