Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 6x^{2} + 17x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}e - 1$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $-e^{2} + e + 4$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-e^{3} + 2e^{2} + 7e - 7$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-e^{3} + 8e + 1$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 6$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $\phantom{-}2e - 1$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}e^{2} - e$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $-2e^{3} + 2e^{2} + 15e - 11$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $-e^{2} + 9$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $-e^{2} + 10$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}3e$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}2e^{3} - e^{2} - 15e + 2$ |
| 83 | $[83, 83, -w - 3]$ | $\phantom{-}e - 10$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $-e^{3} + 3e^{2} + 4e - 10$ |
| 89 | $[89, 89, 2w - 1]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 8$ |
| 101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $\phantom{-}e^{3} - e^{2} - 5e - 1$ |
| 101 | $[101, 101, 2w^{2} - 3w - 3]$ | $-e^{3} + e^{2} + 8e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $1$ |