Base field 4.4.3981.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 2x^{4} - 7x^{3} - 8x^{2} + 11x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{5}{2}e$ |
9 | $[9, 3, -w^{2} + 2]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{3}{2}e^{2} + 5e - 2$ |
13 | $[13, 13, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - e + 5$ |
16 | $[16, 2, 2]$ | $-e - 3$ |
23 | $[23, 23, w^{2} - 2w - 2]$ | $\phantom{-}e^{3} + 3e^{2} - 2e - 8$ |
37 | $[37, 37, w^{3} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{7}{2}e - 7$ |
37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 5e^{2} + \frac{1}{2}e + 6$ |
41 | $[41, 41, w^{3} - 5w + 1]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{5}{2}e^{2} - e - 2$ |
43 | $[43, 43, 2w^{3} - w^{2} - 7w]$ | $-\frac{1}{2}e^{4} - \frac{5}{2}e^{3} + \frac{1}{2}e^{2} + 7e - 1$ |
53 | $[53, 53, 2w - 3]$ | $-\frac{1}{2}e^{4} - e^{3} + 4e^{2} + \frac{7}{2}e - 6$ |
59 | $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ | $\phantom{-}1$ |
67 | $[67, 67, -w - 3]$ | $\phantom{-}2e^{4} + 4e^{3} - 12e^{2} - 13e + 12$ |
67 | $[67, 67, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}\frac{3}{2}e^{4} + 4e^{3} - 6e^{2} - \frac{27}{2}e + 1$ |
71 | $[71, 71, 2w^{3} - 3w^{2} - 7w + 5]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{7}{2}e^{3} - \frac{9}{2}e^{2} - 5e - 6$ |
73 | $[73, 73, w^{3} - 6w]$ | $\phantom{-}e^{3} + 3e^{2} - 2e - 12$ |
73 | $[73, 73, -w^{3} - w^{2} + 5w + 3]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{3}{2}e^{2} + 4e - 6$ |
79 | $[79, 79, w^{3} - 3w - 4]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{5}{2}e^{3} - \frac{17}{2}e^{2} - 6e + 8$ |
83 | $[83, 83, w^{3} - 2w^{2} - 3w + 1]$ | $-\frac{3}{2}e^{4} - 3e^{3} + 6e^{2} + \frac{7}{2}e - 2$ |
83 | $[83, 83, -2w^{3} + 2w^{2} + 6w - 3]$ | $-2e^{3} - 3e^{2} + 12e + 5$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ | $-1$ |