Base field 4.4.14013.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 6x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[21, 21, w^{2} - 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 3x^{3} - 2x^{2} - 9x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 1]$ | $-1$ |
7 | $[7, 7, -w^{3} + 5w - 2]$ | $\phantom{-}e^{3} + e^{2} - 5e - 4$ |
13 | $[13, 13, -w^{3} + 5w + 1]$ | $-e^{2} + 2$ |
16 | $[16, 2, 2]$ | $-2e^{3} - 2e^{2} + 9e + 5$ |
29 | $[29, 29, w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}4e^{3} + 7e^{2} - 12e - 14$ |
31 | $[31, 31, -w^{3} + 4w - 1]$ | $-3e^{3} - 6e^{2} + 7e + 12$ |
41 | $[41, 41, w^{3} - 6w + 1]$ | $-2e^{2} - 3e + 2$ |
43 | $[43, 43, w^{3} + w^{2} - 6w - 1]$ | $-e^{2} + e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 11]$ | $-2e^{3} - 6e^{2} + 7e + 12$ |
49 | $[49, 7, w^{2} + w - 1]$ | $-5e^{3} - 8e^{2} + 20e + 22$ |
59 | $[59, 59, w^{3} - w^{2} - 6w + 4]$ | $-e - 8$ |
59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}4e^{3} + 9e^{2} - 12e - 20$ |
67 | $[67, 67, 2w^{3} + w^{2} - 9w - 2]$ | $-e^{3} - 2e^{2} + 3e + 8$ |
71 | $[71, 71, -3w^{3} - w^{2} + 16w + 5]$ | $\phantom{-}4e^{3} + 7e^{2} - 20e - 24$ |
71 | $[71, 71, 2w - 1]$ | $-2e^{3} + e^{2} + 11e - 4$ |
73 | $[73, 73, w^{3} - 6w + 4]$ | $\phantom{-}e^{3} + 5e^{2} - 2e - 18$ |
83 | $[83, 83, w^{3} - w^{2} - 3w + 4]$ | $-2e^{3} - 4e^{2} + 11e + 16$ |
103 | $[103, 103, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}5e^{3} + 9e^{2} - 24e - 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w - 1]$ | $-1$ |
$7$ | $[7, 7, w + 1]$ | $1$ |