Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 9x^{6} + 25x^{4} - 21x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 5w + 2]$ | $-e^{7} + 8e^{5} - 18e^{3} + 9e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e^{2} - 4$ |
| 11 | $[11, 11, -w^{3} + 5w]$ | $\phantom{-}e^{5} - 7e^{3} + 12e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}e^{7} - 8e^{5} + 20e^{3} - 17e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}1$ |
| 19 | $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ | $\phantom{-}e^{7} - 10e^{5} + 29e^{3} - 22e$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $-e^{7} + 10e^{5} - 27e^{3} + 14e$ |
| 27 | $[27, 3, w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}e^{7} - 8e^{5} + 18e^{3} - 12e$ |
| 31 | $[31, 31, -w - 3]$ | $-e^{6} + 4e^{4} - 2$ |
| 37 | $[37, 37, -w^{3} - w^{2} + 6w + 4]$ | $-e^{3} + 4e$ |
| 41 | $[41, 41, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}2e^{5} - 11e^{3} + 13e$ |
| 43 | $[43, 43, w^{3} - 7w - 2]$ | $-e^{6} + 8e^{4} - 17e^{2}$ |
| 47 | $[47, 47, -2w^{3} + 11w + 2]$ | $-e^{7} + 6e^{5} - 10e^{3} + 5e$ |
| 61 | $[61, 61, w^{2} - 3]$ | $-3e^{7} + 24e^{5} - 57e^{3} + 39e$ |
| 67 | $[67, 67, w^{2} + w - 4]$ | $-4e^{6} + 26e^{4} - 45e^{2} + 16$ |
| 79 | $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ | $\phantom{-}e^{7} - 8e^{5} + 20e^{3} - 11e$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ | $\phantom{-}e^{6} - 6e^{4} + 13e^{2} - 14$ |
| 97 | $[97, 97, -w^{3} + 6w - 3]$ | $\phantom{-}4e^{6} - 28e^{4} + 49e^{2} - 16$ |
| 97 | $[97, 97, -3w^{3} + 16w]$ | $\phantom{-}2e^{7} - 23e^{5} + 76e^{3} - 62e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $-1$ |