Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[25, 25, -w^{3} + w^{2} + 3w - 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + x^{4} - 12x^{3} - 9x^{2} + 20x + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}0$ |
7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}\frac{1}{3}e^{4} - 4e^{2} + \frac{17}{3}$ |
13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{1}{6}e^{4} - \frac{1}{2}e^{3} + 2e^{2} + \frac{7}{2}e - \frac{13}{3}$ |
29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $-\frac{1}{3}e^{4} + 4e^{2} - \frac{26}{3}$ |
29 | $[29, 29, -w^{2} + 2w + 3]$ | $-\frac{1}{3}e^{4} + 3e^{2} - 2e - \frac{2}{3}$ |
31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{1}{6}e^{4} - \frac{1}{2}e^{3} - 3e^{2} + \frac{9}{2}e + \frac{19}{3}$ |
31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 6e^{2} + \frac{11}{2}e - 9$ |
32 | $[32, 2, 2]$ | $\phantom{-}\frac{5}{6}e^{4} + \frac{1}{2}e^{3} - 10e^{2} - \frac{7}{2}e + \frac{29}{3}$ |
43 | $[43, 43, -w^{2} - w + 4]$ | $-\frac{1}{3}e^{4} - e^{3} + 4e^{2} + 10e - \frac{17}{3}$ |
53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $\phantom{-}e^{2} - 3e - 7$ |
53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}e^{4} + e^{3} - 10e^{2} - 8e + 8$ |
73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $\phantom{-}e^{3} + e^{2} - 8e - 8$ |
73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $-\frac{2}{3}e^{4} - e^{3} + 6e^{2} + 6e - \frac{4}{3}$ |
81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $\phantom{-}e^{3} + e^{2} - 11e - 4$ |
83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $\phantom{-}\frac{2}{3}e^{4} + e^{3} - 7e^{2} - 5e + \frac{10}{3}$ |
89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{1}{3}e^{4} + 3e^{2} - 2e - \frac{20}{3}$ |
97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}e^{4} + e^{3} - 11e^{2} - 5e + 12$ |
101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $-3e$ |
103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $-e^{2} - 3e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w^{2} - w - 2]$ | $1$ |