Base field 3.3.1373.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -w + 2]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 7x^{17} - 4x^{16} + 126x^{15} - 154x^{14} - 823x^{13} + 1685x^{12} + 2322x^{11} - 6965x^{10} - 2333x^{9} + 13880x^{8} - 1076x^{7} - 13774x^{6} + 3262x^{5} + 6333x^{4} - 1612x^{3} - 1020x^{2} + 205x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $...$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}1$ |
| 25 | $[25, 5, w^{2} - 8]$ | $...$ |
| 29 | $[29, 29, 2w + 3]$ | $...$ |
| 37 | $[37, 37, w + 4]$ | $...$ |
| 37 | $[37, 37, -3w^{2} + 2w + 24]$ | $...$ |
| 37 | $[37, 37, w^{2} + 2w - 2]$ | $...$ |
| 47 | $[47, 47, w^{2} - 2]$ | $...$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $...$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $...$ |
| 71 | $[71, 71, 2w - 1]$ | $...$ |
| 71 | $[71, 71, -w^{2} + 4w + 2]$ | $...$ |
| 71 | $[71, 71, -w^{2} + 4w - 2]$ | $...$ |
| 73 | $[73, 73, -w^{2} + 4w + 4]$ | $...$ |
| 79 | $[79, 79, -2w + 7]$ | $...$ |
| 83 | $[83, 83, -2w^{2} + 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w + 2]$ | $-1$ |