Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 9x^{6} + 26x^{4} - 27x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 2]$ | $-e^{6} + 7e^{4} - 13e^{2} + 4$ |
| 5 | $[5, 5, -3w + 25]$ | $\phantom{-}e^{7} - 8e^{5} + 18e^{3} - 10e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e^{3} - 3e$ |
| 11 | $[11, 11, w - 9]$ | $\phantom{-}e^{6} - 10e^{4} + 28e^{2} - 18$ |
| 11 | $[11, 11, -w - 9]$ | $\phantom{-}2e^{4} - 9e^{2} + 6$ |
| 17 | $[17, 17, w + 6]$ | $-3e^{6} + 22e^{4} - 46e^{2} + 24$ |
| 17 | $[17, 17, w + 11]$ | $\phantom{-}2e^{6} - 14e^{4} + 24e^{2} - 8$ |
| 23 | $[23, 23, w + 1]$ | $-e^{7} + 9e^{5} - 25e^{3} + 23e$ |
| 23 | $[23, 23, w + 22]$ | $-2e^{7} + 16e^{5} - 38e^{3} + 23e$ |
| 31 | $[31, 31, 4w - 33]$ | $-e^{7} + 11e^{5} - 35e^{3} + 28e$ |
| 31 | $[31, 31, 4w + 33]$ | $-e^{7} + 7e^{5} - 10e^{3} - 4e$ |
| 37 | $[37, 37, w + 12]$ | $-3e^{7} + 21e^{5} - 39e^{3} + 16e$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}2e^{7} - 15e^{5} + 31e^{3} - 16e$ |
| 53 | $[53, 53, w + 21]$ | $-e^{7} + 6e^{5} - 10e^{3} + 10e$ |
| 53 | $[53, 53, w + 32]$ | $\phantom{-}3e^{7} - 23e^{5} + 47e^{3} - 22e$ |
| 61 | $[61, 61, -w - 3]$ | $-2e^{7} + 13e^{5} - 18e^{3} - 6e$ |
| 61 | $[61, 61, w - 3]$ | $\phantom{-}5e^{7} - 42e^{5} + 102e^{3} - 62e$ |
| 73 | $[73, 73, w + 17]$ | $\phantom{-}4e^{6} - 28e^{4} + 55e^{2} - 32$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |