Base field 5.5.195829.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[16, 16, -w^{4} + 2w^{3} + 5w^{2} - 7w - 7]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2w + 1]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $\phantom{-}6$ |
| 13 | $[13, 13, -w^{4} + 3w^{3} + 3w^{2} - 9w - 3]$ | $-2$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}2$ |
| 16 | $[16, 2, w^{4} - 3w^{3} - 4w^{2} + 10w + 5]$ | $-5$ |
| 17 | $[17, 17, -w^{4} + 2w^{3} + 5w^{2} - 6w - 5]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}6$ |
| 29 | $[29, 29, w^{4} - 2w^{3} - 5w^{2} + 7w + 4]$ | $-6$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 3w^{2} + 8w + 4]$ | $-2$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}2$ |
| 37 | $[37, 37, 3w^{4} - 6w^{3} - 13w^{2} + 17w + 12]$ | $\phantom{-}10$ |
| 59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 2w + 2]$ | $\phantom{-}12$ |
| 59 | $[59, 59, -w^{4} + 2w^{3} + 5w^{2} - 5w - 4]$ | $-6$ |
| 59 | $[59, 59, -w^{4} + 2w^{3} + 3w^{2} - 3w]$ | $-6$ |
| 79 | $[79, 79, 2w^{4} - 5w^{3} - 6w^{2} + 14w + 4]$ | $\phantom{-}14$ |
| 79 | $[79, 79, -w^{4} + 3w^{3} + 3w^{2} - 9w - 5]$ | $\phantom{-}14$ |
| 83 | $[83, 83, -2w^{4} + 5w^{3} + 8w^{2} - 16w - 10]$ | $-12$ |
| 101 | $[101, 101, w^{4} - 3w^{3} - 4w^{2} + 11w + 4]$ | $\phantom{-}6$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 5w^{2} - 5w - 6]$ | $\phantom{-}4$ |
| 107 | $[107, 107, -2w^{4} + 4w^{3} + 8w^{2} - 10w - 7]$ | $-18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + 2w + 1]$ | $-1$ |