Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, -w^{2} + w + 4]$ |
Dimension: | $5$ |
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:
\(x^{5} - 5x^{4} + 3x^{3} + 13x^{2} - 9x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w - 1]$ | $-e^{3} + e^{2} + 4e$ |
8 | $[8, 2, 2]$ | $-e^{4} + 3e^{3} + 2e^{2} - 7e - 1$ |
9 | $[9, 3, -w^{2} + 2w + 4]$ | $\phantom{-}e^{4} - 2e^{3} - 5e^{2} + 6e + 8$ |
11 | $[11, 11, -w^{2} + 2w + 2]$ | $-e^{3} + 3e^{2} - 2$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}1$ |
19 | $[19, 19, w + 3]$ | $\phantom{-}e^{4} - 3e^{3} + e^{2} + e - 4$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $-e^{4} + 2e^{3} + 5e^{2} - 7e - 4$ |
19 | $[19, 19, -w^{2} + 3w + 2]$ | $-2e^{3} + 4e^{2} + 4e - 2$ |
23 | $[23, 23, w^{2} - w - 3]$ | $-2e^{4} + 7e^{3} + 3e^{2} - 17e - 2$ |
23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}e^{4} - 2e^{3} - 3e^{2} + 2e + 6$ |
23 | $[23, 23, -w + 4]$ | $\phantom{-}2e^{4} - 5e^{3} - 8e^{2} + 12e + 12$ |
31 | $[31, 31, w^{2} - 5]$ | $-e^{4} + 5e^{3} - 2e^{2} - 10e$ |
43 | $[43, 43, w^{2} - 3w - 3]$ | $\phantom{-}e^{3} - 3e^{2} - e + 2$ |
49 | $[49, 7, w^{2} - 6]$ | $-2e^{4} + 5e^{3} + 10e^{2} - 15e - 18$ |
53 | $[53, 53, 2w - 5]$ | $-e^{4} + 3e^{3} - e + 2$ |
61 | $[61, 61, 2w^{2} - 2w - 9]$ | $\phantom{-}2e^{4} - 3e^{3} - 14e^{2} + 9e + 20$ |
71 | $[71, 71, 2w - 3]$ | $\phantom{-}2e^{4} - 9e^{3} + 7e^{2} + 13e - 8$ |
73 | $[73, 73, 2w^{2} - 5w - 5]$ | $-3e^{4} + 9e^{3} + 3e^{2} - 13e$ |
83 | $[83, 83, w^{2} - w - 9]$ | $-4e^{4} + 9e^{3} + 13e^{2} - 16e - 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{2} + w + 4]$ | $-1$ |