Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[13, 13, w + 6]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $132$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 18x^{4} + 15x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{17}{2}e^{2} + 2$ |
5 | $[5, 5, w]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 4]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 2]$ | $\phantom{-}\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + \frac{17}{3}e$ |
7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + \frac{17}{3}e$ |
9 | $[9, 3, 3]$ | $-\frac{5}{6}e^{4} - \frac{89}{6}e^{2} - \frac{13}{3}$ |
11 | $[11, 11, w]$ | $-\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + e$ |
11 | $[11, 11, w + 10]$ | $-\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + e$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}1$ |
17 | $[17, 17, -w - 8]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{19}{3}e^{2} + \frac{16}{3}$ |
31 | $[31, 31, w + 14]$ | $\phantom{-}2e^{5} + 35e^{3} + 14e$ |
31 | $[31, 31, w + 16]$ | $\phantom{-}2e^{5} + 35e^{3} + 14e$ |
37 | $[37, 37, w + 15]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{19}{3}e^{3} + \frac{25}{3}e$ |
37 | $[37, 37, w + 21]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{19}{3}e^{3} + \frac{25}{3}e$ |
41 | $[41, 41, w + 18]$ | $\phantom{-}e^{5} + 18e^{3} + 15e$ |
41 | $[41, 41, w + 22]$ | $\phantom{-}e^{5} + 18e^{3} + 15e$ |
43 | $[43, 43, -w - 3]$ | $-2e^{4} - 35e^{2} - 18$ |
43 | $[43, 43, w - 4]$ | $-2e^{4} - 35e^{2} - 18$ |
53 | $[53, 53, -w - 1]$ | $-\frac{1}{2}e^{4} - \frac{19}{2}e^{2} - 11$ |
53 | $[53, 53, w - 2]$ | $-\frac{1}{2}e^{4} - \frac{19}{2}e^{2} - 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w + 6]$ | $-1$ |