Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $84$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 27x^{6} + 193x^{4} + 432x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-\frac{1}{21}e^{6} - \frac{8}{7}e^{4} - \frac{128}{21}e^{2} - \frac{51}{7}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{1}{112}e^{7} - \frac{65}{336}e^{5} - \frac{65}{112}e^{3} + \frac{47}{21}e$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{1}{112}e^{7} - \frac{65}{336}e^{5} - \frac{65}{112}e^{3} + \frac{47}{21}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{11}{672}e^{7} + \frac{313}{672}e^{5} + \frac{2395}{672}e^{3} + \frac{139}{21}e$ |
| 11 | $[11, 11, w + 10]$ | $-\frac{11}{672}e^{7} - \frac{313}{672}e^{5} - \frac{2395}{672}e^{3} - \frac{139}{21}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{1}{21}e^{6} - \frac{8}{7}e^{4} - \frac{128}{21}e^{2} - \frac{30}{7}$ |
| 17 | $[17, 17, -w - 8]$ | $\phantom{-}\frac{1}{21}e^{6} + \frac{8}{7}e^{4} + \frac{128}{21}e^{2} + \frac{58}{7}$ |
| 31 | $[31, 31, w + 14]$ | $-\frac{5}{56}e^{7} - \frac{127}{56}e^{5} - \frac{773}{56}e^{3} - \frac{135}{7}e$ |
| 31 | $[31, 31, w + 16]$ | $-\frac{19}{336}e^{7} - \frac{449}{336}e^{5} - \frac{2243}{336}e^{3} - \frac{127}{21}e$ |
| 37 | $[37, 37, w + 15]$ | $\phantom{-}\frac{83}{672}e^{7} + \frac{699}{224}e^{5} + \frac{12451}{672}e^{3} + \frac{171}{7}e$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}\frac{3}{224}e^{7} + \frac{65}{224}e^{5} + \frac{307}{224}e^{3} + \frac{29}{7}e$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}\frac{13}{112}e^{7} + \frac{319}{112}e^{5} + \frac{1741}{112}e^{3} + \frac{109}{7}e$ |
| 41 | $[41, 41, w + 22]$ | $\phantom{-}\frac{5}{168}e^{7} + \frac{127}{168}e^{5} + \frac{829}{168}e^{3} + \frac{205}{21}e$ |
| 43 | $[43, 43, -w - 3]$ | $-\frac{5}{42}e^{6} - \frac{113}{42}e^{4} - \frac{493}{42}e^{2} - \frac{92}{21}$ |
| 43 | $[43, 43, w - 4]$ | $-\frac{5}{42}e^{6} - \frac{127}{42}e^{4} - \frac{787}{42}e^{2} - \frac{484}{21}$ |
| 53 | $[53, 53, -w - 1]$ | $-\frac{5}{42}e^{6} - \frac{113}{42}e^{4} - \frac{451}{42}e^{2} - \frac{50}{21}$ |
| 53 | $[53, 53, w - 2]$ | $\phantom{-}\frac{1}{42}e^{6} + \frac{17}{42}e^{4} - \frac{61}{42}e^{2} - \frac{298}{21}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $-1$ |