Base field 4.4.16609.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[12, 12, -w^{3} + w^{2} + 3w - 3]$ |
Dimension: | $5$ |
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:
\(x^{5} - 3x^{4} - 17x^{3} + 43x^{2} + 56x - 68\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + w + 4]$ | $\phantom{-}0$ |
3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}1$ |
5 | $[5, 5, w^{2} - 4]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{15}{4}e^{2} + \frac{13}{4}e - \frac{9}{2}$ |
17 | $[17, 17, -w^{2} + w + 5]$ | $-\frac{1}{2}e^{3} + \frac{13}{2}e + 1$ |
27 | $[27, 3, -w^{3} + 4w - 2]$ | $\phantom{-}e^{2} - e - 8$ |
29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{11}{2}e + 5$ |
29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e - 3$ |
37 | $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{15}{2}e^{2} - \frac{15}{2}e + 13$ |
41 | $[41, 41, w^{3} - w^{2} - 5w + 2]$ | $-e^{2} + 10$ |
43 | $[43, 43, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{15}{2}e^{2} - \frac{13}{2}e + 13$ |
61 | $[61, 61, w^{2} - 2w - 2]$ | $-e^{3} + 12e + 2$ |
61 | $[61, 61, 2w^{2} - w - 8]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{13}{2}e + 1$ |
67 | $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ | $-e^{4} + 14e^{2} + 3e - 14$ |
73 | $[73, 73, -w^{2} - 2w + 2]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e + 1$ |
79 | $[79, 79, w^{2} - 2w - 4]$ | $\phantom{-}e^{2} - e - 2$ |
89 | $[89, 89, w^{2} + w - 5]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{11}{2}e + 11$ |
89 | $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{11}{2}e + 9$ |
89 | $[89, 89, w^{3} - 5w - 5]$ | $-e^{4} + 15e^{2} + e - 24$ |
89 | $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}e^{4} - 15e^{2} - e + 28$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w^{2} + w + 4]$ | $-1$ |
$3$ | $[3, 3, -w^{2} + w + 3]$ | $-1$ |