Base field 4.4.17600.1
Generator \(w\), with minimal polynomial \(x^{4} - 14x^{2} + 44\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 36x^{6} + 424x^{4} - 1648x^{2} + 320\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ | $-\frac{1}{8}e^{6} + 3e^{4} - 18e^{2} + 8$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 11e$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 11e$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ | $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 17e$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + 14e^{2}$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + 14e^{2}$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ | $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 17e$ |
| 25 | $[25, 5, \frac{1}{2}w^{2} - 1]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + 14e^{2} + 6$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{3}{2}e^{5} + 10e^{3} - 17e$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{3}{2}e^{5} + 10e^{3} - 17e$ |
| 31 | $[31, 31, -w - 1]$ | $-\frac{1}{2}e^{3} + 6e$ |
| 31 | $[31, 31, w - 1]$ | $-\frac{1}{2}e^{3} + 6e$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ | $-\frac{1}{16}e^{7} + \frac{11}{8}e^{5} - \frac{13}{2}e^{3} - 7e$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ | $-\frac{1}{16}e^{7} + \frac{11}{8}e^{5} - \frac{13}{2}e^{3} - 7e$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ | $-\frac{1}{16}e^{7} + \frac{13}{8}e^{5} - 12e^{3} + 21e$ |
| 49 | $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ | $-\frac{1}{16}e^{7} + \frac{13}{8}e^{5} - 12e^{3} + 21e$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ | $-\frac{1}{8}e^{6} + \frac{5}{2}e^{4} - 11e^{2}$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ | $-\frac{1}{8}e^{6} + \frac{5}{2}e^{4} - 11e^{2}$ |
| 61 | $[61, 61, \frac{1}{2}w^{2} + w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} - 2e^{2} - 12$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).