Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, w^{2} - 3w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 7x^{2} + 3x + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $-e^{2} + e + 5$ |
11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}e^{3} - 2e^{2} - 3e + 3$ |
13 | $[13, 13, w^{2} - 3w - 2]$ | $-1$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{3} - 2e^{2} - 2e + 4$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}e^{2} - 2e$ |
17 | $[17, 17, -w^{2} + 2w + 3]$ | $-e^{2} + 4$ |
23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}e^{3} - 5e + 2$ |
27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $-e^{3} + 3e^{2} + 4e - 7$ |
29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $-e^{2} - e + 9$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $-2e^{3} + 4e^{2} + 8e - 10$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}2e^{3} - 2e^{2} - 7e + 3$ |
31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $-e^{2} - 2e + 8$ |
31 | $[31, 31, -w^{2} + 2w + 1]$ | $-2e^{3} + 3e^{2} + 9e - 8$ |
37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}2e^{3} - 4e^{2} - 6e + 12$ |
43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}e + 7$ |
71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}e^{3} - 5e^{2} + e + 16$ |
71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $\phantom{-}2e^{3} - 6e^{2} - 4e + 22$ |
89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 11$ |
97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $-e^{3} + 4e^{2} - 2e - 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w^{2} - 3w - 2]$ | $1$ |