Base field 4.4.13676.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[10, 10, w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 4x^{2} - 26x + 69\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -w^{2} - w + 3]$ | $\phantom{-}2$ |
| 5 | $[5, 5, w^{3} - 5w + 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{3} + 6w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 4]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 5$ |
| 17 | $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ | $-e + 3$ |
| 37 | $[37, 37, w^{3} + w^{2} - 6w - 3]$ | $-\frac{1}{3}e^{2} + \frac{5}{3}e + 3$ |
| 37 | $[37, 37, -w^{3} + 6w - 4]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 8$ |
| 41 | $[41, 41, -w^{3} + 5w - 5]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - 7$ |
| 43 | $[43, 43, w^{3} - 4w + 4]$ | $-\frac{2}{3}e^{2} + \frac{1}{3}e + 13$ |
| 43 | $[43, 43, -2w^{3} + 11w - 2]$ | $-\frac{2}{3}e^{2} + \frac{1}{3}e + 13$ |
| 47 | $[47, 47, -2w^{3} - w^{2} + 12w]$ | $-\frac{1}{3}e^{2} + \frac{5}{3}e + 7$ |
| 47 | $[47, 47, 2w - 1]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 13$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 5]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - 5$ |
| 71 | $[71, 71, w^{3} + w^{2} - 4w - 3]$ | $-\frac{2}{3}e^{2} - \frac{2}{3}e + 20$ |
| 71 | $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - 1$ |
| 79 | $[79, 79, w^{3} + w^{2} - 6w - 5]$ | $-\frac{2}{3}e^{2} + \frac{1}{3}e + 13$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 15$ |
| 83 | $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ | $-\frac{2}{3}e^{2} + \frac{1}{3}e + 20$ |
| 97 | $[97, 97, w^{3} + w^{2} - 6w + 1]$ | $-e^{2} + 23$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 1]$ | $-1$ |
| $5$ | $[5, 5, w^{3} - 5w + 1]$ | $-1$ |