Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[15, 15, -w^{3} + 5w + 1]$ |
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:
\(x^{4} + 2x^{3} - 16x^{2} - 36x - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $-1$ |
5 | $[5, 5, -w^{3} + 5w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}1$ |
11 | $[11, 11, -w^{3} + 5w]$ | $\phantom{-}\frac{1}{2}e^{3} - 8e - 6$ |
13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $-4$ |
16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{2} + e + 4$ |
19 | $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 8e + 7$ |
25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 9e - 13$ |
27 | $[27, 3, w^{3} - w^{2} - 5w + 4]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 7e + 11$ |
31 | $[31, 31, -w - 3]$ | $-\frac{1}{2}e^{3} - e^{2} + 9e + 10$ |
37 | $[37, 37, -w^{3} - w^{2} + 6w + 4]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 7e - 1$ |
41 | $[41, 41, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}0$ |
43 | $[43, 43, w^{3} - 7w - 2]$ | $-2e + 2$ |
47 | $[47, 47, -2w^{3} + 11w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} + e - 3$ |
61 | $[61, 61, w^{2} - 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 9e + 7$ |
67 | $[67, 67, w^{2} + w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 9e - 14$ |
79 | $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ | $-e^{2} + e + 10$ |
97 | $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ | $\phantom{-}e^{2} - 2e - 8$ |
97 | $[97, 97, -w^{3} + 6w - 3]$ | $-e^{2} + 10$ |
97 | $[97, 97, -3w^{3} + 16w]$ | $\phantom{-}\frac{3}{2}e^{3} + e^{2} - 22e - 16$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |
$5$ | $[5, 5, w - 1]$ | $-1$ |