Base field 3.3.1384.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[11, 11, -w^{2} - w + 11]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 13x^{6} + 50x^{4} - 52x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
2 | $[2, 2, w^{2} + 2w - 5]$ | $-\frac{1}{4}e^{6} + \frac{11}{4}e^{4} - 8e^{2} + 4$ |
7 | $[7, 7, w^{2} + w - 7]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 8e$ |
11 | $[11, 11, -w^{2} - w + 11]$ | $\phantom{-}1$ |
11 | $[11, 11, 2w^{2} + 2w - 15]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + 4e$ |
11 | $[11, 11, w^{2} + w - 9]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 10e$ |
13 | $[13, 13, 2w - 5]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{2} - w + 5]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 7e$ |
27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{9}{2}e^{4} + 10e^{2} - 4$ |
29 | $[29, 29, w^{2} + w - 3]$ | $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 22e^{2} + 12$ |
37 | $[37, 37, -2w^{2} + 15]$ | $-e^{7} + \frac{25}{2}e^{5} - \frac{87}{2}e^{3} + 33e$ |
43 | $[43, 43, 3w^{2} + w - 27]$ | $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 24e^{2} + 12$ |
49 | $[49, 7, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + 19e$ |
67 | $[67, 67, 2w^{2} + 2w - 17]$ | $-\frac{1}{2}e^{7} + 6e^{5} - \frac{41}{2}e^{3} + 14e$ |
71 | $[71, 71, 2w - 1]$ | $-\frac{1}{2}e^{6} + \frac{9}{2}e^{4} - 8e^{2} + 4$ |
79 | $[79, 79, 3w^{2} + w - 25]$ | $-4e$ |
83 | $[83, 83, w^{2} + 3w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{11}{2}e^{4} + 16e^{2} - 8$ |
89 | $[89, 89, -4w^{2} - 4w + 31]$ | $-e^{7} + \frac{27}{2}e^{5} - \frac{105}{2}e^{3} + 45e$ |
89 | $[89, 89, -2w^{2} + 17]$ | $-4e^{2} + 10$ |
89 | $[89, 89, 2w^{2} + 2w - 19]$ | $-\frac{3}{2}e^{7} + \frac{33}{2}e^{5} - 48e^{3} + 23e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, -w^{2} - w + 11]$ | $-1$ |