Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[8, 2, 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 14x^{4} + 36x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{3}{2}e^{3} + \frac{5}{2}e$ |
7 | $[7, 7, w - 3]$ | $-\frac{1}{2}e^{2} + 1$ |
8 | $[8, 2, 2]$ | $-1$ |
9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{7}{2}e^{3} + 8e$ |
13 | $[13, 13, w + 3]$ | $-\frac{1}{4}e^{4} + 3e^{2} - 3$ |
13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{1}{4}e^{4} - 3e^{2} + 1$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{1}{4}e^{5} + 3e^{3} - 6e$ |
23 | $[23, 23, w^{2} - 4w + 1]$ | $-\frac{1}{4}e^{4} + 3e^{2} - 5$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{3}{4}e^{5} + \frac{19}{2}e^{3} - 18e$ |
31 | $[31, 31, w^{2} - 2w - 9]$ | $\phantom{-}\frac{5}{8}e^{5} - \frac{17}{2}e^{3} + \frac{37}{2}e$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - 11e$ |
41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{8}e^{5} - 2e^{3} + \frac{21}{2}e$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{5}{8}e^{5} + 9e^{3} - \frac{55}{2}e$ |
41 | $[41, 41, w^{2} - w - 10]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 1$ |
43 | $[43, 43, -2w - 3]$ | $-\frac{3}{8}e^{5} + 5e^{3} - \frac{21}{2}e$ |
47 | $[47, 47, -w^{2} - w + 4]$ | $-\frac{1}{4}e^{4} + 2e^{2} - 1$ |
49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - 6e^{2} + 12$ |
59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{3}{2}e^{3} + \frac{5}{2}e$ |
59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{5}{8}e^{5} - 8e^{3} + \frac{29}{2}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$8$ | $[8, 2, 2]$ | $1$ |