Base field \(\Q(\sqrt{42}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 42\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[7, 7, w - 7]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 14x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-\frac{1}{2}e^{3} - \frac{13}{2}e$ |
3 | $[3, 3, w]$ | $\phantom{-}0$ |
7 | $[7, 7, w - 7]$ | $\phantom{-}1$ |
11 | $[11, 11, w + 3]$ | $-e^{3} - 13e$ |
11 | $[11, 11, w + 8]$ | $-e^{3} - 13e$ |
13 | $[13, 13, w + 4]$ | $-\frac{1}{2}e^{3} - \frac{15}{2}e$ |
13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{15}{2}e$ |
17 | $[17, 17, -w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{7}{2}$ |
17 | $[17, 17, -w + 5]$ | $-\frac{1}{2}e^{2} - \frac{7}{2}$ |
19 | $[19, 19, w + 2]$ | $-e^{3} - 15e$ |
19 | $[19, 19, w + 17]$ | $\phantom{-}e^{3} + 15e$ |
25 | $[25, 5, 5]$ | $-2$ |
29 | $[29, 29, w + 10]$ | $\phantom{-}0$ |
29 | $[29, 29, w + 19]$ | $\phantom{-}0$ |
41 | $[41, 41, -w - 1]$ | $-\frac{3}{2}e^{2} - \frac{21}{2}$ |
41 | $[41, 41, w - 1]$ | $\phantom{-}\frac{3}{2}e^{2} + \frac{21}{2}$ |
47 | $[47, 47, -2w + 11]$ | $-e^{2} - 7$ |
47 | $[47, 47, 4w - 25]$ | $\phantom{-}e^{2} + 7$ |
53 | $[53, 53, w + 25]$ | $-2e^{3} - 26e$ |
53 | $[53, 53, w + 28]$ | $-2e^{3} - 26e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w - 7]$ | $-1$ |