Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[25, 25, -w^{4} + w^{3} + 4w^{2} - 2w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 5x^{3} - 2x^{2} - 24x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}0$ |
7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - 1$ |
7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - 2e - 6$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $-\frac{2}{3}e^{3} - \frac{7}{3}e^{2} + \frac{13}{3}e + 8$ |
23 | $[23, 23, -w^{2} + 3]$ | $-e - 3$ |
32 | $[32, 2, 2]$ | $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + 3e - 3$ |
37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{2}{3}e^{2} - \frac{5}{3}e - 1$ |
41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - 5e - 3$ |
43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} - \frac{10}{3}e + 1$ |
43 | $[43, 43, -w^{2} + w + 3]$ | $-e^{2} - 3e + 3$ |
47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $\phantom{-}e^{3} + 2e^{2} - 9e - 9$ |
61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} + \frac{2}{3}e + 1$ |
79 | $[79, 79, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} - \frac{19}{3}e + 7$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}e^{3} + \frac{14}{3}e^{2} + \frac{2}{3}e - 17$ |
79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $-e^{3} - \frac{10}{3}e^{2} + \frac{11}{3}e + 4$ |
97 | $[97, 97, w^{3} - 6w]$ | $\phantom{-}\frac{5}{3}e^{2} + \frac{17}{3}e - 2$ |
101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-2e^{2} - e + 15$ |
101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $-2e^{3} - 8e^{2} + 9e + 24$ |
107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $-2e^{3} - 6e^{2} + 10e + 15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,w^{4}-w^{3}-5w^{2}+3w+1]$ | $1$ |