Base field 4.4.8525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 8x^{2} + 9x + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[11,11,w^{2} - 5]$ |
Dimension: | $3$ |
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:
\(x^{3} + 2x^{2} - 14x - 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $-\frac{1}{2}e^{2} + 5$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 9$ |
11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}e^{2} - 10$ |
11 | $[11, 11, w^{2} - 5]$ | $\phantom{-}1$ |
16 | $[16, 2, 2]$ | $-e^{2} + 9$ |
19 | $[19, 19, -w]$ | $-\frac{3}{2}e^{2} + e + 13$ |
19 | $[19, 19, -w + 1]$ | $\phantom{-}2e^{2} - 2e - 26$ |
31 | $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ | $-e^{2} + 14$ |
31 | $[31, 31, -w^{2} + 2w + 7]$ | $-e^{2} + 4$ |
31 | $[31, 31, -w^{3} + 5w + 5]$ | $\phantom{-}e^{2} - 2e - 16$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $-2e^{2} + 2e + 28$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $-\frac{1}{2}e^{2} - e + 3$ |
59 | $[59, 59, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{7}{2}e^{2} + 3e + 41$ |
59 | $[59, 59, -w^{3} + w^{2} + 4w + 5]$ | $-\frac{1}{2}e^{2} - e + 7$ |
59 | $[59, 59, w^{3} - 5w^{2} - w + 18]$ | $\phantom{-}5e^{2} - 6e - 62$ |
59 | $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}2e^{2} - 2e - 28$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{3}{2}e^{2} - e - 19$ |
89 | $[89, 89, -w^{3} + 3w^{2} - 3]$ | $-\frac{7}{2}e^{2} + 2e + 41$ |
89 | $[89, 89, -4w^{2} + 5w + 20]$ | $\phantom{-}3e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,w^{2} - 5]$ | $-1$ |