Base field 5.5.170701.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 5x^{11} - 17x^{10} + 118x^{9} + x^{8} - 802x^{7} + 758x^{6} + 1868x^{5} - 2741x^{4} - 857x^{3} + 2071x^{2} - 90x - 145\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $...$ |
| 8 | $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ | $...$ |
| 11 | $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ | $...$ |
| 13 | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $...$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}e^{11} - 3e^{10} - 23e^{9} + 72e^{8} + 145e^{7} - 512e^{6} - 266e^{5} + 1336e^{4} - 69e^{3} - 995e^{2} + 80e + 74$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $...$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $...$ |
| 47 | $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $...$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $...$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ | $...$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 4w - 1]$ | $...$ |
| 71 | $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ | $...$ |
| 71 | $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ | $...$ |
| 71 | $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ | $...$ |
| 73 | $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ | $...$ |
| 79 | $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ | $...$ |
| 83 | $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ | $...$ |
| 89 | $[89, 89, w^{3} - w^{2} - 5w + 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $-1$ |