Base field 4.4.13525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 8x + 29\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, \frac{2}{5}w^{3} - \frac{14}{5}w - \frac{3}{5}]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w + 2]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $-1$ |
9 | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ | $-2e - 1$ |
9 | $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ | $\phantom{-}e$ |
11 | $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ | $\phantom{-}\frac{3}{2}e - \frac{1}{2}$ |
11 | $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ | $-\frac{5}{2}e - \frac{1}{2}$ |
16 | $[16, 2, 2]$ | $-\frac{1}{2}e + \frac{3}{2}$ |
29 | $[29, 29, -w]$ | $\phantom{-}\frac{5}{2}e - \frac{5}{2}$ |
29 | $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ | $-\frac{1}{2}e + \frac{5}{2}$ |
41 | $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ | $\phantom{-}\frac{9}{2}e + \frac{1}{2}$ |
41 | $[41, 41, -w^{2} + 10]$ | $\phantom{-}2e - 5$ |
41 | $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ | $\phantom{-}2e - 5$ |
41 | $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ | $\phantom{-}\frac{1}{2}e - \frac{15}{2}$ |
49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ | $\phantom{-}1$ |
49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ | $-3e$ |
59 | $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ | $-3e + 2$ |
59 | $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ | $-5$ |
61 | $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ | $\phantom{-}\frac{5}{2}e - \frac{1}{2}$ |
61 | $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ | $-\frac{3}{2}e - \frac{17}{2}$ |
71 | $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ | $\phantom{-}3e + 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w + 2]$ | $-1$ |
$5$ | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $1$ |