Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[6, 6, w - 6]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 26x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
3 | $[3, 3, w]$ | $-1$ |
5 | $[5, 5, -w + 5]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{11}{6}e$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{2}e$ |
13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{14}{3}e$ |
13 | $[13, 13, w + 11]$ | $-\frac{1}{12}e^{3} + \frac{17}{6}e$ |
17 | $[17, 17, w + 8]$ | $-\frac{1}{3}e^{2} + \frac{10}{3}$ |
17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{16}{3}$ |
19 | $[19, 19, w + 7]$ | $-\frac{1}{3}e^{2} + \frac{22}{3}$ |
19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{4}{3}$ |
29 | $[29, 29, -w - 1]$ | $\phantom{-}\frac{5}{12}e^{3} - \frac{55}{6}e$ |
29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{5}{12}e^{3} - \frac{55}{6}e$ |
37 | $[37, 37, w + 17]$ | $-\frac{1}{6}e^{3} + \frac{8}{3}e$ |
37 | $[37, 37, w + 20]$ | $-\frac{5}{12}e^{3} + \frac{61}{6}e$ |
71 | $[71, 71, 2w - 7]$ | $-\frac{2}{3}e^{3} + \frac{50}{3}e$ |
71 | $[71, 71, -2w - 7]$ | $-\frac{1}{6}e^{3} + \frac{5}{3}e$ |
83 | $[83, 83, w + 14]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{10}{3}$ |
83 | $[83, 83, w + 69]$ | $-\frac{1}{3}e^{2} + \frac{16}{3}$ |
101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{1}{2}e^{3} - 15e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $1$ |
$3$ | $[3, 3, w]$ | $1$ |