Base field 3.3.1849.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 14x - 8\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[8, 4, -w]$ |
Dimension: | $5$ |
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:
\(x^{5} - x^{4} - 8x^{3} + 8x^{2} + 11x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $\phantom{-}0$ |
2 | $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ | $-1$ |
2 | $[2, 2, w + 3]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}e^{3} - 5e$ |
11 | $[11, 11, -2w - 1]$ | $-e^{4} + 8e^{2} - 9$ |
11 | $[11, 11, -w^{2} + w + 11]$ | $-e^{4} + 6e^{2} - 3$ |
27 | $[27, 3, 3]$ | $-e^{3} + 7e - 2$ |
41 | $[41, 41, 2w + 5]$ | $\phantom{-}2e^{4} - 12e^{2} + 2e + 6$ |
41 | $[41, 41, -w^{2} + 3w + 3]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 6$ |
41 | $[41, 41, -w^{2} + w + 15]$ | $-2e^{4} + 14e^{2} - 18$ |
43 | $[43, 43, -3w^{2} + 11w + 11]$ | $-2e^{4} - e^{3} + 16e^{2} + 5e - 22$ |
47 | $[47, 47, -w^{2} - w + 5]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 8e + 3$ |
47 | $[47, 47, w^{2} - 5w - 3]$ | $\phantom{-}2e^{4} + 2e^{3} - 16e^{2} - 8e + 24$ |
47 | $[47, 47, -2w^{2} + 4w + 23]$ | $-e^{4} + e^{3} + 8e^{2} - 3e - 15$ |
59 | $[59, 59, -w^{2} + w + 13]$ | $\phantom{-}2e^{3} + 2e^{2} - 10e - 6$ |
59 | $[59, 59, w^{2} - 3w - 5]$ | $-e^{4} + 8e^{2} - 2e - 9$ |
59 | $[59, 59, -2w - 3]$ | $-3e^{4} - e^{3} + 22e^{2} + e - 21$ |
97 | $[97, 97, 7w^{2} - 11w - 91]$ | $\phantom{-}2e^{4} - 16e^{2} + 20$ |
97 | $[97, 97, -2w^{2} - 8w - 5]$ | $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 10e + 17$ |
97 | $[97, 97, 5w^{2} - 19w - 15]$ | $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 14e + 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $-1$ |
$2$ | $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ | $1$ |