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: | $[4,2,\frac{1}{2}w^{2} + \frac{3}{2}w + 1]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 2x^{2} - 3x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $\phantom{-}e$ |
2 | $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ | $\phantom{-}1$ |
2 | $[2, 2, w + 3]$ | $-1$ |
11 | $[11, 11, -w^{2} + 3w + 7]$ | $-e^{2} + 2e + 1$ |
11 | $[11, 11, -2w - 1]$ | $-e^{2} + 4e + 1$ |
11 | $[11, 11, -w^{2} + w + 11]$ | $-2e^{2} + 2e + 4$ |
27 | $[27, 3, 3]$ | $-2e^{2} + 4e$ |
41 | $[41, 41, 2w + 5]$ | $\phantom{-}2e - 2$ |
41 | $[41, 41, -w^{2} + 3w + 3]$ | $-2e + 8$ |
41 | $[41, 41, -w^{2} + w + 15]$ | $-e^{2} + 4e + 1$ |
43 | $[43, 43, -3w^{2} + 11w + 11]$ | $-6$ |
47 | $[47, 47, -w^{2} - w + 5]$ | $-e^{2} + 3$ |
47 | $[47, 47, w^{2} - 5w - 3]$ | $-3e^{2} + 2e + 5$ |
47 | $[47, 47, -2w^{2} + 4w + 23]$ | $\phantom{-}2e^{2} - 4e - 2$ |
59 | $[59, 59, -w^{2} + w + 13]$ | $\phantom{-}2e^{2} - 2e - 10$ |
59 | $[59, 59, w^{2} - 3w - 5]$ | $-4e + 8$ |
59 | $[59, 59, -2w - 3]$ | $-2e^{2} + 10$ |
97 | $[97, 97, 7w^{2} - 11w - 91]$ | $\phantom{-}6e^{2} - 12e - 12$ |
97 | $[97, 97, -2w^{2} - 8w - 5]$ | $\phantom{-}4e^{2} - 12e - 10$ |
97 | $[97, 97, 5w^{2} - 19w - 15]$ | $-2e^{2} + 2e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,\frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ | $-1$ |
$2$ | $[2,2,w + 3]$ | $1$ |