Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{2} + w + 3]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} + 8x^{17} + 5x^{16} - 114x^{15} - 263x^{14} + 496x^{13} + 2040x^{12} - 210x^{11} - 6704x^{10} - 3748x^{9} + 10502x^{8} + 9904x^{7} - 7554x^{6} - 10072x^{5} + 1744x^{4} + 4314x^{3} + 330x^{2} - 600x - 125\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 2w - 3]$ | $...$ |
| 5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $...$ |
| 8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + 3w + 1]$ | $...$ |
| 23 | $[23, 23, w^{2} - 3]$ | $...$ |
| 25 | $[25, 5, -w^{2} + 2w + 1]$ | $...$ |
| 37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $...$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $...$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $...$ |
| 59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $...$ |
| 67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $...$ |
| 71 | $[71, 71, 2w - 3]$ | $...$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $...$ |
| 79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $...$ |
| 79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
| 83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{2} + w + 3]$ | $-1$ |