Base field 4.4.11348.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 4, -w^{3} + 2w^{2} + 3w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 19x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-e^{2} + 10$ |
19 | $[19, 19, -2w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{16}{3}e$ |
29 | $[29, 29, -w^{3} + w^{2} + 2w - 1]$ | $-\frac{1}{3}e^{3} + \frac{10}{3}e$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{1}{3}e^{3} + \frac{13}{3}e$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 5]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{26}{3}e$ |
43 | $[43, 43, -2w^{3} + 2w^{2} + 8w + 3]$ | $-4$ |
43 | $[43, 43, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{25}{3}e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e^{2} - 4$ |
53 | $[53, 53, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{1}{3}e^{3} + \frac{19}{3}e$ |
59 | $[59, 59, 2w^{3} - 2w^{2} - 10w + 3]$ | $\phantom{-}3e$ |
61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e$ |
61 | $[61, 61, w^{2} + w - 3]$ | $-\frac{1}{3}e^{3} + \frac{22}{3}e$ |
71 | $[71, 71, -w^{3} + 5w + 1]$ | $-e^{2} + 4$ |
71 | $[71, 71, w^{3} - w^{2} - 4w - 3]$ | $\phantom{-}e^{2} - 4$ |
81 | $[81, 3, -3]$ | $-e^{2} + 14$ |
83 | $[83, 83, -3w^{3} + 5w^{2} + 12w - 9]$ | $\phantom{-}e^{2} - 4$ |
83 | $[83, 83, -3w^{3} + 6w^{2} + 13w - 13]$ | $-\frac{1}{3}e^{3} + \frac{19}{3}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |
$2$ | $[2, 2, w + 1]$ | $-1$ |