Base field 5.5.186037.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 2x^{2} + 5x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + w + 3]$ |
| Dimension: | $24$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} - x^{23} - 35x^{22} + 37x^{21} + 519x^{20} - 573x^{19} - 4252x^{18} + 4848x^{17} + 21061x^{16} - 24520x^{15} - 64961x^{14} + 76193x^{13} + 124355x^{12} - 143909x^{11} - 144221x^{10} + 157841x^{9} + 98632x^{8} - 92142x^{7} - 39805x^{6} + 24588x^{5} + 8983x^{4} - 1870x^{3} - 776x^{2} - 10x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 5]$ | $...$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $...$ |
| 16 | $[16, 2, w^{4} - w^{3} - 6w^{2} + 2w + 5]$ | $...$ |
| 19 | $[19, 19, -w^{4} + 7w^{2} + 2w - 3]$ | $...$ |
| 23 | $[23, 23, w^{3} - w^{2} - 4w + 1]$ | $...$ |
| 23 | $[23, 23, -w^{4} + 7w^{2} + 4w - 7]$ | $...$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}1$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $...$ |
| 31 | $[31, 31, w^{4} - 6w^{2} - 2w + 3]$ | $...$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 4w + 3]$ | $...$ |
| 67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 3]$ | $...$ |
| 79 | $[79, 79, -w^{4} + 6w^{2} + 3w - 1]$ | $...$ |
| 83 | $[83, 83, 2w^{4} - 14w^{2} - 7w + 11]$ | $...$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $...$ |
| 83 | $[83, 83, -w^{4} + 8w^{2} + 3w - 7]$ | $...$ |
| 97 | $[97, 97, w^{4} - 2w^{3} - 4w^{2} + 4w + 1]$ | $...$ |
| 101 | $[101, 101, 2w^{4} - 14w^{2} - 6w + 11]$ | $...$ |
| 101 | $[101, 101, -w^{4} + 8w^{2} + 2w - 9]$ | $...$ |
| 107 | $[107, 107, -w^{3} + 2w^{2} + 4w - 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{2} + w + 3]$ | $-1$ |