Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 4, -w^{3} + 2w^{2} + 3w - 4]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 22x^{4} + 92x^{2} - 72\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2]$ | $\phantom{-}0$ |
2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}0$ |
5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $-\frac{1}{24}e^{5} + \frac{2}{3}e^{3} + \frac{7}{6}e$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + \frac{15}{2}e$ |
19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{11}{6}e^{3} + \frac{20}{3}e$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{1}{4}e^{4} + \frac{9}{2}e^{2} - 6$ |
31 | $[31, 31, -w^{2} + w + 1]$ | $-\frac{1}{6}e^{5} + \frac{19}{6}e^{3} - \frac{19}{3}e$ |
47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + 13e$ |
49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{4}{3}e^{3} + \frac{2}{3}e$ |
53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{19}{2}e^{2} + 21$ |
53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $-\frac{1}{4}e^{4} + 4e^{2} - 3$ |
61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $-\frac{1}{24}e^{5} + \frac{7}{6}e^{3} - \frac{35}{6}e$ |
61 | $[61, 61, 2w^{2} - 7]$ | $-\frac{1}{6}e^{5} + \frac{19}{6}e^{3} - \frac{22}{3}e$ |
71 | $[71, 71, w^{2} - 3w - 5]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{2}e^{2}$ |
73 | $[73, 73, 2w - 3]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{41}{6}e^{3} + \frac{62}{3}e$ |
73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $-\frac{1}{24}e^{5} + \frac{1}{6}e^{3} + \frac{37}{6}e$ |
79 | $[79, 79, 2w^{2} - 5]$ | $-\frac{1}{4}e^{4} + \frac{7}{2}e^{2} - 4$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 13$ |
101 | $[101, 101, 2w^{2} - 4w - 9]$ | $-\frac{1}{8}e^{5} + \frac{7}{2}e^{3} - \frac{39}{2}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w^{2} + 2]$ | $-1$ |
$2$ | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $-1$ |