Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[15, 15, -w^{2} + 2w + 5]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 9x^{2} - 9x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 1]$ | $-1$ |
4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $-1$ |
7 | $[7, 7, w - 2]$ | $\phantom{-}2$ |
11 | $[11, 11, w^{2} - 2w - 4]$ | $-4e^{3} - 2e^{2} + 36e + 18$ |
23 | $[23, 23, -w^{2} + 2w + 1]$ | $-2e^{3} - e^{2} + 19e + 14$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-e^{3} + 11e + 2$ |
27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $-e^{3} + 7e + 2$ |
31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $\phantom{-}5e^{3} + 3e^{2} - 48e - 24$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}e^{3} - 7e - 2$ |
37 | $[37, 37, w^{2} - 2w - 6]$ | $-4e^{3} - 2e^{2} + 38e + 18$ |
37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}2e^{3} + 3e^{2} - 19e - 18$ |
43 | $[43, 43, w^{2} - 3w - 2]$ | $-2e^{3} - e^{2} + 17e + 2$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $-e^{3} + 11e$ |
73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $-3e^{3} + 27e + 10$ |
83 | $[83, 83, -w - 3]$ | $-2e^{3} + 18e + 14$ |
89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $-2e^{3} - e^{2} + 21e + 18$ |
89 | $[89, 89, 2w - 1]$ | $\phantom{-}2e^{3} - 20e$ |
101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $\phantom{-}8e^{3} + 4e^{2} - 74e - 34$ |
101 | $[101, 101, 2w^{2} - 3w - 3]$ | $\phantom{-}6e^{3} + 4e^{2} - 60e - 34$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w - 1]$ | $1$ |
$5$ | $[5, 5, w]$ | $1$ |