Base field 4.4.16609.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[15, 15, w^{3} - 5w - 3]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 2x^{5} - 10x^{4} - 21x^{3} + 20x^{2} + 55x + 21\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + w + 4]$ | $\phantom{-}e$ |
3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}1$ |
5 | $[5, 5, w^{2} - 4]$ | $\phantom{-}1$ |
8 | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $-e^{5} + 11e^{3} + 2e^{2} - 28e - 13$ |
17 | $[17, 17, -w^{2} + w + 5]$ | $\phantom{-}e^{3} + e^{2} - 5e - 3$ |
27 | $[27, 3, -w^{3} + 4w - 2]$ | $-e^{4} - e^{3} + 6e^{2} + 5e - 1$ |
29 | $[29, 29, -w^{2} + w + 1]$ | $-e^{4} - e^{3} + 7e^{2} + 5e - 8$ |
29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}e^{5} + e^{4} - 8e^{3} - 5e^{2} + 11e + 2$ |
37 | $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ | $-e^{4} - e^{3} + 8e^{2} + 5e - 9$ |
41 | $[41, 41, w^{3} - w^{2} - 5w + 2]$ | $-e^{5} - e^{4} + 8e^{3} + 7e^{2} - 13e - 10$ |
43 | $[43, 43, -w^{3} + w^{2} + 3w - 4]$ | $-2e^{5} - e^{4} + 22e^{3} + 10e^{2} - 58e - 35$ |
61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}3e^{5} + e^{4} - 31e^{3} - 12e^{2} + 74e + 43$ |
61 | $[61, 61, 2w^{2} - w - 8]$ | $\phantom{-}2e^{5} + e^{4} - 23e^{3} - 12e^{2} + 61e + 41$ |
67 | $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ | $\phantom{-}2e^{5} + e^{4} - 23e^{3} - 12e^{2} + 63e + 41$ |
73 | $[73, 73, -w^{2} - 2w + 2]$ | $-3e^{5} - 2e^{4} + 28e^{3} + 16e^{2} - 57e - 36$ |
79 | $[79, 79, w^{2} - 2w - 4]$ | $\phantom{-}2e^{5} + e^{4} - 21e^{3} - 13e^{2} + 51e + 44$ |
89 | $[89, 89, w^{2} + w - 5]$ | $\phantom{-}3e^{5} + e^{4} - 30e^{3} - 8e^{2} + 67e + 29$ |
89 | $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ | $-e^{4} - e^{3} + 7e^{2} + e - 4$ |
89 | $[89, 89, w^{3} - 5w - 5]$ | $-e^{5} - 2e^{4} + 8e^{3} + 14e^{2} - 11e - 18$ |
89 | $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}3e^{5} + 3e^{4} - 29e^{3} - 23e^{2} + 66e + 46$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w^{2} + w + 3]$ | $-1$ |
$5$ | $[5, 5, w^{2} - 4]$ | $-1$ |