Base field 4.4.14725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 11x + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 12x^{4} + 41x^{2} - 40\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{11}{3}]$ | $-\frac{1}{2}e^{5} + 4e^{3} - \frac{11}{2}e$ |
9 | $[9, 3, w - 2]$ | $\phantom{-}e$ |
11 | $[11, 11, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{8}{3}]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{23}{2}e$ |
11 | $[11, 11, \frac{2}{3}w^{3} + \frac{2}{3}w^{2} - \frac{19}{3}w - \frac{13}{3}]$ | $\phantom{-}e^{3} - 5e$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{4} - 9e^{2} + 13$ |
19 | $[19, 19, w + 2]$ | $-\frac{1}{2}e^{5} + 4e^{3} - \frac{13}{2}e$ |
25 | $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ | $\phantom{-}1$ |
29 | $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ | $\phantom{-}2e^{4} - 17e^{2} + 30$ |
29 | $[29, 29, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{14}{3}]$ | $\phantom{-}e^{2} - 10$ |
29 | $[29, 29, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - \frac{8}{3}]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{15}{2}e$ |
29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{23}{2}e$ |
31 | $[31, 31, w]$ | $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} + \frac{5}{2}e$ |
31 | $[31, 31, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{8}{3}w + \frac{13}{3}]$ | $-2e^{4} + 18e^{2} - 32$ |
31 | $[31, 31, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{5}{3}]$ | $-e^{5} + 10e^{3} - 19e$ |
41 | $[41, 41, \frac{1}{3}w^{3} + \frac{4}{3}w^{2} - \frac{8}{3}w - \frac{20}{3}]$ | $-e^{2} - 2$ |
41 | $[41, 41, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{40}{3}]$ | $-2e^{4} + 19e^{2} - 32$ |
49 | $[49, 7, -\frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{8}{3}w + \frac{38}{3}]$ | $\phantom{-}2e^{4} - 21e^{2} + 40$ |
49 | $[49, 7, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{43}{3}]$ | $-2e^{4} + 17e^{2} - 30$ |
59 | $[59, 59, \frac{5}{3}w^{3} + \frac{8}{3}w^{2} - \frac{40}{3}w - \frac{49}{3}]$ | $\phantom{-}e^{4} - 7e^{2}$ |
59 | $[59, 59, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - \frac{16}{3}w + \frac{11}{3}]$ | $-3e^{4} + 25e^{2} - 40$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ | $-1$ |