Base field \(\Q(\sqrt{5}, \sqrt{21})\)
Generator \(w\), with minimal polynomial \(x^{4} - 13x^{2} + 16\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 4, -w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 18x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{11}{4}w + 5]$ | $\phantom{-}0$ |
4 | $[4, 2, \frac{1}{8}w^{3} - \frac{1}{2}w^{2} - \frac{5}{8}w + \frac{3}{2}]$ | $\phantom{-}2$ |
5 | $[5, 5, -\frac{3}{8}w^{3} + \frac{35}{8}w - \frac{1}{2}]$ | $\phantom{-}e$ |
5 | $[5, 5, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{1}{2}]$ | $-\frac{1}{6}e^{3} + 3e$ |
9 | $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ | $\phantom{-}1$ |
41 | $[41, 41, \frac{1}{8}w^{3} - \frac{1}{8}w + \frac{3}{2}]$ | $\phantom{-}\frac{1}{2}e^{3} - 8e$ |
41 | $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{3}{2}]$ | $-\frac{1}{3}e^{3} + 5e$ |
41 | $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{3}{2}]$ | $\phantom{-}\frac{1}{6}e^{3} - e$ |
41 | $[41, 41, -\frac{1}{8}w^{3} + \frac{1}{8}w + \frac{3}{2}]$ | $-\frac{1}{6}e^{3}$ |
49 | $[49, 7, \frac{1}{8}w^{3} - \frac{17}{8}w + \frac{7}{2}]$ | $\phantom{-}8$ |
59 | $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w - \frac{5}{2}]$ | $-\frac{2}{3}e^{3} + 9e$ |
59 | $[59, 59, -\frac{7}{8}w^{3} + \frac{3}{2}w^{2} + \frac{83}{8}w - \frac{35}{2}]$ | $\phantom{-}\frac{1}{6}e^{3} - e$ |
59 | $[59, 59, -\frac{3}{4}w^{3} + \frac{3}{2}w^{2} + \frac{33}{4}w - 16]$ | $-\frac{1}{3}e^{3} + 5e$ |
59 | $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w + \frac{5}{2}]$ | $\phantom{-}\frac{1}{2}e^{3} - 5e$ |
79 | $[79, 79, \frac{3}{8}w^{3} - w^{2} - \frac{35}{8}w + \frac{21}{2}]$ | $\phantom{-}e^{2} - 13$ |
79 | $[79, 79, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 5]$ | $\phantom{-}e^{2} - 1$ |
79 | $[79, 79, \frac{7}{8}w^{3} - \frac{79}{8}w - \frac{1}{2}]$ | $-e^{2} + 17$ |
79 | $[79, 79, -\frac{3}{8}w^{3} - w^{2} + \frac{35}{8}w + \frac{21}{2}]$ | $-e^{2} + 5$ |
89 | $[89, 89, \frac{1}{8}w^{3} - \frac{1}{8}w - \frac{5}{2}]$ | $\phantom{-}\frac{1}{3}e^{3} - 7e$ |
89 | $[89, 89, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{5}{2}]$ | $\phantom{-}\frac{7}{6}e^{3} - 14e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,\frac{1}{4}w^{3}-\frac{1}{2}w^{2}-\frac{11}{4}w+5]$ | $1$ |