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: | $[1381,1381,-9w - 34]$ |
| Dimension: | $19$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{19} - 7x^{18} - 33x^{17} + 325x^{16} + 209x^{15} - 5929x^{14} + 4361x^{13} + 53883x^{12} - 79790x^{11} - 254924x^{10} + 528428x^{9} + 585068x^{8} - 1709688x^{7} - 408624x^{6} + 2740352x^{5} - 579520x^{4} - 1886592x^{3} + 897792x^{2} + 292864x - 176128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -2w + 1]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, -3w + 2]$ | $...$ |
| 11 | $[11, 11, -3w + 1]$ | $...$ |
| 19 | $[19, 19, -4w + 3]$ | $...$ |
| 19 | $[19, 19, -4w + 1]$ | $...$ |
| 29 | $[29, 29, w + 5]$ | $...$ |
| 29 | $[29, 29, -w + 6]$ | $...$ |
| 31 | $[31, 31, -5w + 2]$ | $...$ |
| 31 | $[31, 31, -5w + 3]$ | $...$ |
| 41 | $[41, 41, -6w + 5]$ | $...$ |
| 41 | $[41, 41, w - 7]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 59 | $[59, 59, 2w - 9]$ | $...$ |
| 59 | $[59, 59, 7w - 5]$ | $...$ |
| 61 | $[61, 61, 3w - 10]$ | $...$ |
| 61 | $[61, 61, -3w - 7]$ | $...$ |
| 71 | $[71, 71, -8w + 7]$ | $...$ |
| 71 | $[71, 71, w - 9]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $1381$ | $[1381,1381,-9w - 34]$ | $1$ |