Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 8x^{4} + 10x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $\phantom{-}e^{4} - 7e^{2} + 5$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $-e^{5} + 8e^{3} - 11e$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $\phantom{-}e^{3} - 6e$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $\phantom{-}2e^{5} - 16e^{3} + 20e$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}3e^{5} - 23e^{3} + 21e$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $-4e^{5} + 30e^{3} - 26e$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $\phantom{-}2e^{5} - 15e^{3} + 14e$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}2e^{5} - 17e^{3} + 22e$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $-e^{4} + 7e^{2} - 2$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $-e^{5} + 8e^{3} - 9e$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $-e^{5} + 10e^{3} - 23e$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $\phantom{-}2e^{4} - 12e^{2} + 6$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $-4e^{5} + 30e^{3} - 28e$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $-e^{4} + 9e^{2} - 8$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $-e^{5} + 7e^{3} - e$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $-5e^{5} + 38e^{3} - 37e$ |
| 81 | $[81, 3, -3]$ | $-2e^{4} + 16e^{2} - 19$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).