Base field 4.4.16448.2
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14, 14, w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 13x^{5} + 3x^{4} + 50x^{3} - 19x^{2} - 52x + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w^{3} - 6w - 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{3} + 5w + 3]$ | $\phantom{-}e^{2} + e - 4$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $\phantom{-}e^{4} - 7e^{2} + 2e + 8$ |
| 31 | $[31, 31, -w^{2} - w + 1]$ | $-e^{6} - 2e^{5} + 10e^{4} + 16e^{3} - 27e^{2} - 26e + 14$ |
| 31 | $[31, 31, -w^{2} + 3w - 1]$ | $\phantom{-}e^{6} + 2e^{5} - 10e^{4} - 17e^{3} + 27e^{2} + 31e - 16$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w + 1]$ | $-e^{4} - e^{3} + 6e^{2} + 4e - 4$ |
| 41 | $[41, 41, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}e^{6} + e^{5} - 10e^{4} - 8e^{3} + 24e^{2} + 14e - 6$ |
| 41 | $[41, 41, w^{3} + w^{2} - 8w - 11]$ | $-e^{6} - e^{5} + 11e^{4} + 7e^{3} - 32e^{2} - 10e + 18$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $-e^{5} - e^{4} + 8e^{3} + 4e^{2} - 12e$ |
| 47 | $[47, 47, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e^{5} - 10e^{3} + e^{2} + 22e$ |
| 49 | $[49, 7, 2w^{2} - 2w - 9]$ | $-e^{4} + 7e^{2} - 2e - 4$ |
| 71 | $[71, 71, 5w^{3} - 16w^{2} - 17w + 61]$ | $-2e$ |
| 71 | $[71, 71, -2w^{3} - 2w^{2} + 10w + 13]$ | $-e^{5} - e^{4} + 9e^{3} + 7e^{2} - 20e - 6$ |
| 73 | $[73, 73, 3w^{3} + w^{2} - 18w - 17]$ | $-2e^{6} - 2e^{5} + 21e^{4} + 15e^{3} - 57e^{2} - 23e + 26$ |
| 73 | $[73, 73, w^{3} - 5w - 1]$ | $\phantom{-}e^{6} + 2e^{5} - 9e^{4} - 15e^{3} + 17e^{2} + 22e + 8$ |
| 73 | $[73, 73, w^{3} - 7w - 3]$ | $\phantom{-}e^{6} + e^{5} - 10e^{4} - 6e^{3} + 25e^{2} + 5e - 10$ |
| 73 | $[73, 73, -3w^{3} + 10w^{2} + 7w - 31]$ | $-e^{6} - 2e^{5} + 11e^{4} + 17e^{3} - 33e^{2} - 32e + 20$ |
| 81 | $[81, 3, -3]$ | $-e^{5} + 8e^{3} - 2e^{2} - 11e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ | $-1$ |
| $7$ | $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ | $-1$ |