Base field \(\Q(\sqrt{5}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[181, 181, -14w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{2} + 8x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -2w + 1]$ | $-e^{3} - \frac{1}{2}e^{2} + 11e - \frac{5}{2}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}$ |
| 11 | $[11, 11, -3w + 2]$ | $\phantom{-}\frac{5}{2}e^{3} + e^{2} - \frac{61}{2}e + 9$ |
| 11 | $[11, 11, -3w + 1]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{37}{2}e + 8$ |
| 19 | $[19, 19, -4w + 3]$ | $-2e^{3} - e^{2} + 24e - 7$ |
| 19 | $[19, 19, -4w + 1]$ | $\phantom{-}\frac{5}{2}e^{3} + e^{2} - \frac{57}{2}e + 7$ |
| 29 | $[29, 29, w + 5]$ | $\phantom{-}e^{2} + 2e - 5$ |
| 29 | $[29, 29, -w + 6]$ | $-4e^{3} - 2e^{2} + 46e - 14$ |
| 31 | $[31, 31, -5w + 2]$ | $-4e^{3} - 2e^{2} + 46e - 12$ |
| 31 | $[31, 31, -5w + 3]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{11}{2}e + 1$ |
| 41 | $[41, 41, -6w + 5]$ | $-2e^{3} + 24e - 10$ |
| 41 | $[41, 41, w - 7]$ | $-2e^{3} - \frac{1}{2}e^{2} + 26e - \frac{15}{2}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}3e^{3} + e^{2} - 35e + 7$ |
| 59 | $[59, 59, 2w - 9]$ | $\phantom{-}\frac{9}{2}e^{3} + e^{2} - \frac{111}{2}e + 23$ |
| 59 | $[59, 59, 7w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{9}{2}e - 5$ |
| 61 | $[61, 61, 3w - 10]$ | $-3e^{3} - \frac{1}{2}e^{2} + 37e - \frac{17}{2}$ |
| 61 | $[61, 61, -3w - 7]$ | $\phantom{-}e^{3} - e^{2} - 11e + 17$ |
| 71 | $[71, 71, -8w + 7]$ | $\phantom{-}e^{3} - 11e + 2$ |
| 71 | $[71, 71, w - 9]$ | $\phantom{-}e^{3} - 13e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $181$ | $[181, 181, -14w - 1]$ | $1$ |