Base field 4.4.18432.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7,7,-\frac{1}{3}w^{2} + w + 1]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 13x^{6} + 54x^{4} - 71x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $\phantom{-}e$ |
7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $-\frac{1}{2}e^{6} + 4e^{4} - 8e^{2} + \frac{9}{2}$ |
7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $-1$ |
7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $-\frac{1}{2}e^{6} + 5e^{4} - 12e^{2} + \frac{5}{2}$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $\phantom{-}e^{2} - 3$ |
9 | $[9, 3, w - 3]$ | $-\frac{1}{2}e^{7} + 7e^{5} - 31e^{3} + \frac{87}{2}e$ |
41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $\phantom{-}\frac{3}{2}e^{7} - 20e^{5} + 84e^{3} - \frac{215}{2}e$ |
41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $-\frac{1}{2}e^{7} + 8e^{5} - 38e^{3} + \frac{105}{2}e$ |
41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $-e^{7} + 12e^{5} - 47e^{3} + 60e$ |
41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $-\frac{3}{2}e^{7} + 17e^{5} - 60e^{3} + \frac{131}{2}e$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $\phantom{-}2e^{5} - 16e^{3} + 26e$ |
47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $\phantom{-}4e^{5} - 33e^{3} + 63e$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $\phantom{-}e^{7} - 13e^{5} + 54e^{3} - 70e$ |
47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $-\frac{1}{2}e^{7} + 8e^{5} - 42e^{3} + \frac{141}{2}e$ |
89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $\phantom{-}2e^{7} - 23e^{5} + 83e^{3} - 92e$ |
89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $-3e^{7} + 34e^{5} - 118e^{3} + 121e$ |
89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $\phantom{-}2e^{7} - 25e^{5} + 100e^{3} - 129e$ |
89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{7} - 2e^{5} - 13e^{3} + \frac{97}{2}e$ |
97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $-2e^{6} + 19e^{4} - 45e^{2} + 6$ |
97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $-e^{4} + 8e^{2} - 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7,7,-\frac{1}{3}w^{2} + w + 1]$ | $1$ |