Base field 5.5.176281.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 3x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - 8x^{3} - 27x^{2} - 14x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $-6e^{4} - 16e^{3} + 53e^{2} + 144e + 38$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-1$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}7e^{4} + 19e^{3} - 62e^{2} - 171e - 46$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-5e^{4} - 14e^{3} + 44e^{2} + 126e + 34$ |
| 23 | $[23, 23, -w^{4} + 5w^{2} + w - 4]$ | $-14e^{4} - 38e^{3} + 124e^{2} + 344e + 90$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $\phantom{-}24e^{4} + 64e^{3} - 212e^{2} - 578e - 154$ |
| 32 | $[32, 2, 2]$ | $-6e^{4} - 16e^{3} + 52e^{2} + 144e + 41$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $\phantom{-}3e^{4} + 9e^{3} - 26e^{2} - 84e - 26$ |
| 41 | $[41, 41, w^{4} - w^{3} - 3w^{2} + w + 1]$ | $\phantom{-}24e^{4} + 65e^{3} - 212e^{2} - 587e - 158$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w]$ | $-16e^{4} - 44e^{3} + 140e^{2} + 398e + 114$ |
| 61 | $[61, 61, -w^{4} + 6w^{2} + w - 4]$ | $\phantom{-}6e^{4} + 16e^{3} - 53e^{2} - 148e - 42$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 4w - 3]$ | $-3e^{4} - 7e^{3} + 28e^{2} + 63e + 12$ |
| 71 | $[71, 71, w^{4} - 6w^{2} + 7]$ | $-16e^{4} - 42e^{3} + 142e^{2} + 378e + 100$ |
| 73 | $[73, 73, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-7e^{4} - 18e^{3} + 62e^{2} + 162e + 40$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $\phantom{-}10e^{4} + 26e^{3} - 88e^{2} - 234e - 64$ |
| 83 | $[83, 83, -w^{4} + 5w^{2} + 2w - 4]$ | $-16e^{4} - 44e^{3} + 140e^{2} + 396e + 108$ |
| 83 | $[83, 83, w^{4} - 5w^{2} + 2]$ | $\phantom{-}12e^{4} + 34e^{3} - 104e^{2} - 306e - 94$ |
| 89 | $[89, 89, -2w^{4} + 2w^{3} + 9w^{2} - 6w - 4]$ | $\phantom{-}10e^{4} + 26e^{3} - 87e^{2} - 236e - 76$ |
| 101 | $[101, 101, -2w^{4} + 2w^{3} + 8w^{2} - 3w - 3]$ | $-e^{4} - 3e^{3} + 8e^{2} + 26e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + 2]$ | $1$ |