Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[9, 3, -w^{2} + 10]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 14x^{2} - 12x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 2]$ | $-1$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
7 | $[7, 7, w^{2} + w - 7]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 11]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{5}{2}e - 1$ |
7 | $[7, 7, -w^{2} + 9]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{7}{2}e - 1$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{7}{2}e - 2$ |
13 | $[13, 13, -w]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{5}{2}e + 1$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{7}{2}e + 5$ |
23 | $[23, 23, w^{2} + w - 10]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 5e + 6$ |
29 | $[29, 29, 2w^{2} - 21]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 6e$ |
37 | $[37, 37, 2w^{2} + w - 17]$ | $\phantom{-}e^{2} - 10$ |
43 | $[43, 43, 3w^{2} + 3w - 22]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{4}e^{2} - \frac{7}{2}e + 11$ |
47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 2$ |
47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 2$ |
47 | $[47, 47, -w^{2} + 12]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 7e + 2$ |
53 | $[53, 53, w^{2} - w - 4]$ | $\phantom{-}e^{2} - 3e - 10$ |
61 | $[61, 61, w^{2} - 5]$ | $-\frac{5}{4}e^{3} - \frac{1}{4}e^{2} + \frac{25}{2}e + 3$ |
67 | $[67, 67, w^{2} - w - 7]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{11}{2}e + 7$ |
73 | $[73, 73, 7w^{2} + 3w - 66]$ | $-\frac{1}{4}e^{3} + \frac{7}{4}e^{2} + \frac{5}{2}e - 17$ |
79 | $[79, 79, 2w^{2} - 19]$ | $\phantom{-}e^{2} + e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w - 2]$ | $1$ |
$3$ | $[3, 3, w - 1]$ | $-1$ |