Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 104x^{2} + 1296\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 11]$ | $\phantom{-}2$ |
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}0$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}0$ |
7 | $[7, 7, w + 1]$ | $-\frac{1}{72}e^{3} + \frac{17}{18}e$ |
7 | $[7, 7, w + 5]$ | $-\frac{1}{72}e^{3} + \frac{17}{18}e$ |
11 | $[11, 11, w + 5]$ | $-\frac{1}{72}e^{3} + \frac{35}{18}e$ |
13 | $[13, 13, w + 6]$ | $-\frac{1}{72}e^{3} + \frac{17}{18}e$ |
17 | $[17, 17, w - 10]$ | $-\frac{1}{8}e^{2} + \frac{13}{2}$ |
17 | $[17, 17, w + 9]$ | $-\frac{1}{8}e^{2} + \frac{13}{2}$ |
19 | $[19, 19, w + 3]$ | $-\frac{1}{48}e^{3} + \frac{17}{12}e$ |
19 | $[19, 19, w + 15]$ | $-\frac{1}{48}e^{3} + \frac{17}{12}e$ |
29 | $[29, 29, -2w + 21]$ | $\phantom{-}\frac{1}{4}e^{2} - 13$ |
29 | $[29, 29, 5w - 54]$ | $\phantom{-}\frac{1}{4}e^{2} - 13$ |
47 | $[47, 47, w + 18]$ | $\phantom{-}\frac{1}{72}e^{3} - \frac{35}{18}e$ |
47 | $[47, 47, w + 28]$ | $\phantom{-}\frac{1}{72}e^{3} - \frac{35}{18}e$ |
59 | $[59, 59, w + 27]$ | $-\frac{1}{36}e^{3} + \frac{35}{9}e$ |
59 | $[59, 59, w + 31]$ | $-\frac{1}{36}e^{3} + \frac{35}{9}e$ |
71 | $[71, 71, w + 21]$ | $\phantom{-}\frac{1}{72}e^{3} - \frac{35}{18}e$ |
71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{1}{72}e^{3} - \frac{35}{18}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $1$ |