Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 16x^{6} + 76x^{4} - 112x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $-\frac{1}{4}e^{5} + 3e^{3} - \frac{15}{2}e$ |
5 | $[5, 5, w^{2} - w - 5]$ | $\phantom{-}e$ |
11 | $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ | $\phantom{-}e^{2} - 4$ |
11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $\phantom{-}\frac{1}{4}e^{4} - 3e^{2} + \frac{7}{2}$ |
11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{13}{4}e^{4} + \frac{17}{2}e^{2} + \frac{1}{2}$ |
11 | $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ | $-\frac{1}{4}e^{6} + \frac{13}{4}e^{4} - \frac{19}{2}e^{2} + \frac{3}{2}$ |
29 | $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{13}{4}e^{5} + \frac{19}{2}e^{3} - \frac{7}{2}e$ |
29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{4}e^{5} - 2e^{3} - \frac{1}{2}e$ |
29 | $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ | $-\frac{3}{4}e^{7} + \frac{43}{4}e^{5} - \frac{83}{2}e^{3} + \frac{87}{2}e$ |
29 | $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ | $\phantom{-}\frac{1}{4}e^{5} - 4e^{3} + \frac{27}{2}e$ |
41 | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $\phantom{-}1$ |
41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ | $\phantom{-}\frac{3}{4}e^{6} - \frac{19}{2}e^{4} + \frac{55}{2}e^{2} - 11$ |
41 | $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + \frac{23}{2}e^{2} - 5$ |
41 | $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ | $-\frac{1}{4}e^{6} + 3e^{4} - \frac{13}{2}e^{2} - 4$ |
79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{7} - 4e^{5} + \frac{35}{2}e^{3} - 20e$ |
79 | $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ | $-\frac{1}{2}e^{7} + \frac{29}{4}e^{5} - 27e^{3} + \frac{39}{2}e$ |
79 | $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ | $-\frac{1}{4}e^{7} + \frac{9}{2}e^{5} - \frac{51}{2}e^{3} + 47e$ |
79 | $[79, 79, w^{3} - w^{2} - 6w + 9]$ | $\phantom{-}e^{7} - \frac{57}{4}e^{5} + 55e^{3} - \frac{119}{2}e$ |
81 | $[81, 3, -3]$ | $-\frac{3}{4}e^{6} + \frac{17}{2}e^{4} - \frac{33}{2}e^{2} - 13$ |
109 | $[109, 109, w^{2} - w - 7]$ | $\phantom{-}2e^{5} - 24e^{3} + 59e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $-1$ |