Base field 5.5.173513.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[79, 79, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $125$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{4} + 2w^{3} + 4w^{2} - w - 1]$ | $\phantom{-}4$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $-2$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 7w^{2} + w - 5]$ | $-4$ |
| 17 | $[17, 17, w^{4} - 2w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}3$ |
| 19 | $[19, 19, w^{4} - w^{3} - 7w^{2} - w + 2]$ | $-2$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}4$ |
| 23 | $[23, 23, -w^{3} + 3w^{2} + 2w - 2]$ | $-5$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}0$ |
| 25 | $[25, 5, -w^{4} + 2w^{3} + 5w^{2} - 2w - 1]$ | $-1$ |
| 27 | $[27, 3, -2w^{4} + 4w^{3} + 9w^{2} - 4w - 3]$ | $\phantom{-}4$ |
| 31 | $[31, 31, 2w^{4} - 4w^{3} - 9w^{2} + 4w + 4]$ | $-4$ |
| 32 | $[32, 2, -2]$ | $\phantom{-}5$ |
| 41 | $[41, 41, w^{4} - 3w^{3} - 2w^{2} + 5w]$ | $-6$ |
| 43 | $[43, 43, w^{4} - w^{3} - 7w^{2} + 3]$ | $-8$ |
| 47 | $[47, 47, w^{2} - 2w - 1]$ | $\phantom{-}7$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $-2$ |
| 67 | $[67, 67, -w^{4} + 2w^{3} + 5w^{2} - 4w - 2]$ | $\phantom{-}7$ |
| 71 | $[71, 71, -2w^{4} + 4w^{3} + 10w^{2} - 5w - 4]$ | $\phantom{-}16$ |
| 73 | $[73, 73, w^{4} - w^{3} - 7w^{2} + 6]$ | $\phantom{-}5$ |
| 73 | $[73, 73, 2w^{4} - 3w^{3} - 11w^{2} - w + 6]$ | $-13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $79$ | $[79, 79, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $1$ |