Base field 4.4.18432.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[4, 2, \frac{1}{3}w^{2} - 2]$ |
Dimension: | $4$ |
CM: | yes |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 8x^{3} - 4x^{2} - 128x - 164\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $\phantom{-}0$ |
7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $\phantom{-}e$ |
7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $-\frac{3}{2}e^{3} - 4e^{2} + 28e + 42$ |
7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 10e - 12$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $\phantom{-}e^{3} + 3e^{2} - 19e - 38$ |
9 | $[9, 3, w - 3]$ | $\phantom{-}0$ |
41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $\phantom{-}0$ |
41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $\phantom{-}0$ |
41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $\phantom{-}0$ |
41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $\phantom{-}0$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $\phantom{-}0$ |
47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $\phantom{-}0$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $\phantom{-}0$ |
47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $\phantom{-}0$ |
89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $\phantom{-}0$ |
89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $\phantom{-}0$ |
89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $\phantom{-}0$ |
89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $\phantom{-}0$ |
97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $\phantom{-}6e^{3} + 17e^{2} - 110e - 186$ |
97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $-3e^{3} - 9e^{2} + 52e + 102$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $-1$ |