Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[25, 25, w^{2} - 2w - 5]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 33x^{4} + 128x^{2} - 128\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $\phantom{-}0$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{33}{8}e^{2} + 11$ |
11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}2$ |
11 | $[11, 11, -w + 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{3}{16}e^{5} - \frac{91}{16}e^{3} + \frac{19}{2}e$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{32}e^{5} - \frac{33}{32}e^{3} + 5e$ |
17 | $[17, 17, -w^{2} + w + 8]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{33}{8}e^{2} + 10$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{7}{32}e^{5} + \frac{215}{32}e^{3} - \frac{25}{2}e$ |
19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}\frac{3}{16}e^{5} - \frac{91}{16}e^{3} + \frac{17}{2}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{4}e^{5} + \frac{31}{4}e^{3} - \frac{35}{2}e$ |
25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{9}{32}e^{5} - \frac{281}{32}e^{3} + \frac{41}{2}e$ |
27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{33}{4}e^{2} + 22$ |
31 | $[31, 31, w^{2} - 2w - 8]$ | $-\frac{1}{2}e^{4} + \frac{31}{2}e^{2} - 32$ |
37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{5}{8}e^{4} + \frac{157}{8}e^{2} - 38$ |
41 | $[41, 41, -w - 4]$ | $-\frac{3}{8}e^{4} + \frac{91}{8}e^{2} - 20$ |
41 | $[41, 41, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{29}{4}e^{2} + 12$ |
47 | $[47, 47, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{3}{16}e^{5} - \frac{91}{16}e^{3} + \frac{15}{2}e$ |
53 | $[53, 53, -w^{2} + w + 9]$ | $-\frac{1}{8}e^{4} + \frac{33}{8}e^{2} - 8$ |
61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-\frac{23}{32}e^{5} + \frac{711}{32}e^{3} - \frac{89}{2}e$ |
67 | $[67, 67, 2w - 1]$ | $-e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $-1$ |