Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-1$ |
9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $-3$ |
9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-1$ |
17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-1$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{2}{3}e - \frac{1}{3}$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{3}e + \frac{7}{3}$ |
31 | $[31, 31, w^{3} - 4w + 2]$ | $\phantom{-}\frac{5}{3}e - \frac{13}{3}$ |
32 | $[32, 2, 2]$ | $-\frac{4}{3}e + \frac{17}{3}$ |
37 | $[37, 37, w^{3} - 3w - 1]$ | $-\frac{4}{3}e - \frac{13}{3}$ |
53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $-\frac{4}{3}e - \frac{1}{3}$ |
59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{10}{3}e + \frac{11}{3}$ |
61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $\phantom{-}\frac{4}{3}e - \frac{14}{3}$ |
67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{4}{3}e + \frac{13}{3}$ |
71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $-3e + 4$ |
79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $\phantom{-}3e - 6$ |
83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $-\frac{2}{3}e + \frac{19}{3}$ |
83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $-\frac{4}{3}e - \frac{34}{3}$ |
83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{3}e + \frac{25}{3}$ |
83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $\phantom{-}\frac{5}{3}e + \frac{11}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $1$ |