Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[27, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 14x^{3} - 6x^{2} + 12x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-1$ |
9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $-1$ |
9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-\frac{1}{2}e^{4} + 7e^{2} + 2e - 6$ |
17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-\frac{1}{2}e^{4} + 7e^{2} + 4e - 6$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 7e^{2} - 3e - 8$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 7e - 2$ |
31 | $[31, 31, w^{3} - 4w + 2]$ | $-e^{4} + \frac{1}{2}e^{3} + 13e^{2} - 2e - 6$ |
32 | $[32, 2, 2]$ | $\phantom{-}e^{4} - 14e^{2} - 6e + 9$ |
37 | $[37, 37, w^{3} - 3w - 1]$ | $-\frac{1}{2}e^{4} + 6e^{2} + 3e + 2$ |
53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $-\frac{3}{2}e^{4} + \frac{1}{2}e^{3} + 19e^{2} + 3e - 8$ |
59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}e^{4} - \frac{1}{2}e^{3} - 13e^{2} + 4$ |
61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 6e^{2} + 11e + 2$ |
67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 6e^{2} + e - 8$ |
71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 5e + 10$ |
79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $-\frac{1}{2}e^{3} + 3e$ |
83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{3}{2}e^{3} - 20e^{2} + 11e + 18$ |
83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{3}{2}e^{3} - 21e^{2} + 12e + 20$ |
83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $\phantom{-}e^{4} - e^{3} - 14e^{2} + 6e + 14$ |
83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 7e^{2} + 9e - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $1$ |
$9$ | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $1$ |