Base field 5.5.153424.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 8x^{2} - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[4, 2, w^{4} - w^{3} - 5w^{2} + 4w + 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $1$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}4$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}4$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-2$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 5w^{2} - 3w - 1]$ | $-4$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-4$ |
| 29 | $[29, 29, -w^{3} + 4w - 1]$ | $-6$ |
| 43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $-8$ |
| 43 | $[43, 43, -w + 3]$ | $\phantom{-}4$ |
| 47 | $[47, 47, -w^{4} + 2w^{3} + 4w^{2} - 6w - 1]$ | $\phantom{-}4$ |
| 47 | $[47, 47, w^{4} - 6w^{2} - w + 7]$ | $\phantom{-}8$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}12$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 2w - 3]$ | $-2$ |
| 61 | $[61, 61, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ | $\phantom{-}6$ |
| 73 | $[73, 73, -w^{4} + w^{3} + 4w^{2} - 5w - 1]$ | $\phantom{-}10$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}16$ |
| 83 | $[83, 83, -w^{3} + w^{2} + 3w - 5]$ | $\phantom{-}0$ |
| 89 | $[89, 89, -w^{3} - w^{2} + 4w + 1]$ | $\phantom{-}14$ |
| 101 | $[101, 101, w^{3} - 3w^{2} - 4w + 11]$ | $\phantom{-}6$ |
| 101 | $[101, 101, w^{4} - 6w^{2} - 2w + 5]$ | $-2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |