Base field 3.3.940.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[4, 4, w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 8x^{2} + 2x + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{2} + w + 7]$ | $-\frac{1}{2}e^{3} - e^{2} + 2e + 4$ |
5 | $[5, 5, -w^{2} + w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e + 2$ |
17 | $[17, 17, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - 4e + 2$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-e^{3} + 8e$ |
27 | $[27, 3, 3]$ | $-2e^{2} - 2e + 8$ |
29 | $[29, 29, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 4e$ |
37 | $[37, 37, w^{2} + w + 1]$ | $-\frac{3}{2}e^{3} - e^{2} + 10e$ |
41 | $[41, 41, w^{2} - w - 9]$ | $-\frac{3}{2}e^{3} - e^{2} + 8e + 4$ |
43 | $[43, 43, -3w^{2} + 3w + 17]$ | $\phantom{-}e^{3} + 2e^{2} - 8e - 8$ |
47 | $[47, 47, 2w^{2} - 2w - 13]$ | $-e^{3} - 2e^{2} + 6e + 4$ |
47 | $[47, 47, -2w + 5]$ | $\phantom{-}2e^{2} - 2e - 8$ |
53 | $[53, 53, 3w^{2} - w - 19]$ | $\phantom{-}\frac{3}{2}e^{3} - 8e - 2$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}e^{3} - 10e$ |
67 | $[67, 67, w^{2} + w - 5]$ | $\phantom{-}2e^{2} + 2e - 12$ |
71 | $[71, 71, -3w^{2} + w + 21]$ | $\phantom{-}e^{3} - 4e - 4$ |
79 | $[79, 79, 3w^{2} - w - 23]$ | $\phantom{-}e^{3} - 6e + 8$ |
89 | $[89, 89, 2w^{2} - 4w - 7]$ | $-\frac{3}{2}e^{3} - 2e^{2} + 6e + 14$ |
89 | $[89, 89, -2w^{2} - 2w + 5]$ | $-\frac{1}{2}e^{3} + e^{2} + 6e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 2]$ | $-1$ |