Base field 4.4.8768.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 9x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e$ |
7 | $[7, 7, w]$ | $-e^{2} - 2e + 1$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $-2e^{3} - 4e^{2} + 5e + 1$ |
7 | $[7, 7, w^{2} - 2]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 3$ |
7 | $[7, 7, w - 1]$ | $\phantom{-}e^{3} + 2e^{2} - 2e - 1$ |
23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}1$ |
23 | $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e^{3} + 4e^{2} + e - 6$ |
31 | $[31, 31, w^{2} - 5]$ | $-5e^{3} - 8e^{2} + 17e + 3$ |
31 | $[31, 31, -w^{2} + 2w + 4]$ | $-e^{3} - e^{2} + 3e$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}3e^{3} + 5e^{2} - 6e + 1$ |
41 | $[41, 41, w^{3} - w^{2} - 3w - 3]$ | $\phantom{-}4e^{3} + 8e^{2} - 11e - 6$ |
47 | $[47, 47, w^{2} - 2w - 5]$ | $-3e^{3} - 3e^{2} + 11e - 1$ |
47 | $[47, 47, w^{2} - 6]$ | $-5e^{3} - 10e^{2} + 12e + 5$ |
71 | $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e^{3} + 6e^{2} + 2e - 12$ |
71 | $[71, 71, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}7e^{3} + 9e^{2} - 23e + 8$ |
79 | $[79, 79, -w - 3]$ | $-2e^{3} - 4e^{2} + 4e + 5$ |
79 | $[79, 79, w - 4]$ | $\phantom{-}5e^{3} + 9e^{2} - 13e - 4$ |
81 | $[81, 3, -3]$ | $\phantom{-}4e^{3} - 23e + 17$ |
89 | $[89, 89, w^{2} - 3w - 2]$ | $-6e^{2} - 13e + 11$ |
89 | $[89, 89, w^{2} + w - 4]$ | $\phantom{-}e^{3} - e^{2} - 11e - 5$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-1$ |