Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23, 23, -w - 3]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 8x^{4} + 15x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 2$ |
7 | $[7, 7, -w - 1]$ | $\phantom{-}2e$ |
7 | $[7, 7, w - 1]$ | $\phantom{-}e^{5} - 7e^{3} + 10e$ |
17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{19}{2}e^{3} + 9e$ |
17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}e^{5} - 8e^{3} + 15e$ |
23 | $[23, 23, -w - 3]$ | $-1$ |
23 | $[23, 23, w - 3]$ | $-e^{4} + 5e^{2} - 4$ |
25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}e^{5} - 8e^{3} + 15e$ |
25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $-\frac{3}{2}e^{5} + \frac{21}{2}e^{3} - 11e$ |
41 | $[41, 41, w^{3} - 4w - 1]$ | $-\frac{1}{2}e^{5} + \frac{5}{2}e^{3} + e$ |
41 | $[41, 41, -w^{3} + 4w - 1]$ | $-e^{5} + 8e^{3} - 13e$ |
71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $\phantom{-}3e^{5} - 21e^{3} + 26e$ |
71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $\phantom{-}\frac{5}{2}e^{5} - \frac{41}{2}e^{3} + 32e$ |
73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $-\frac{3}{2}e^{4} + \frac{13}{2}e^{2} + 8$ |
73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $-\frac{5}{2}e^{4} + \frac{29}{2}e^{2} - 8$ |
79 | $[79, 79, 2w^{2} - 2w - 9]$ | $\phantom{-}e^{5} - 11e^{3} + 28e$ |
79 | $[79, 79, -2w^{3} + 8w + 5]$ | $-\frac{1}{2}e^{5} + \frac{17}{2}e^{3} - 26e$ |
81 | $[81, 3, -3]$ | $\phantom{-}2e^{4} - 12e^{2} + 2$ |
89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23,23,-w-3]$ | $1$ |