Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 21x^{2} + 80\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}1$ |
4 | $[4, 2, -w^{2} + 7]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $-\frac{1}{4}e^{3} + \frac{5}{4}e^{2} + \frac{9}{4}e - 9$ |
5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $-\frac{1}{4}e^{3} + \frac{5}{4}e^{2} + \frac{9}{4}e - 9$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $\phantom{-}e$ |
11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $\phantom{-}e$ |
31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $-e^{3} + 3e^{2} + 11e - 20$ |
31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $-e^{3} + 3e^{2} + 11e - 20$ |
41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{11}{4}e^{2} - \frac{35}{4}e + 15$ |
41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{9}{2}e - 8$ |
41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{9}{2}e - 8$ |
41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{11}{4}e^{2} - \frac{35}{4}e + 15$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{5}{2}e + 16$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{5}{2}e + 16$ |
71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $-e^{3} + 3e^{2} + 9e - 20$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $-e^{3} + 3e^{2} + 9e - 20$ |
81 | $[81, 3, -3]$ | $\phantom{-}18$ |
89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{17}{4}e + 3$ |
89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{15}{2}e + 24$ |
89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{15}{2}e + 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, w^{2} - 2w - 6]$ | $-1$ |
$4$ | $[4, 2, -w^{2} + 7]$ | $-1$ |