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: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | yes |
| Base change: | no |
| Newspace dimension: | $69$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 39x^{4} - 22x^{3} + 1521x^{2} - 429x + 121\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -2w + 19]$ | $-\frac{1}{351}e^{4} + \frac{2}{351}e^{3} - \frac{1}{9}e^{2} + \frac{11}{351}e - \frac{1036}{351}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{1}{39}e^{3} - e + \frac{11}{39}$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{2}{99}e^{5} + \frac{1003}{1287}e^{3} - \frac{5}{9}e^{2} + \frac{1003}{33}e - \frac{1003}{117}$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{2}{99}e^{5} - \frac{1}{117}e^{4} - \frac{26}{33}e^{3} + \frac{2}{9}e^{2} - \frac{38996}{1287}e$ |
| 37 | $[37, 37, w + 2]$ | $-\frac{2}{99}e^{5} - \frac{970}{1287}e^{3} + \frac{5}{9}e^{2} - \frac{970}{33}e + \frac{970}{117}$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{2}{99}e^{5} + \frac{1}{117}e^{4} + \frac{26}{33}e^{3} - \frac{2}{9}e^{2} + \frac{37709}{1287}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}14$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 4w - 37]$ | $\phantom{-}0$ |
| 61 | $[61, 61, w + 28]$ | $\phantom{-}\frac{2}{99}e^{5} + \frac{1}{117}e^{4} + \frac{26}{33}e^{3} - \frac{2}{9}e^{2} + \frac{41570}{1287}e$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{2}{99}e^{5} - \frac{1069}{1287}e^{3} + \frac{5}{9}e^{2} - \frac{1069}{33}e + \frac{1069}{117}$ |
| 71 | $[71, 71, w + 22]$ | $\phantom{-}0$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).