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: | $[19,19,w - 1]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 9x^{4} + 26x^{3} - 23x^{2} - 8x + 14\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $-3e^{4} + 23e^{3} - 47e^{2} + 5e + 32$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}2e^{4} - 15e^{3} + 30e^{2} - 2e - 20$ |
11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}e^{2} - 4e + 2$ |
11 | $[11, 11, w^{2} - 5]$ | $-e^{2} + 2e + 4$ |
16 | $[16, 2, 2]$ | $-3e^{4} + 22e^{3} - 43e^{2} + 6e + 25$ |
19 | $[19, 19, -w]$ | $-3e^{4} + 22e^{3} - 42e^{2} + 2e + 30$ |
19 | $[19, 19, -w + 1]$ | $-1$ |
31 | $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}7e^{4} - 54e^{3} + 112e^{2} - 16e - 74$ |
31 | $[31, 31, -w^{2} + 2w + 7]$ | $\phantom{-}e^{4} - 8e^{3} + 18e^{2} - 6e - 10$ |
31 | $[31, 31, -w^{3} + 5w + 5]$ | $-4e^{4} + 30e^{3} - 59e^{2} + 2e + 42$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $-6e^{4} + 48e^{3} - 104e^{2} + 18e + 68$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}3e^{4} - 24e^{3} + 50e^{2} - 4e - 28$ |
59 | $[59, 59, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}3e^{4} - 24e^{3} + 51e^{2} - 6e - 34$ |
59 | $[59, 59, -w^{3} + w^{2} + 4w + 5]$ | $-e^{4} + 5e^{3} - 4e^{2} - 4$ |
59 | $[59, 59, w^{3} - 5w^{2} - w + 18]$ | $-3e^{4} + 24e^{3} - 50e^{2} + 2e + 36$ |
59 | $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ | $-e^{4} + 5e^{3} - 3e^{2} - 6e - 2$ |
81 | $[81, 3, -3]$ | $\phantom{-}10e^{4} - 74e^{3} + 146e^{2} - 16e - 94$ |
89 | $[89, 89, -w^{3} + 3w^{2} - 3]$ | $\phantom{-}4e^{4} - 29e^{3} + 52e^{2} + e - 22$ |
89 | $[89, 89, -4w^{2} + 5w + 20]$ | $\phantom{-}2e^{4} - 11e^{3} + 8e^{2} + 15e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,w - 1]$ | $1$ |