Base field 3.3.1101.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[12, 6, w^{2} + w - 9]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 8x^{3} + 6x^{2} + 13x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, -w + 3]$ | $-1$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 3e^{2} + \frac{5}{2}$ |
4 | $[4, 2, w^{2} + w - 7]$ | $\phantom{-}1$ |
19 | $[19, 19, w + 1]$ | $-e^{2} + 5$ |
23 | $[23, 23, w^{2} - 2w - 1]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 6$ |
31 | $[31, 31, -2w^{2} + 19]$ | $-\frac{3}{2}e^{4} + 9e^{2} - e - \frac{5}{2}$ |
31 | $[31, 31, -w^{2} + 5]$ | $-\frac{1}{2}e^{4} + e^{3} + 3e^{2} - 5e - \frac{5}{2}$ |
31 | $[31, 31, -3w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - 4e^{2} + 11e + \frac{13}{2}$ |
41 | $[41, 41, w^{2} + 2w - 7]$ | $-e^{3} + 3e$ |
43 | $[43, 43, w^{2} - 11]$ | $-\frac{1}{2}e^{4} - e^{3} + 2e^{2} + 4e + \frac{7}{2}$ |
47 | $[47, 47, 3w - 7]$ | $-\frac{1}{2}e^{4} + e^{3} - 4e + \frac{15}{2}$ |
53 | $[53, 53, -3w^{2} - 6w + 11]$ | $\phantom{-}\frac{1}{2}e^{4} + 2e^{3} - 2e^{2} - 10e - \frac{9}{2}$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}\frac{3}{2}e^{4} - e^{3} - 8e^{2} + 3e + \frac{9}{2}$ |
67 | $[67, 67, 2w^{2} + w - 19]$ | $-e^{4} - e^{3} + 8e^{2} + 7e - 13$ |
67 | $[67, 67, 3w^{2} + 2w - 25]$ | $-e^{4} + e^{3} + 8e^{2} - 9e - 7$ |
67 | $[67, 67, w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - 2e^{2} + 4e - \frac{5}{2}$ |
73 | $[73, 73, -4w^{2} - 3w + 29]$ | $-e^{4} - 2e^{3} + 7e^{2} + 10e - 4$ |
73 | $[73, 73, 2w^{2} - w - 11]$ | $\phantom{-}\frac{3}{2}e^{4} - 3e^{3} - 11e^{2} + 14e + \frac{25}{2}$ |
73 | $[73, 73, w^{2} + 2w - 11]$ | $\phantom{-}2e^{3} + 2e^{2} - 14e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w + 3]$ | $1$ |
$4$ | $[4, 2, w^{2} + w - 7]$ | $-1$ |