Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 12x^{2} - x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
7 | $[7, 7, w - 1]$ | $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{11}{3}e + 1$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - \frac{22}{3}e$ |
13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $\phantom{-}1$ |
16 | $[16, 2, 2]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{14}{3}e - 5$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $-e^{3} + 10e - 1$ |
17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{19}{3}e - 4$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}e^{3} - 13e$ |
19 | $[19, 19, w^{2} - w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{14}{3}e - 2$ |
29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - \frac{25}{3}e - 1$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{4}{3}e^{3} - \frac{2}{3}e^{2} - \frac{44}{3}e - 1$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e^{3} - 11e - 3$ |
43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $-\frac{4}{3}e^{3} - \frac{1}{3}e^{2} + \frac{44}{3}e - 1$ |
47 | $[47, 47, w^{3} - 7w - 4]$ | $-e^{3} + 13e + 3$ |
53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $-e^{3} + e^{2} + 14e - 5$ |
61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{1}{3}e^{2} - \frac{44}{3}e - 3$ |
73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $-2e - 5$ |
73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $-\frac{5}{3}e^{3} - \frac{2}{3}e^{2} + \frac{55}{3}e - 1$ |
81 | $[81, 3, -3]$ | $-e^{3} + 14e - 2$ |
83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{31}{3}e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-1$ |