Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16,4,w^{2} - 2w - 7]$ |
| Dimension: | $14$ |
| 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:
| \(x^{14} + 6x^{13} - 14x^{12} - 141x^{11} - 60x^{10} + 1043x^{9} + 1491x^{8} - 2425x^{7} - 5740x^{6} - 360x^{5} + 4765x^{4} + 1475x^{3} - 1045x^{2} - 150x + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + 7]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $...$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $...$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $...$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $...$ |
| 31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $...$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $...$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $...$ |
| 41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $...$ |
| 41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $...$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $...$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $...$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $...$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $...$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
| 89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $...$ |
| 89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $...$ |
| 89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,w^{2} - 7]$ | $-1$ |