Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 2, w^{3} - w^{2} - 5w + 3]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 4x^{4} - 3x^{3} - 22x^{2} - 19x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{3} + 5w + 1]$ | $\phantom{-}2e^{4} + 7e^{3} - 10e^{2} - 39e - 16$ |
11 | $[11, 11, -w + 2]$ | $-2e^{4} - 6e^{3} + 11e^{2} + 32e + 12$ |
13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $-2e - 2$ |
17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-e^{3} - 2e^{2} + 7e + 6$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $-e^{4} - 4e^{3} + 4e^{2} + 22e + 10$ |
23 | $[23, 23, w^{3} - 6w]$ | $-2e^{4} - 6e^{3} + 12e^{2} + 32e + 8$ |
27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}2e^{4} + 6e^{3} - 10e^{2} - 31e - 16$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $\phantom{-}2e^{4} + 6e^{3} - 12e^{2} - 32e - 14$ |
41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-2e^{3} - 4e^{2} + 13e + 14$ |
53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $-2e^{4} - 6e^{3} + 12e^{2} + 32e + 6$ |
59 | $[59, 59, 2w^{3} - 11w - 2]$ | $\phantom{-}3e^{4} + 10e^{3} - 16e^{2} - 56e - 20$ |
67 | $[67, 67, w^{3} - 7w - 1]$ | $\phantom{-}e^{4} + 4e^{3} - 4e^{2} - 26e - 20$ |
71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}0$ |
79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $\phantom{-}2e^{4} + 8e^{3} - 8e^{2} - 48e - 24$ |
89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $-2e^{4} - 5e^{3} + 12e^{2} + 25e + 6$ |
101 | $[101, 101, -2w^{3} + 13w + 6]$ | $-2e^{4} - 8e^{3} + 8e^{2} + 50e + 30$ |
101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}4e^{4} + 14e^{3} - 20e^{2} - 82e - 34$ |
101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $\phantom{-}4e^{4} + 14e^{3} - 20e^{2} - 76e - 34$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 1]$ | $-1$ |