Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, -2w + 19]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $90$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} + 8x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e^{3} + 3e^{2} + 8e + 3$ |
| 3 | $[3, 3, -2w + 19]$ | $-1$ |
| 5 | $[5, 5, w]$ | $-\frac{7}{8}e^{3} - 3e^{2} - 7e - \frac{21}{8}$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{9}{8}e^{3} + 3e^{2} + 7e + \frac{3}{8}$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{3}{8}e^{3} - e^{2} - 3e - \frac{1}{8}$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{3}{8}e^{3} + e^{2} + 3e + \frac{9}{8}$ |
| 17 | $[17, 17, w + 3]$ | $-\frac{7}{8}e^{3} - 3e^{2} - 7e - \frac{21}{8}$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}\frac{9}{8}e^{3} + 3e^{2} + 7e + \frac{3}{8}$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{21}{8}e^{3} + 9e^{2} + 21e + \frac{63}{8}$ |
| 19 | $[19, 19, w + 12]$ | $\phantom{-}\frac{27}{8}e^{3} + 9e^{2} + 21e + \frac{9}{8}$ |
| 37 | $[37, 37, w + 2]$ | $-\frac{9}{8}e^{3} - 3e^{2} - 9e - \frac{27}{8}$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{9}{8}e^{3} + 3e^{2} + 9e + \frac{3}{8}$ |
| 49 | $[49, 7, -7]$ | $-2$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{21}{2}$ |
| 59 | $[59, 59, 4w - 37]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}$ |
| 61 | $[61, 61, w + 28]$ | $\phantom{-}\frac{33}{8}e^{3} + 11e^{2} + 33e + \frac{11}{8}$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{33}{8}e^{3} - 11e^{2} - 33e - \frac{99}{8}$ |
| 71 | $[71, 71, w + 22]$ | $-\frac{9}{8}e^{3} - 3e^{2} - 9e - \frac{27}{8}$ |
| 71 | $[71, 71, w + 48]$ | $-\frac{9}{8}e^{3} - 3e^{2} - 9e - \frac{3}{8}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w + 19]$ | $1$ |