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: | $8$ |
| CM: | no |
| 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:
| \(x^{8} + 11x^{6} + 94x^{4} + 297x^{2} + 729\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{11}{2538}e^{7} + \frac{1}{27}e^{5} + \frac{11}{27}e^{3} + \frac{121}{94}e$ |
| 3 | $[3, 3, -2w + 19]$ | $\phantom{-}\frac{1}{94}e^{6} - \frac{173}{94}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{11}{2538}e^{7} + \frac{1}{27}e^{5} + \frac{11}{27}e^{3} + \frac{121}{94}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{50}{1269}e^{6} - \frac{14}{27}e^{4} - \frac{100}{27}e^{2} - \frac{550}{47}$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{77}{1269}e^{6} + \frac{14}{27}e^{4} + \frac{100}{27}e^{2} + \frac{189}{47}$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{25}{1269}e^{7} + \frac{7}{27}e^{5} + \frac{50}{27}e^{3} + \frac{275}{47}e$ |
| 17 | $[17, 17, w + 13]$ | $-\frac{1}{94}e^{7} + \frac{361}{94}e$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{11}{1269}e^{6} + \frac{2}{27}e^{4} + \frac{22}{27}e^{2} + \frac{27}{47}$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{11}{1269}e^{6} - \frac{2}{27}e^{4} - \frac{22}{27}e^{2} - \frac{121}{47}$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{121}{2538}e^{6} + \frac{11}{27}e^{4} + \frac{40}{27}e^{2} + \frac{297}{94}$ |
| 37 | $[37, 37, w + 34]$ | $-\frac{20}{1269}e^{6} - \frac{11}{27}e^{4} - \frac{40}{27}e^{2} - \frac{220}{47}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{47}e^{6} - \frac{314}{47}$ |
| 59 | $[59, 59, -4w - 33]$ | $-\frac{11}{846}e^{7} - \frac{1}{9}e^{5} - \frac{11}{9}e^{3} - \frac{81}{94}e$ |
| 59 | $[59, 59, 4w - 37]$ | $\phantom{-}\frac{11}{846}e^{7} + \frac{1}{9}e^{5} + \frac{11}{9}e^{3} + \frac{81}{94}e$ |
| 61 | $[61, 61, w + 28]$ | $-\frac{8}{1269}e^{6} + \frac{1}{27}e^{4} - \frac{16}{27}e^{2} - \frac{88}{47}$ |
| 61 | $[61, 61, w + 32]$ | $-\frac{11}{2538}e^{6} - \frac{1}{27}e^{4} + \frac{16}{27}e^{2} - \frac{27}{94}$ |
| 71 | $[71, 71, w + 22]$ | $-\frac{67}{2538}e^{7} - \frac{11}{27}e^{5} - \frac{67}{27}e^{3} - \frac{737}{94}e$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}\frac{1}{47}e^{7} - \frac{220}{47}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).