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: | $[3,3,-w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} - 2x^{2} - 17x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{2}{5}e^{3} + e^{2} - \frac{9}{5}e - \frac{18}{5}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 4]$ | $-\frac{7}{5}e^{3} - 4e^{2} + \frac{39}{5}e + \frac{68}{5}$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}\frac{4}{5}e^{3} + 2e^{2} - \frac{28}{5}e - \frac{46}{5}$ |
| 13 | $[13, 13, w + 2]$ | $-\frac{1}{5}e^{3} + \frac{7}{5}e + \frac{4}{5}$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{1}{5}e^{3} + \frac{12}{5}e - \frac{16}{5}$ |
| 19 | $[19, 19, w + 5]$ | $-e^{2} - e + 1$ |
| 19 | $[19, 19, w + 14]$ | $\phantom{-}\frac{3}{5}e^{3} + 2e^{2} - \frac{6}{5}e - \frac{22}{5}$ |
| 23 | $[23, 23, w + 6]$ | $-\frac{4}{5}e^{3} - 3e^{2} + \frac{3}{5}e + \frac{56}{5}$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}2e^{3} + 5e^{2} - 9e - 17$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{3}{5}e^{3} + e^{2} - \frac{26}{5}e - \frac{22}{5}$ |
| 29 | $[29, 29, w + 13]$ | $\phantom{-}\frac{2}{5}e^{3} + e^{2} - \frac{14}{5}e - \frac{43}{5}$ |
| 29 | $[29, 29, w + 16]$ | $\phantom{-}\frac{2}{5}e^{3} + e^{2} - \frac{19}{5}e - \frac{23}{5}$ |
| 31 | $[31, 31, w + 12]$ | $-e^{3} - 3e^{2} + 5e + 12$ |
| 31 | $[31, 31, w + 19]$ | $-e^{3} - 3e^{2} + 5e + 12$ |
| 41 | $[41, 41, w]$ | $\phantom{-}\frac{3}{5}e^{3} - \frac{21}{5}e + \frac{13}{5}$ |
| 49 | $[49, 7, -7]$ | $-e^{3} - 2e^{2} + 4e - 1$ |
| 53 | $[53, 53, w + 20]$ | $\phantom{-}\frac{3}{5}e^{3} + 3e^{2} - \frac{21}{5}e - \frac{72}{5}$ |
| 53 | $[53, 53, w + 33]$ | $\phantom{-}\frac{3}{5}e^{3} + 2e^{2} - \frac{16}{5}e - \frac{12}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $-1$ |