Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[5,5,-w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $150$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 22x^{4} + 153x^{2} - 338\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 9]$ | $\phantom{-}1$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{2}{13}e^{5} - \frac{31}{13}e^{3} + \frac{111}{13}e$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}e^{2} - 8$ |
5 | $[5, 5, w + 3]$ | $-1$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{3}{13}e^{5} - \frac{53}{13}e^{3} + \frac{212}{13}e$ |
7 | $[7, 7, w + 4]$ | $-\frac{3}{13}e^{5} + \frac{53}{13}e^{3} - \frac{212}{13}e$ |
13 | $[13, 13, w + 1]$ | $-e^{4} + 16e^{2} - 58$ |
13 | $[13, 13, w + 12]$ | $\phantom{-}e^{4} - 15e^{2} + 52$ |
43 | $[43, 43, -w - 6]$ | $\phantom{-}\frac{8}{13}e^{5} - \frac{124}{13}e^{3} + \frac{457}{13}e$ |
43 | $[43, 43, w - 6]$ | $-\frac{6}{13}e^{5} + \frac{93}{13}e^{3} - \frac{333}{13}e$ |
47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{5}{13}e^{5} - \frac{84}{13}e^{3} + \frac{336}{13}e$ |
47 | $[47, 47, w + 28]$ | $\phantom{-}\frac{7}{13}e^{5} - \frac{115}{13}e^{3} + \frac{434}{13}e$ |
59 | $[59, 59, w + 16]$ | $-\frac{6}{13}e^{5} + \frac{93}{13}e^{3} - \frac{333}{13}e$ |
59 | $[59, 59, w + 43]$ | $\phantom{-}\frac{3}{13}e^{5} - \frac{53}{13}e^{3} + \frac{251}{13}e$ |
71 | $[71, 71, w + 24]$ | $-\frac{5}{13}e^{5} + \frac{58}{13}e^{3} - \frac{102}{13}e$ |
71 | $[71, 71, w + 47]$ | $\phantom{-}e^{3} - 8e$ |
73 | $[73, 73, 3w - 28]$ | $\phantom{-}e^{4} - 12e^{2} + 32$ |
73 | $[73, 73, 12w - 107]$ | $-e^{4} + 19e^{2} - 78$ |
79 | $[79, 79, -w]$ | $-\frac{9}{13}e^{5} + \frac{133}{13}e^{3} - \frac{454}{13}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,-w + 2]$ | $1$ |