Base field 4.4.10273.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + x + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, -w^{2} + 2w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 3x^{3} - 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}e^{3} + e^{2} - 2e$ |
8 | $[8, 2, w^{3} - 2w^{2} - 5w + 1]$ | $-e^{3} - 3e^{2} + 2$ |
13 | $[13, 13, -w^{2} + 2w + 3]$ | $\phantom{-}e^{2} - 3$ |
17 | $[17, 17, -w^{2} + 3w + 3]$ | $\phantom{-}e^{3} + 2e^{2} - 2e - 3$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}1$ |
27 | $[27, 3, w^{3} - w^{2} - 6w - 5]$ | $\phantom{-}5e^{2} + 6e - 8$ |
29 | $[29, 29, w^{3} - 2w^{2} - 2w + 1]$ | $-2e^{3} - 4e^{2} + 5e + 7$ |
47 | $[47, 47, w^{3} - 2w^{2} - 4w - 3]$ | $\phantom{-}3e^{3} + 3e^{2} - 6e$ |
49 | $[49, 7, w^{3} - 3w^{2} - 3w + 1]$ | $-5e^{3} - 12e^{2} + 3e + 9$ |
49 | $[49, 7, -2w^{3} + 5w^{2} + 7w - 3]$ | $\phantom{-}2e^{3} - 7e$ |
59 | $[59, 59, -2w^{3} + 6w^{2} + 5w - 7]$ | $-2e^{3} + 11e - 2$ |
61 | $[61, 61, 2w^{3} - 4w^{2} - 9w - 3]$ | $-8e^{3} - 15e^{2} + 12e + 12$ |
71 | $[71, 71, w^{3} - 3w^{2} - 3w + 7]$ | $-3e^{3} - 7e^{2} + e + 10$ |
73 | $[73, 73, 2w^{3} - 6w^{2} - 3w + 5]$ | $\phantom{-}6e^{3} + 16e^{2} - 5e - 15$ |
73 | $[73, 73, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}9e^{3} + 21e^{2} - 7e - 15$ |
83 | $[83, 83, -2w^{3} + 5w^{2} + 8w - 3]$ | $\phantom{-}3e^{3} + 4e^{2} - 5e - 6$ |
89 | $[89, 89, -2w^{3} + 6w^{2} + 4w - 7]$ | $-3e^{3} + 13e - 4$ |
89 | $[89, 89, w^{3} - 2w^{2} - 6w + 3]$ | $\phantom{-}5e^{3} + 13e^{2} - 3e - 18$ |
97 | $[97, 97, -3w - 1]$ | $-4e^{3} - 8e^{2} + e + 9$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{2} + 2w + 1]$ | $-1$ |