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: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $64$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} + 2x^{2} - 4x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} + 2e - 1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} + e - 2$ |
| 11 | $[11, 11, w + 4]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{2}{3}e^{2} - \frac{1}{3}e + \frac{2}{3}$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{2}{3}e^{3} - \frac{5}{3}e^{2} - \frac{5}{3}e + \frac{10}{3}$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{2}{3}e^{2} + \frac{2}{3}e - \frac{4}{3}$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{1}{6}e^{3} - \frac{2}{3}e^{2} - \frac{2}{3}e - \frac{2}{3}$ |
| 19 | $[19, 19, w + 5]$ | $-\frac{1}{6}e^{3} - \frac{2}{3}e^{2} + \frac{7}{3}e - \frac{2}{3}$ |
| 19 | $[19, 19, w + 14]$ | $\phantom{-}\frac{5}{3}e^{3} + \frac{11}{3}e^{2} + \frac{11}{3}e - \frac{22}{3}$ |
| 23 | $[23, 23, w + 6]$ | $\phantom{-}e^{3} + 3e^{2} + 4e - 2$ |
| 23 | $[23, 23, w + 17]$ | $-e^{2}$ |
| 25 | $[25, 5, -5]$ | $-4$ |
| 29 | $[29, 29, w + 13]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{10}{3}e^{2} + \frac{10}{3}e - \frac{20}{3}$ |
| 29 | $[29, 29, w + 16]$ | $-\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + \frac{2}{3}e - \frac{4}{3}$ |
| 31 | $[31, 31, w + 12]$ | $-e^{3} - e^{2} - 4e + 2$ |
| 31 | $[31, 31, w + 19]$ | $-2e^{3} - 5e^{2} - 8e + 4$ |
| 41 | $[41, 41, w]$ | $-e^{3} - 2e^{2} - 4e + 2$ |
| 49 | $[49, 7, -7]$ | $-4$ |
| 53 | $[53, 53, w + 20]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{10}{3}e^{2} + \frac{10}{3}e - \frac{20}{3}$ |
| 53 | $[53, 53, w + 33]$ | $-\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + \frac{2}{3}e - \frac{4}{3}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).