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: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 20x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{1}{4}e^{3} - \frac{9}{2}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{4}e^{3} - \frac{11}{2}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{1}{4}e^{3} - \frac{11}{2}e$ |
| 5 | $[5, 5, -3w + 25]$ | $-\frac{1}{4}e^{2} - \frac{5}{2}$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{4}e^{3} - \frac{9}{2}e$ |
| 11 | $[11, 11, w - 9]$ | $\phantom{-}2$ |
| 11 | $[11, 11, -w - 9]$ | $\phantom{-}2$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{1}{2}e^{3} + 11e$ |
| 17 | $[17, 17, w + 11]$ | $\phantom{-}\frac{1}{2}e^{3} + 11e$ |
| 23 | $[23, 23, w + 1]$ | $-\frac{1}{2}e^{3} - 9e$ |
| 23 | $[23, 23, w + 22]$ | $-\frac{1}{2}e^{3} - 9e$ |
| 31 | $[31, 31, 4w - 33]$ | $-\frac{1}{2}e^{2} - 5$ |
| 31 | $[31, 31, 4w + 33]$ | $-\frac{1}{2}e^{2} - 5$ |
| 37 | $[37, 37, w + 12]$ | $\phantom{-}e^{3} + 18e$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}e^{3} + 18e$ |
| 53 | $[53, 53, w + 21]$ | $-\frac{1}{2}e^{3} - 9e$ |
| 53 | $[53, 53, w + 32]$ | $-\frac{1}{2}e^{3} - 9e$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{3}{4}e^{2} + \frac{15}{2}$ |
| 61 | $[61, 61, w - 3]$ | $\phantom{-}\frac{3}{4}e^{2} + \frac{15}{2}$ |
| 73 | $[73, 73, w + 17]$ | $-\frac{3}{2}e^{3} - 33e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).