Base field 6.6.980125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 5x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 16x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{2} + 2]$ | $-\frac{1}{8}e^{3} + \frac{3}{2}e$ |
11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $-\frac{1}{8}e^{3} + \frac{5}{2}e$ |
11 | $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ | $\phantom{-}\frac{1}{8}e^{3} - 2e$ |
19 | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}\frac{3}{8}e^{3} - 5e$ |
29 | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - 7$ |
31 | $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $-\frac{3}{8}e^{3} + \frac{9}{2}e$ |
41 | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ | $-e^{2} + 10$ |
41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ | $-\frac{3}{8}e^{3} + \frac{9}{2}e$ |
41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}\frac{3}{8}e^{3} - \frac{11}{2}e$ |
59 | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ | $-\frac{1}{2}e^{2} - 7$ |
59 | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ | $\phantom{-}1$ |
59 | $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ | $\phantom{-}\frac{7}{4}e^{2} - 11$ |
61 | $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ | $\phantom{-}\frac{5}{8}e^{3} - \frac{11}{2}e$ |
64 | $[64, 2, -2]$ | $-5$ |
71 | $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ | $\phantom{-}\frac{1}{4}e^{2} - 8$ |
81 | $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ | $\phantom{-}\frac{9}{8}e^{3} - \frac{35}{2}e$ |
89 | $[89, 89, -w^{5} + 6w^{3} - 7w]$ | $-\frac{1}{2}e^{2} - 2$ |
89 | $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ | $-\frac{5}{8}e^{3} + 9e$ |
101 | $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ | $-7$ |
101 | $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ | $-\frac{7}{8}e^{3} + \frac{31}{2}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ | $-1$ |