Base field 4.4.12400.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, w^{2} - 6]$ |
Dimension: | $4$ |
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:
\(x^{4} - 2x^{3} - 24x^{2} + 62x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ | $-2$ |
5 | $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ | $-1$ |
9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ | $\phantom{-}e$ |
9 | $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{6}e^{2} - \frac{25}{6}e + \frac{31}{6}$ |
19 | $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ | $-\frac{1}{12}e^{3} - \frac{5}{12}e^{2} + \frac{7}{12}e + \frac{83}{12}$ |
19 | $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{23}{4}e - \frac{17}{4}$ |
29 | $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ | $-\frac{1}{3}e^{3} - \frac{1}{6}e^{2} + \frac{22}{3}e - \frac{41}{6}$ |
29 | $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{3}e^{2} - \frac{13}{6}e - \frac{13}{3}$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{5}{6}e^{2} - \frac{19}{6}e - \frac{47}{6}$ |
59 | $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{19}{4}e - \frac{43}{4}$ |
59 | $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{4}e^{2} - \frac{19}{4}e + \frac{19}{4}$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{11}{4}e - \frac{5}{4}$ |
61 | $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ | $-\frac{7}{12}e^{3} + \frac{1}{12}e^{2} + \frac{157}{12}e - \frac{139}{12}$ |
71 | $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{19}{4}e - \frac{57}{4}$ |
71 | $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{19}{4}e - \frac{57}{4}$ |
79 | $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{16}{3}e + \frac{31}{3}$ |
79 | $[79, 79, -2w^{2} + w + 10]$ | $\phantom{-}\frac{7}{12}e^{3} - \frac{1}{12}e^{2} - \frac{145}{12}e + \frac{115}{12}$ |
79 | $[79, 79, 2w^{2} + w - 10]$ | $-\frac{5}{12}e^{3} - \frac{1}{12}e^{2} + \frac{83}{12}e - \frac{101}{12}$ |
79 | $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{21}{2}e + \frac{31}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,-\frac{1}{2}w^{3}+w^{2}+\frac{5}{2}w-4]$ | $-1$ |
$5$ | $[5,5,-\frac{1}{2}w^{2}-w+\frac{3}{2}]$ | $1$ |