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: | $[4, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 25x^{6} + 182x^{4} - 512x^{2} + 484\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}\frac{7}{66}e^{7} - \frac{51}{22}e^{5} + \frac{395}{33}e^{3} - \frac{538}{33}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{7}{66}e^{7} - \frac{51}{22}e^{5} + \frac{395}{33}e^{3} - \frac{538}{33}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{3}e^{6} + 7e^{4} - \frac{97}{3}e^{2} + \frac{122}{3}$ |
| 11 | $[11, 11, w]$ | $-\frac{2}{33}e^{7} + \frac{50}{33}e^{5} - \frac{114}{11}e^{3} + \frac{650}{33}e$ |
| 11 | $[11, 11, w + 10]$ | $-\frac{2}{33}e^{7} + \frac{50}{33}e^{5} - \frac{114}{11}e^{3} + \frac{650}{33}e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{23}{3}e^{4} + \frac{134}{3}e^{2} - 70$ |
| 17 | $[17, 17, -w - 8]$ | $-e^{6} + \frac{64}{3}e^{4} - \frac{314}{3}e^{2} + \frac{422}{3}$ |
| 31 | $[31, 31, w + 14]$ | $\phantom{-}\frac{37}{66}e^{7} - \frac{793}{66}e^{5} + \frac{653}{11}e^{3} - \frac{2630}{33}e$ |
| 31 | $[31, 31, w + 16]$ | $\phantom{-}\frac{37}{66}e^{7} - \frac{793}{66}e^{5} + \frac{653}{11}e^{3} - \frac{2630}{33}e$ |
| 37 | $[37, 37, w + 15]$ | $-\frac{1}{3}e^{7} + \frac{22}{3}e^{5} - 39e^{3} + \frac{175}{3}e$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{1}{3}e^{7} + \frac{22}{3}e^{5} - 39e^{3} + \frac{175}{3}e$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}\frac{25}{66}e^{7} - \frac{179}{22}e^{5} + \frac{1340}{33}e^{3} - \frac{1813}{33}e$ |
| 41 | $[41, 41, w + 22]$ | $\phantom{-}\frac{25}{66}e^{7} - \frac{179}{22}e^{5} + \frac{1340}{33}e^{3} - \frac{1813}{33}e$ |
| 43 | $[43, 43, -w - 3]$ | $-\frac{1}{3}e^{6} + \frac{22}{3}e^{4} - 40e^{2} + \frac{196}{3}$ |
| 43 | $[43, 43, w - 4]$ | $-\frac{1}{3}e^{6} + \frac{22}{3}e^{4} - 40e^{2} + \frac{196}{3}$ |
| 53 | $[53, 53, -w - 1]$ | $-e^{6} + \frac{64}{3}e^{4} - \frac{311}{3}e^{2} + \frac{392}{3}$ |
| 53 | $[53, 53, w - 2]$ | $-e^{6} + \frac{64}{3}e^{4} - \frac{311}{3}e^{2} + \frac{392}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |