Base field \(\Q(\sqrt{2}, \sqrt{5})\)
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[49,7,-\frac{1}{2}w^{3} + 2w - 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 5x^{2} + 3x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 2w]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} - 3e + \frac{5}{2}$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} - 3e + \frac{5}{2}$ |
| 25 | $[25, 5, w^{2} - 3]$ | $-3e^{2} + 10e + 1$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w]$ | $\phantom{-}\frac{5}{2}e^{2} - 7e - \frac{11}{2}$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} - w + 3]$ | $-2e^{2} + 7e - 3$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + w + 3]$ | $\phantom{-}\frac{5}{2}e^{2} - 7e - \frac{11}{2}$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w]$ | $-2e^{2} + 7e - 3$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - w + 3]$ | $-2e^{2} + 9e - 3$ |
| 41 | $[41, 41, w^{3} + w^{2} - 5w - 3]$ | $-2e^{2} + 9e - 3$ |
| 41 | $[41, 41, -\frac{3}{2}w^{2} - w + 5]$ | $-2e^{2} + 2e + 12$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - w^{2} + w + 3]$ | $-2e^{2} + 2e + 12$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + 2w - 3]$ | $-1$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - 2w - 3]$ | $\phantom{-}3e^{2} - 10e + 5$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 5]$ | $\phantom{-}2e - 8$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 5]$ | $\phantom{-}2e - 8$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 5]$ | $-\frac{3}{2}e^{2} + 3e + \frac{29}{2}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 5]$ | $-\frac{3}{2}e^{2} + 3e + \frac{29}{2}$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} - 3e + \frac{5}{2}$ |
| 79 | $[79, 79, -w^{3} - \frac{1}{2}w^{2} + 6w]$ | $\phantom{-}2e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49,7,-\frac{1}{2}w^{3} + 2w - 3]$ | $1$ |