Base field 5.5.36497.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 3x^{3} + 5x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[53, 53, -2w^{4} + 3w^{3} + 7w^{2} - 7w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 3x^{3} - 3x^{2} + 5x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 2$ |
23 | $[23, 23, 2w^{4} - 3w^{3} - 6w^{2} + 5w + 1]$ | $-e^{3} + 3e^{2} + 2e - 7$ |
25 | $[25, 5, -w^{2} + 2w + 2]$ | $-3e^{3} + 9e^{2} + 4e - 7$ |
29 | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $\phantom{-}e^{3} - 5e^{2} + 2e + 12$ |
31 | $[31, 31, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-e^{3} + 2e^{2} + 2e + 4$ |
32 | $[32, 2, 2]$ | $-e^{3} + 6e^{2} - 7e - 10$ |
37 | $[37, 37, w^{4} - 2w^{3} - 2w^{2} + 4w + 1]$ | $-3e^{3} + 12e^{2} - 14$ |
47 | $[47, 47, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ | $-e^{3} + 3e^{2} + 2e + 4$ |
47 | $[47, 47, 2w^{4} - 3w^{3} - 6w^{2} + 6w + 2]$ | $\phantom{-}4e^{3} - 13e^{2} - 6e + 11$ |
49 | $[49, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $\phantom{-}2e^{2} - 5e - 1$ |
53 | $[53, 53, -2w^{4} + 3w^{3} + 7w^{2} - 7w - 2]$ | $\phantom{-}1$ |
59 | $[59, 59, -2w^{4} + 3w^{3} + 6w^{2} - 5w - 2]$ | $-4e^{3} + 13e^{2} + 4e - 12$ |
67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 7w]$ | $-e^{3} + 3e^{2} + 5e - 1$ |
67 | $[67, 67, -w^{4} + 3w^{3} + w^{2} - 7w + 1]$ | $\phantom{-}e^{2} - 2e - 5$ |
71 | $[71, 71, w^{4} - 2w^{3} - 4w^{2} + 3w + 3]$ | $-3e^{3} + 6e^{2} + 15e - 9$ |
71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}3e^{3} - 12e^{2} + 4e + 17$ |
79 | $[79, 79, 2w^{4} - 3w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}4e^{3} - 12e^{2} - 7e + 5$ |
81 | $[81, 3, -w^{4} + 3w^{3} + 3w^{2} - 8w - 2]$ | $-e^{3} + 4e^{2} - 5e - 2$ |
83 | $[83, 83, -3w^{4} + 3w^{3} + 10w^{2} - 2w - 2]$ | $-3e^{3} + 9e^{2} + 2e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$53$ | $[53, 53, -2w^{4} + 3w^{3} + 7w^{2} - 7w - 2]$ | $-1$ |