Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, -w^{3} + 4w]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 5x^{4} - 14x^{3} - 76x^{2} + 40x + 256\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $-1$ |
5 | $[5, 5, -w^{2} + w + 2]$ | $-1$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{19}{4}e^{2} - 4e + 22$ |
13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{3}{8}e^{3} - \frac{5}{2}e^{2} - \frac{7}{2}e + 14$ |
16 | $[16, 2, 2]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{7}{2}e + 3$ |
19 | $[19, 19, -w^{2} + w + 1]$ | $-\frac{1}{8}e^{4} - \frac{3}{8}e^{3} + \frac{5}{2}e^{2} + \frac{9}{2}e - 10$ |
23 | $[23, 23, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{1}{8}e^{3} - \frac{13}{4}e^{2} - \frac{1}{2}e + 20$ |
25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{9}{2}e^{2} - \frac{13}{2}e + 22$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{3}{8}e^{4} + \frac{5}{8}e^{3} - 8e^{2} - \frac{11}{2}e + 36$ |
29 | $[29, 29, -w + 3]$ | $-\frac{1}{4}e^{3} - \frac{3}{4}e^{2} + 2e + 8$ |
31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{1}{2}e^{3} - 2e^{2} + \frac{9}{2}e + 12$ |
37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{11}{2}e^{2} + 2e - 22$ |
37 | $[37, 37, w^{3} - 3w + 1]$ | $-\frac{1}{4}e^{4} - \frac{3}{4}e^{3} + 4e^{2} + 6e - 12$ |
53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}\frac{3}{8}e^{4} + \frac{9}{8}e^{3} - \frac{9}{2}e^{2} - \frac{15}{2}e + 6$ |
59 | $[59, 59, w^{2} + w - 4]$ | $-\frac{1}{8}e^{4} + \frac{1}{8}e^{3} + 4e^{2} - \frac{3}{2}e - 28$ |
61 | $[61, 61, -2w^{2} + w + 8]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 8e^{2} - 12e + 30$ |
73 | $[73, 73, -w^{3} + 5w - 1]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{8}e^{3} - \frac{5}{2}e^{2} + 2e$ |
79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{3}{8}e^{4} - \frac{9}{8}e^{3} + \frac{9}{2}e^{2} + \frac{17}{2}e - 6$ |
79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{7}{8}e^{3} - e^{2} - \frac{21}{2}e + 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $1$ |
$5$ | $[5, 5, -w^{2} + w + 2]$ | $1$ |