Base field 4.4.9301.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[15, 15, -w^{2} + 2w + 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 8x - 6\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $-1$ |
5 | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $-1$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + w + 2]$ | $-e^{2} + 2e + 6$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{2} - e - 3$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}e$ |
23 | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e^{2} - 6$ |
27 | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $-4$ |
37 | $[37, 37, -w^{3} + 4w + 1]$ | $\phantom{-}3e^{2} - 2e - 12$ |
37 | $[37, 37, -w^{3} + w^{2} + 2w + 1]$ | $\phantom{-}2e + 4$ |
49 | $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ | $-2e^{2} + 2e + 10$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}e + 6$ |
61 | $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ | $-2e^{2} + 2e + 14$ |
67 | $[67, 67, w^{2} - 3w - 2]$ | $-3e^{2} + e + 16$ |
71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}e^{2} - 6e - 6$ |
71 | $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ | $-4e + 6$ |
71 | $[71, 71, w^{2} - 2w - 5]$ | $-e^{2} + 6e + 6$ |
79 | $[79, 79, w^{2} - 3w - 1]$ | $\phantom{-}2e - 6$ |
79 | $[79, 79, w^{3} - 6w - 1]$ | $-2e^{2} + e + 6$ |
89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ | $-3e^{2} + 2e + 18$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $1$ |
$5$ | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $1$ |