Base field 4.4.4400.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[44, 22, w^{3} + w^{2} - 3w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 9x^{2} + 2x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{2} + w + 3]$ | $-1$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{3} + w^{2} + 4w - 4]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e - 1$ |
11 | $[11, 11, w]$ | $-1$ |
29 | $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e + 1$ |
29 | $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ | $\phantom{-}e + 2$ |
31 | $[31, 31, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - \frac{3}{2}e - 6$ |
31 | $[31, 31, -w^{3} - w^{2} + 4w + 2]$ | $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{3}{2}e + 10$ |
41 | $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + 6$ |
41 | $[41, 41, w^{3} - 5w + 2]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e - 5$ |
49 | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}2e^{3} + 4e^{2} - 12e - 4$ |
49 | $[49, 7, w^{3} + w^{2} - 4w - 1]$ | $-2e^{3} - 4e^{2} + 12e + 6$ |
59 | $[59, 59, -3w^{2} - w + 10]$ | $-\frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{21}{2}e + 8$ |
59 | $[59, 59, -3w^{2} + w + 10]$ | $\phantom{-}e^{3} + 2e^{2} - 5e + 4$ |
61 | $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 4$ |
61 | $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ | $-\frac{5}{2}e^{3} - \frac{7}{2}e^{2} + \frac{39}{2}e - 2$ |
71 | $[71, 71, 2w^{2} + w - 9]$ | $\phantom{-}2e^{3} + 4e^{2} - 10e - 6$ |
71 | $[71, 71, 2w^{2} - w - 9]$ | $-3e^{3} - 5e^{2} + 21e + 2$ |
81 | $[81, 3, -3]$ | $-e^{3} - e^{2} + 11e + 2$ |
101 | $[101, 101, 2w^{2} - w - 10]$ | $-2e^{2} - 5e + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{2} + w + 3]$ | $1$ |
$11$ | $[11, 11, w]$ | $1$ |