Base field 4.4.14656.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 4x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[15, 15, -w^{2} + 2w + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 5x^{2} - 2x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w^{2} + w + 1]$ | $-1$ |
| 11 | $[11, 11, w^{2} - 3]$ | $-e^{2}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-e^{3} - 2e^{2} + 4e + 2$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e^{2} - 4$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - w + 5]$ | $\phantom{-}e^{3} - 4e$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + w - 1]$ | $-e^{3} - 4e^{2} + 10$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 2w - 1]$ | $\phantom{-}2e^{3} + e^{2} - 6e + 2$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}e^{3} + 4e^{2} - 12$ |
| 47 | $[47, 47, w^{2} - 2w - 5]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 8$ |
| 47 | $[47, 47, -2w^{3} + 6w^{2} + w - 5]$ | $-e^{3} - 2e^{2}$ |
| 61 | $[61, 61, -2w^{3} + 5w^{2} + 4w - 7]$ | $-2e^{3} - 2e^{2} + 8e + 2$ |
| 67 | $[67, 67, -2w^{2} + 2w + 9]$ | $\phantom{-}3e^{3} + 3e^{2} - 10e - 8$ |
| 67 | $[67, 67, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}3e^{3} + 8e^{2} - 8e - 16$ |
| 71 | $[71, 71, w^{3} - w^{2} - 6w + 3]$ | $-5e^{3} - 4e^{2} + 18e + 4$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 5w + 1]$ | $-e^{3} + 4e - 4$ |
| 89 | $[89, 89, -w - 3]$ | $-4e^{3} - 3e^{2} + 12e + 6$ |
| 89 | $[89, 89, -w^{2} - 2w + 1]$ | $\phantom{-}5e^{3} + 7e^{2} - 12e - 10$ |
| 97 | $[97, 97, w^{3} - w^{2} - 6w + 1]$ | $\phantom{-}2e^{3} + 2e^{2} - 6e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |
| $5$ | $[5, 5, -w^{2} + w + 1]$ | $1$ |