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: | $[2, 2, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 7x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{1}{3}e^{3} - \frac{8}{3}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e^{3} + 7e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -3w + 25]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w]$ | $-e^{3} - 8e$ |
| 11 | $[11, 11, w - 9]$ | $\phantom{-}e^{2} + 3$ |
| 11 | $[11, 11, -w - 9]$ | $-e^{2} - 4$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}2e^{3} + 15e$ |
| 17 | $[17, 17, w + 11]$ | $\phantom{-}e^{3} + 9e$ |
| 23 | $[23, 23, w + 1]$ | $\phantom{-}3e^{3} + 19e$ |
| 23 | $[23, 23, w + 22]$ | $-2e^{3} - 11e$ |
| 31 | $[31, 31, 4w - 33]$ | $-e^{2} - 4$ |
| 31 | $[31, 31, 4w + 33]$ | $\phantom{-}e^{2} + 3$ |
| 37 | $[37, 37, w + 12]$ | $\phantom{-}2e^{3} + 15e$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}e^{3} + 9e$ |
| 53 | $[53, 53, w + 21]$ | $-3e^{3} - 22e$ |
| 53 | $[53, 53, w + 32]$ | $-e^{3} - 10e$ |
| 61 | $[61, 61, -w - 3]$ | $-3e^{2} - 6$ |
| 61 | $[61, 61, w - 3]$ | $\phantom{-}3e^{2} + 15$ |
| 73 | $[73, 73, w + 17]$ | $-4e^{3} - 23e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{1}{3}e^{3} + \frac{8}{3}e$ |