Base field 4.4.10889.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 16, -w^{2} + 3w]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 4x^{2} - 8x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 1]$ | $\phantom{-}0$ |
7 | $[7, 7, -w + 2]$ | $\phantom{-}e$ |
8 | $[8, 2, -w^{3} + 5w + 3]$ | $\phantom{-}\frac{1}{4}e^{2} - e + 1$ |
11 | $[11, 11, w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 4$ |
11 | $[11, 11, w^{3} - w^{2} - 4w + 1]$ | $-e + 4$ |
17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $-\frac{1}{2}e^{2} + 2e + 2$ |
25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}2$ |
25 | $[25, 5, -w^{2} + 2]$ | $\phantom{-}e^{2} - 4e - 6$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $-\frac{1}{2}e^{2} + e + 2$ |
29 | $[29, 29, -w^{3} + 4w + 2]$ | $-\frac{1}{2}e^{2} + e + 6$ |
37 | $[37, 37, 4w^{3} - 2w^{2} - 21w - 4]$ | $-\frac{1}{2}e^{2} + 6$ |
43 | $[43, 43, 4w^{3} - 2w^{2} - 20w - 3]$ | $-e + 4$ |
47 | $[47, 47, -w^{3} + 6w]$ | $\phantom{-}\frac{1}{2}e^{2} + e - 12$ |
53 | $[53, 53, w^{3} - w^{2} - 5w - 2]$ | $-3e + 6$ |
81 | $[81, 3, -3]$ | $-e^{2} + 3e + 10$ |
83 | $[83, 83, 2w^{3} - w^{2} - 10w - 4]$ | $\phantom{-}2e - 4$ |
89 | $[89, 89, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{3}{2}e^{2} - 4e - 6$ |
89 | $[89, 89, 2w - 3]$ | $\phantom{-}2e - 6$ |
101 | $[101, 101, 6w^{3} - 3w^{2} - 31w - 5]$ | $-2e^{2} + 6e + 14$ |
107 | $[107, 107, -w^{3} + w^{2} + 4w - 5]$ | $-\frac{1}{2}e^{2} + 3e + 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 1]$ | $1$ |