Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 82x^{16} + 8x^{15} + 2719x^{14} - 400x^{13} - 46840x^{12} + 6543x^{11} + 448861x^{10} - 32133x^{9} - 2376546x^{8} - 105626x^{7} + 6406238x^{6} + 1112705x^{5} - 7091813x^{4} - 1663416x^{3} + 2455521x^{2} + 828062x + 48904\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2w^{2} - 2w - 13]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 9]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 2w + 6]$ | $...$ |
| 29 | $[29, 29, w^{2} - 7]$ | $...$ |
| 29 | $[29, 29, -w^{2} + 2w + 8]$ | $...$ |
| 31 | $[31, 31, -2w^{2} + w + 12]$ | $...$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $...$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $...$ |
| 49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - 3w - 14]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |