Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 16, w^{3} - 2w^{2} - 4w]$ |
Dimension: | $4$ |
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:
\(x^{4} - 11x^{2} + 27\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}0$ |
5 | $[5, 5, w^{2} - 2w - 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $\phantom{-}e^{2} - 6$ |
8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e$ |
17 | $[17, 17, -w^{2} + 3w + 1]$ | $-e^{2} + 3$ |
23 | $[23, 23, w^{2} - 3]$ | $-\frac{2}{3}e^{3} + \frac{10}{3}e$ |
25 | $[25, 5, -w^{2} + 2w + 1]$ | $-\frac{5}{3}e^{3} + \frac{31}{3}e$ |
37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $-\frac{1}{3}e^{3} + \frac{11}{3}e$ |
41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{19}{3}e$ |
49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $\phantom{-}2e^{3} - 13e$ |
49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}2e^{3} - 11e$ |
59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $-6e^{2} + 30$ |
67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $\phantom{-}4e^{2} - 22$ |
71 | $[71, 71, 2w - 3]$ | $-\frac{2}{3}e^{3} + \frac{4}{3}e$ |
71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $-4e^{2} + 24$ |
79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{2}{3}e$ |
79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $\phantom{-}2e$ |
81 | $[81, 3, -3]$ | $\phantom{-}3e^{2} - 7$ |
83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $-2e^{3} + 16e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $-1$ |