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: | $[151,151,-5w - 11]$ |
| 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:
| \(x^{3} - x^{2} - 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -2w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{3}{2}$ |
| 9 | $[9, 3, 3]$ | $-\frac{3}{2}e^{2} + e + \frac{9}{2}$ |
| 11 | $[11, 11, -3w + 2]$ | $-e^{2} - e + 4$ |
| 11 | $[11, 11, -3w + 1]$ | $\phantom{-}e^{2} - 2e - 3$ |
| 19 | $[19, 19, -4w + 3]$ | $-e^{2} + e + 2$ |
| 19 | $[19, 19, -4w + 1]$ | $\phantom{-}e^{2} - 5$ |
| 29 | $[29, 29, w + 5]$ | $\phantom{-}e^{2} + 2e - 5$ |
| 29 | $[29, 29, -w + 6]$ | $\phantom{-}2e^{2} - 2e - 10$ |
| 31 | $[31, 31, -5w + 2]$ | $-\frac{3}{2}e^{2} + 5e + \frac{13}{2}$ |
| 31 | $[31, 31, -5w + 3]$ | $\phantom{-}e^{2} + 2e - 3$ |
| 41 | $[41, 41, -6w + 5]$ | $-2e^{2} + 2e + 6$ |
| 41 | $[41, 41, w - 7]$ | $\phantom{-}\frac{5}{2}e^{2} - 3e - \frac{11}{2}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{2}e^{2} - e + \frac{9}{2}$ |
| 59 | $[59, 59, 2w - 9]$ | $-4e + 4$ |
| 59 | $[59, 59, 7w - 5]$ | $\phantom{-}\frac{7}{2}e^{2} - 3e - \frac{25}{2}$ |
| 61 | $[61, 61, 3w - 10]$ | $-\frac{5}{2}e^{2} + e + \frac{11}{2}$ |
| 61 | $[61, 61, -3w - 7]$ | $-2e^{2} + 6e + 6$ |
| 71 | $[71, 71, -8w + 7]$ | $-e^{2} + 4e + 1$ |
| 71 | $[71, 71, w - 9]$ | $-\frac{5}{2}e^{2} + e + \frac{31}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $151$ | $[151,151,-5w - 11]$ | $1$ |