Base field 6.6.1997632.1
Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[13, 13, w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 21x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $-\frac{1}{3}e^{3} + 6e$ |
13 | $[13, 13, w]$ | $-1$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}\frac{1}{3}e^{3} - 7e$ |
27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $\phantom{-}2$ |
27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $\phantom{-}2$ |
29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $-2e$ |
29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $-\frac{2}{3}e^{3} + 14e$ |
41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}e^{2} - 9$ |
41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $-\frac{2}{3}e^{3} + 12e$ |
41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $-\frac{2}{3}e^{3} + 12e$ |
41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $-e^{2} + 12$ |
43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $\phantom{-}e$ |
43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $\phantom{-}\frac{1}{3}e^{3} - 7e$ |
49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $-4$ |
97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $\phantom{-}2e$ |
97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $\phantom{-}\frac{2}{3}e^{3} - 12e$ |
97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{2}{3}e^{3} - 12e$ |
97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $\phantom{-}\frac{2}{3}e^{3} - 14e$ |
113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $-e^{3} + 23e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w]$ | $1$ |