Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[12, 6, -2w - 12]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 15x^{2} - 18x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 6]$ | $\phantom{-}1$ |
3 | $[3, 3, -w + 7]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} - 3e + 2$ |
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, 4w + 25]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 4e + 1$ |
5 | $[5, 5, -4w + 29]$ | $\phantom{-}e$ |
11 | $[11, 11, w - 8]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - 3e + 5$ |
11 | $[11, 11, -w - 7]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 3e - 2$ |
13 | $[13, 13, 3w + 19]$ | $-\frac{5}{3}e^{3} + \frac{10}{3}e^{2} + 17e - 1$ |
13 | $[13, 13, 3w - 22]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - 4e - 3$ |
29 | $[29, 29, 6w + 37]$ | $\phantom{-}e^{3} - \frac{4}{3}e^{2} - 10e - 3$ |
29 | $[29, 29, 6w - 43]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 3e - 2$ |
37 | $[37, 37, 2w - 13]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + 3e - 4$ |
37 | $[37, 37, 2w + 11]$ | $-e^{3} + \frac{7}{3}e^{2} + 9e$ |
43 | $[43, 43, -w - 1]$ | $\phantom{-}e^{3} - \frac{4}{3}e^{2} - 13e - 4$ |
43 | $[43, 43, w - 2]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{4}{3}e^{2} - 4e$ |
49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 5e - 6$ |
59 | $[59, 59, 5w - 37]$ | $\phantom{-}e^{3} - 4e^{2} - 8e + 17$ |
59 | $[59, 59, 5w + 32]$ | $\phantom{-}\frac{4}{3}e^{3} - \frac{10}{3}e^{2} - 10e + 8$ |
67 | $[67, 67, 21w + 131]$ | $-\frac{4}{3}e^{3} + 4e^{2} + 10e - 18$ |
67 | $[67, 67, 21w - 152]$ | $\phantom{-}\frac{1}{3}e^{3} - 2e^{2} + e + 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w - 6]$ | $-1$ |
$4$ | $[4, 2, 2]$ | $1$ |