Base field 4.4.12400.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 30x^{6} + 260x^{4} - 600x^{2} + 400\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ | $\phantom{-}\frac{3}{50}e^{7} - \frac{17}{10}e^{5} + \frac{64}{5}e^{3} - 15e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ | $\phantom{-}\frac{3}{50}e^{7} - \frac{17}{10}e^{5} + \frac{64}{5}e^{3} - 15e$ |
| 19 | $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ | $-\frac{1}{25}e^{7} + \frac{11}{10}e^{5} - \frac{41}{5}e^{3} + 12e$ |
| 19 | $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ | $-\frac{1}{25}e^{7} + \frac{11}{10}e^{5} - \frac{41}{5}e^{3} + 12e$ |
| 29 | $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ | $\phantom{-}\frac{1}{10}e^{6} - \frac{13}{5}e^{4} + 17e^{2} - 14$ |
| 29 | $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ | $\phantom{-}\frac{1}{10}e^{6} - \frac{13}{5}e^{4} + 17e^{2} - 14$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-\frac{9}{50}e^{7} + \frac{26}{5}e^{5} - \frac{202}{5}e^{3} + 52e$ |
| 59 | $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ | $-\frac{1}{5}e^{6} + 6e^{4} - 48e^{2} + 60$ |
| 59 | $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ | $-\frac{1}{5}e^{6} + 6e^{4} - 48e^{2} + 60$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ | $\phantom{-}\frac{2}{25}e^{7} - \frac{12}{5}e^{5} + \frac{97}{5}e^{3} - 27e$ |
| 61 | $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}\frac{2}{25}e^{7} - \frac{12}{5}e^{5} + \frac{97}{5}e^{3} - 27e$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ | $\phantom{-}\frac{1}{10}e^{7} - \frac{14}{5}e^{5} + 20e^{3} - 16e$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ | $\phantom{-}\frac{1}{10}e^{7} - \frac{14}{5}e^{5} + 20e^{3} - 16e$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ | $-\frac{9}{50}e^{7} + 5e^{5} - \frac{182}{5}e^{3} + 40e$ |
| 79 | $[79, 79, -2w^{2} + w + 10]$ | $-\frac{1}{10}e^{6} + 3e^{4} - 24e^{2} + 32$ |
| 79 | $[79, 79, 2w^{2} + w - 10]$ | $-\frac{1}{10}e^{6} + 3e^{4} - 24e^{2} + 32$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ | $-\frac{9}{50}e^{7} + 5e^{5} - \frac{182}{5}e^{3} + 40e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,-\frac{1}{2}w^{3}-\frac{1}{2}w^{2}+\frac{7}{2}w+\frac{11}{2}]$ | $1$ |