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: | $[16, 2, 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - 11x^{3} - 21x^{2} + 34x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -w^{2} + 7]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $\phantom{-}e$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $-\frac{1}{3}e^{4} - \frac{2}{3}e^{3} + \frac{10}{3}e^{2} + \frac{11}{3}e - 5$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $-\frac{1}{3}e^{4} - \frac{2}{3}e^{3} + \frac{10}{3}e^{2} + \frac{11}{3}e - 5$ |
| 31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{2}{3}e^{3} - \frac{7}{3}e^{2} - \frac{5}{3}e + 1$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{2}{3}e^{3} - \frac{7}{3}e^{2} - \frac{5}{3}e + 1$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $\phantom{-}e^{2} + e$ |
| 41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $-2e^{2} - 3e + 9$ |
| 41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $-2e^{2} - 3e + 9$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $\phantom{-}e^{2} + e$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{17}{3}e^{2} - \frac{46}{3}e + 15$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{17}{3}e^{2} - \frac{46}{3}e + 15$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $-e^{4} - 3e^{3} + 9e^{2} + 18e - 15$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $-e^{4} - 3e^{3} + 9e^{2} + 18e - 15$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{14}{3}e^{2} - \frac{49}{3}e + 5$ |
| 89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $-\frac{2}{3}e^{4} - \frac{10}{3}e^{3} + \frac{14}{3}e^{2} + \frac{64}{3}e - 16$ |
| 89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $\phantom{-}2e^{2} + 5e - 12$ |
| 89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $\phantom{-}2e^{2} + 5e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{2} - 2w - 6]$ | $-1$ |
| $4$ | $[4, 2, -w^{2} + 7]$ | $-1$ |