Base field 4.4.10025.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 10x + 20\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20,10,-w - 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 2x^{4} - 13x^{3} + 12x^{2} + 48x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w + 2]$ | $\phantom{-}1$ |
4 | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ | $\phantom{-}e$ |
5 | $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e - 3$ |
5 | $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ | $\phantom{-}1$ |
19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{13}{4}e^{2} + 3e + 8$ |
19 | $[19, 19, w - 1]$ | $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{13}{4}e^{2} + 4e - 2$ |
31 | $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{13}{4}e^{2} + 5e + 10$ |
31 | $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{5}{2}e^{2} - \frac{13}{2}e + 3$ |
49 | $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{17}{4}e^{2} - 5e - 15$ |
49 | $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ | $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 17e + 14$ |
59 | $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ | $\phantom{-}\frac{5}{4}e^{4} - \frac{7}{2}e^{3} - \frac{41}{4}e^{2} + 18e + 22$ |
59 | $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ | $-e^{3} + e^{2} + 7e + 1$ |
61 | $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{3} + \frac{9}{2}e^{2} - \frac{39}{2}e - 15$ |
61 | $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ | $-\frac{1}{4}e^{4} + \frac{3}{2}e^{3} - \frac{3}{4}e^{2} - 8e + 12$ |
71 | $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ | $-\frac{3}{4}e^{4} + \frac{1}{2}e^{3} + \frac{31}{4}e^{2} - 10$ |
71 | $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ | $-\frac{1}{4}e^{4} + \frac{3}{2}e^{3} + \frac{5}{4}e^{2} - 12e - 8$ |
79 | $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ | $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{5}{2}e - 3$ |
79 | $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ | $\phantom{-}2e^{3} - e^{2} - 16e - 3$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{5}{2}e^{3} - \frac{31}{4}e^{2} + 16e + 24$ |
89 | $[89, 89, w^{3} - 7w + 1]$ | $-\frac{3}{4}e^{4} + \frac{3}{2}e^{3} + \frac{15}{4}e^{2} - 5e + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,w - 2]$ | $-1$ |
$5$ | $[5,5,w^{3} + 2w^{2} - 7w - 9]$ | $-1$ |