Base field \(\Q(\sqrt{82}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 82\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $4$ |
| 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:
| \(x^{4} + 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{1}{9}e^{2}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 4]$ | $-\frac{2}{3}e$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{4}{27}e^{3}$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{1}{27}e^{3}$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{4}{3}e$ |
| 19 | $[19, 19, w + 5]$ | $-\frac{1}{3}e$ |
| 19 | $[19, 19, w + 14]$ | $-\frac{2}{27}e^{3}$ |
| 23 | $[23, 23, w + 6]$ | $\phantom{-}\frac{8}{9}e^{2}$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}\frac{4}{9}e^{2}$ |
| 25 | $[25, 5, -5]$ | $-4$ |
| 29 | $[29, 29, w + 13]$ | $\phantom{-}\frac{2}{9}e^{3}$ |
| 29 | $[29, 29, w + 16]$ | $\phantom{-}2e$ |
| 31 | $[31, 31, w + 12]$ | $-\frac{4}{9}e^{2}$ |
| 31 | $[31, 31, w + 19]$ | $\phantom{-}\frac{7}{9}e^{2}$ |
| 41 | $[41, 41, w]$ | $-\frac{1}{3}e^{2}$ |
| 49 | $[49, 7, -7]$ | $-3$ |
| 53 | $[53, 53, w + 20]$ | $\phantom{-}0$ |
| 53 | $[53, 53, w + 33]$ | $\phantom{-}3e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{1}{9}e^{2}$ |