Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 12x^{6} + 38x^{4} + 13x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-e^{3} - 5e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e^{6} + 12e^{4} + 37e^{2} + 6$ |
| 5 | $[5, 5, w + 2]$ | $-4e^{7} - 47e^{5} - 142e^{3} - 27e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e^{7} + 12e^{5} + 37e^{3} + 7e$ |
| 7 | $[7, 7, w + 6]$ | $-e^{7} - 12e^{5} - 36e^{3} - 2e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}4e^{7} + 47e^{5} + 142e^{3} + 27e$ |
| 19 | $[19, 19, w + 1]$ | $-2e^{4} - 12e^{2} - 5$ |
| 19 | $[19, 19, w - 2]$ | $-e^{4} - 7e^{2} - 1$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}e^{5} + 8e^{3} + 13e$ |
| 23 | $[23, 23, w + 13]$ | $-4e^{7} - 48e^{5} - 150e^{3} - 40e$ |
| 37 | $[37, 37, w + 11]$ | $-5e^{7} - 59e^{5} - 178e^{3} - 26e$ |
| 37 | $[37, 37, w + 25]$ | $-3e^{7} - 34e^{5} - 97e^{3} - 8e$ |
| 59 | $[59, 59, 3w + 10]$ | $\phantom{-}e^{6} + 12e^{4} + 38e^{2} + 12$ |
| 59 | $[59, 59, 3w - 13]$ | $\phantom{-}2e^{6} + 28e^{4} + 97e^{2} + 11$ |
| 73 | $[73, 73, w + 15]$ | $-e^{5} - 2e^{3} + 25e$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}9e^{7} + 107e^{5} + 327e^{3} + 65e$ |
| 89 | $[89, 89, -w - 10]$ | $\phantom{-}5e^{6} + 59e^{4} + 177e^{2} + 33$ |
| 89 | $[89, 89, w - 11]$ | $\phantom{-}3e^{6} + 31e^{4} + 79e^{2} + 6$ |
| 97 | $[97, 97, w + 22]$ | $\phantom{-}e^{5} + 13e^{3} + 40e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $-e^{7} - 12e^{5} - 37e^{3} - 7e$ |