Base field 5.5.126032.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{2} + w + 1]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 5x^{19} - 20x^{18} + 126x^{17} + 138x^{16} - 1302x^{15} - 300x^{14} + 7185x^{13} - 660x^{12} - 23091x^{11} + 3813x^{10} + 43943x^{9} - 4040x^{8} - 47048x^{7} - 3136x^{6} + 23518x^{5} + 5760x^{4} - 2406x^{3} - 400x^{2} + 76x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{4} - 5w^{2} - w + 3]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $...$ |
| 25 | $[25, 5, w^{3} - 5w + 1]$ | $...$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}1$ |
| 37 | $[37, 37, -w^{4} + 5w^{2} + 2w - 1]$ | $...$ |
| 41 | $[41, 41, w^{3} - 4w - 1]$ | $...$ |
| 41 | $[41, 41, -2w^{4} - w^{3} + 10w^{2} + 6w - 5]$ | $...$ |
| 43 | $[43, 43, 2w^{4} + w^{3} - 11w^{2} - 5w + 7]$ | $...$ |
| 47 | $[47, 47, 2w^{4} + 2w^{3} - 11w^{2} - 9w + 9]$ | $...$ |
| 53 | $[53, 53, w^{4} + w^{3} - 6w^{2} - 6w + 5]$ | $...$ |
| 53 | $[53, 53, 2w^{4} - 11w^{2} - 2w + 5]$ | $...$ |
| 53 | $[53, 53, -2w^{3} + w^{2} + 9w - 5]$ | $...$ |
| 59 | $[59, 59, -w^{4} + 6w^{2} + w - 3]$ | $...$ |
| 61 | $[61, 61, w^{4} + w^{3} - 7w^{2} - 5w + 7]$ | $...$ |
| 73 | $[73, 73, -4w^{4} - w^{3} + 23w^{2} + 6w - 19]$ | $...$ |
| 79 | $[79, 79, -2w^{4} - w^{3} + 12w^{2} + 4w - 9]$ | $...$ |
| 81 | $[81, 3, w^{4} - w^{3} - 5w^{2} + 2w + 1]$ | $...$ |
| 83 | $[83, 83, -w^{3} - w^{2} + 4w + 3]$ | $...$ |
| 83 | $[83, 83, -2w^{4} + 11w^{2} - 7]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{2} + w + 1]$ | $-1$ |