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: | $[19, 19, -w]$ |
| 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 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}3e^{4} + 23e^{3} + 47e^{2} + 5e - 32$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}e^{2} + 2e - 4$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}e^{2} + 4e + 2$ |
| 11 | $[11, 11, w^{2} - 5]$ | $-2e^{4} - 15e^{3} - 30e^{2} - 2e + 20$ |
| 16 | $[16, 2, 2]$ | $-3e^{4} - 22e^{3} - 43e^{2} - 6e + 25$ |
| 19 | $[19, 19, -w]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w + 1]$ | $\phantom{-}3e^{4} + 22e^{3} + 42e^{2} + 2e - 30$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}4e^{4} + 30e^{3} + 59e^{2} + 2e - 42$ |
| 31 | $[31, 31, -w^{2} + 2w + 7]$ | $-e^{4} - 8e^{3} - 18e^{2} - 6e + 10$ |
| 31 | $[31, 31, -w^{3} + 5w + 5]$ | $-7e^{4} - 54e^{3} - 112e^{2} - 16e + 74$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}3e^{4} + 24e^{3} + 50e^{2} + 4e - 28$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $-6e^{4} - 48e^{3} - 104e^{2} - 18e + 68$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 6w - 2]$ | $-e^{4} - 5e^{3} - 3e^{2} + 6e - 2$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 4w + 5]$ | $-3e^{4} - 24e^{3} - 50e^{2} - 2e + 36$ |
| 59 | $[59, 59, w^{3} - 5w^{2} - w + 18]$ | $-e^{4} - 5e^{3} - 4e^{2} - 4$ |
| 59 | $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}3e^{4} + 24e^{3} + 51e^{2} + 6e - 34$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}10e^{4} + 74e^{3} + 146e^{2} + 16e - 94$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} - 3]$ | $-2e^{4} - 11e^{3} - 8e^{2} + 15e - 2$ |
| 89 | $[89, 89, -4w^{2} + 5w + 20]$ | $-4e^{4} - 29e^{3} - 52e^{2} + e + 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w]$ | $-1$ |