Base field 4.4.11525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25,5,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 34x^{4} + 26x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $-1$ |
5 | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $\phantom{-}0$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}3e^{5} - 101e^{3} + 44e$ |
11 | $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $-5e^{5} + 168e^{3} - 64e$ |
19 | $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ | $-5e^{4} + 168e^{2} - 65$ |
19 | $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ | $\phantom{-}5e^{5} - 168e^{3} + 64e$ |
19 | $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ | $-8e^{5} + 269e^{3} - 107e$ |
19 | $[19, 19, w - 1]$ | $\phantom{-}2e^{4} - 67e^{2} + 20$ |
29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}5e^{5} - 168e^{3} + 61e$ |
29 | $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ | $\phantom{-}3e^{4} - 101e^{2} + 40$ |
31 | $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ | $-e^{5} + 34e^{3} - 25e$ |
31 | $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ | $-2e^{5} + 67e^{3} - 18e$ |
61 | $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ | $\phantom{-}4e^{5} - 134e^{3} + 36e$ |
61 | $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ | $\phantom{-}6e^{5} - 202e^{3} + 90e$ |
61 | $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ | $\phantom{-}12e^{4} - 403e^{2} + 153$ |
61 | $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ | $-8e^{4} + 269e^{2} - 107$ |
71 | $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ | $\phantom{-}3e^{4} - 101e^{2} + 33$ |
71 | $[71, 71, w^{2} - 8]$ | $-2$ |
79 | $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ | $\phantom{-}e^{5} - 34e^{3} + 24e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,\frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $-1$ |