Base field 5.5.124817.1
Generator \(w\), with minimal polynomial \(x^{5} - 7x^{3} - 6x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 27, -w^{4} + w^{3} + 5w^{2} + 2w + 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} - w + 3]$ | $\phantom{-}3$ |
| 11 | $[11, 11, w^{3} - w^{2} - 6w - 1]$ | $\phantom{-}0$ |
| 17 | $[17, 17, -w^{4} + 2w^{3} + 4w^{2} - 4w]$ | $-3$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 5w^{2} + 3w - 1]$ | $-2$ |
| 19 | $[19, 19, w^{4} - w^{3} - 5w^{2} - w - 1]$ | $\phantom{-}0$ |
| 25 | $[25, 5, 2w^{4} - 2w^{3} - 11w^{2} - 2w + 2]$ | $-3$ |
| 29 | $[29, 29, -w^{4} + 7w^{2} + 5w - 1]$ | $-6$ |
| 32 | $[32, 2, 2]$ | $-3$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w + 1]$ | $-6$ |
| 43 | $[43, 43, -w + 2]$ | $\phantom{-}9$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 3]$ | $-6$ |
| 61 | $[61, 61, 3w^{4} - 2w^{3} - 18w^{2} - 8w + 2]$ | $-8$ |
| 73 | $[73, 73, -2w^{4} + 2w^{3} + 11w^{2} + 3w - 1]$ | $\phantom{-}6$ |
| 79 | $[79, 79, -w^{4} - w^{3} + 8w^{2} + 10w + 1]$ | $\phantom{-}6$ |
| 81 | $[81, 3, 2w^{4} - w^{3} - 12w^{2} - 9w + 1]$ | $-10$ |
| 97 | $[97, 97, w^{4} - 2w^{3} - 5w^{2} + 4w + 3]$ | $\phantom{-}8$ |
| 103 | $[103, 103, -2w^{3} + 3w^{2} + 9w + 1]$ | $-9$ |
| 113 | $[113, 113, -w^{4} + 3w^{3} + 3w^{2} - 8w - 2]$ | $-12$ |
| 125 | $[125, 5, 2w^{4} - 3w^{3} - 9w^{2} + 2w]$ | $-18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{3} - w^{2} - 5w - 1]$ | $1$ |