Base field 3.3.1425.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w^{2} - 2w - 8]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 4x^{15} - 24x^{14} + 98x^{13} + 229x^{12} - 914x^{11} - 1184x^{10} + 4131x^{9} + 3785x^{8} - 9423x^{7} - 7483x^{6} + 10084x^{5} + 7824x^{4} - 3840x^{3} - 2944x^{2} + 256x + 192\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $...$ |
| 5 | $[5, 5, w^{2} - w - 7]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 11 | $[11, 11, w - 1]$ | $...$ |
| 13 | $[13, 13, w^{2} - 2w - 8]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{2} - 2w - 7]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $...$ |
| 19 | $[19, 19, -2w^{2} + 3w + 16]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 2w + 2]$ | $...$ |
| 31 | $[31, 31, 2w^{2} - 3w - 13]$ | $...$ |
| 37 | $[37, 37, w^{2} - w - 10]$ | $...$ |
| 43 | $[43, 43, 3w^{2} - 5w - 19]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $...$ |
| 47 | $[47, 47, w^{2} - 2]$ | $...$ |
| 67 | $[67, 67, w^{2} - 3w - 5]$ | $...$ |
| 79 | $[79, 79, -w^{2} + 3w - 1]$ | $...$ |
| 83 | $[83, 83, w^{2} + w - 4]$ | $...$ |
| 97 | $[97, 97, w^{2} - 11]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} - 2w - 8]$ | $-1$ |