Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, w^{3} - 2w^{2} - 5w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 6x^{6} - 50x^{4} - 43x^{3} + 119x^{2} + 81x - 115\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $-e^{6} - 5e^{5} + 2e^{4} + 34e^{3} + 20e^{2} - 40e - 17$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $-2e^{6} - 8e^{5} + 14e^{4} + 63e^{3} - 32e^{2} - 110e + 70$ |
| 13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-e^{6} - 3e^{5} + 13e^{4} + 31e^{3} - 61e^{2} - 80e + 104$ |
| 16 | $[16, 2, 2]$ | $-e^{5} - 4e^{4} + 5e^{3} + 26e^{2} - 29$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e^{6} + 4e^{5} - 7e^{4} - 31e^{3} + 17e^{2} + 51e - 38$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e^{6} + 5e^{5} - 2e^{4} - 34e^{3} - 20e^{2} + 40e + 15$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}e^{6} + 4e^{5} - 7e^{4} - 32e^{3} + 16e^{2} + 59e - 37$ |
| 19 | $[19, 19, w^{2} - w - 2]$ | $-2e^{6} - 6e^{5} + 24e^{4} + 57e^{3} - 105e^{2} - 133e + 175$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}4e^{6} + 17e^{5} - 24e^{4} - 131e^{3} + 37e^{2} + 218e - 110$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}3e^{6} + 12e^{5} - 23e^{4} - 99e^{3} + 66e^{2} + 186e - 147$ |
| 43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $\phantom{-}e^{6} + 4e^{5} - 9e^{4} - 36e^{3} + 36e^{2} + 80e - 83$ |
| 47 | $[47, 47, w^{3} - 7w - 4]$ | $-2e^{6} - 7e^{5} + 19e^{4} + 60e^{3} - 67e^{2} - 118e + 118$ |
| 53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $\phantom{-}e^{6} + 3e^{5} - 12e^{4} - 28e^{3} + 50e^{2} + 61e - 72$ |
| 61 | $[61, 61, -w - 3]$ | $-7e^{6} - 25e^{5} + 65e^{4} + 214e^{3} - 227e^{2} - 430e + 408$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}2e^{6} + 6e^{5} - 23e^{4} - 54e^{3} + 97e^{2} + 119e - 163$ |
| 73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}2e^{6} + 7e^{5} - 18e^{4} - 57e^{3} + 60e^{2} + 105e - 105$ |
| 81 | $[81, 3, -3]$ | $-e^{6} - 3e^{5} + 13e^{4} + 31e^{3} - 63e^{2} - 82e + 109$ |
| 83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $\phantom{-}4e^{6} + 10e^{5} - 59e^{4} - 111e^{3} + 287e^{2} + 301e - 457$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $-1$ |