Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, w^{3} - 5w + 3]$ |
Dimension: | $5$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 10x^{4} + 20x^{3} + 40x^{2} - 80x - 80\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, w^{3} - 5w + 3]$ | $-1$ |
9 | $[9, 3, w^{3} - 5w + 2]$ | $\phantom{-}e$ |
13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - \frac{1}{2}e^{2} + 3e + 4$ |
13 | $[13, 13, w^{3} - 6w + 4]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - \frac{1}{2}e^{2} + 3e + 4$ |
16 | $[16, 2, 2]$ | $-\frac{1}{4}e^{4} + \frac{9}{4}e^{3} - \frac{7}{2}e^{2} - 6e + 7$ |
17 | $[17, 17, w^{2} + w - 2]$ | $-\frac{1}{8}e^{4} + \frac{3}{4}e^{3} + e^{2} - 6e - 2$ |
17 | $[17, 17, w^{2} + w - 5]$ | $-\frac{1}{8}e^{4} + \frac{3}{4}e^{3} + e^{2} - 6e - 2$ |
23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $-\frac{1}{4}e^{3} + \frac{3}{2}e^{2} + e - 6$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $-\frac{1}{4}e^{3} + \frac{3}{2}e^{2} + e - 6$ |
25 | $[25, 5, -w^{2} + 3]$ | $-\frac{1}{4}e^{4} + 2e^{3} - \frac{5}{2}e^{2} - 5e + 6$ |
25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $-\frac{1}{4}e^{4} + 2e^{3} - \frac{5}{2}e^{2} - 5e + 6$ |
29 | $[29, 29, -w^{2} - 2w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} - 2e^{3} + 2e^{2} + 7e$ |
29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} - 2e^{3} + 2e^{2} + 7e$ |
43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $-\frac{1}{2}e^{3} + 3e^{2} - e - 6$ |
43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $-\frac{1}{2}e^{3} + 3e^{2} - e - 6$ |
53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $-\frac{1}{2}e^{3} + 5e^{2} - 8e - 16$ |
53 | $[53, 53, w^{2} + 2w - 5]$ | $-\frac{1}{2}e^{3} + 5e^{2} - 8e - 16$ |
61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e^{2} + 7e + 12$ |
61 | $[61, 61, w^{3} - 7w + 3]$ | $-\frac{1}{4}e^{4} + \frac{5}{2}e^{3} - 5e^{2} - 10e + 12$ |
61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e^{2} + 7e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, w^{3} - 5w + 3]$ | $1$ |