Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 80x^{6} + 624x^{4} + 1280x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $\phantom{-}1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{1}{128}e^{7} - \frac{19}{32}e^{5} - \frac{5}{2}e^{3}$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{1}{128}e^{7} - \frac{5}{8}e^{5} - \frac{39}{8}e^{3} - \frac{19}{2}e$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{1}{128}e^{7} - \frac{5}{8}e^{5} - \frac{39}{8}e^{3} - \frac{21}{2}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1}{1152}e^{7} - \frac{7}{96}e^{5} - \frac{5}{6}e^{3} - \frac{40}{9}e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}\frac{1}{64}e^{7} + \frac{39}{32}e^{5} + \frac{59}{8}e^{3} + \frac{19}{2}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{5}{576}e^{7} - \frac{67}{96}e^{5} - \frac{137}{24}e^{3} - \frac{269}{18}e$ |
| 17 | $[17, 17, w - 10]$ | $\phantom{-}\frac{5}{192}e^{6} + 2e^{4} + 10e^{2} + \frac{22}{3}$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{5}{192}e^{6} + 2e^{4} + 10e^{2} + \frac{22}{3}$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{1}{144}e^{7} + \frac{53}{96}e^{5} + \frac{97}{24}e^{3} + \frac{109}{18}e$ |
| 19 | $[19, 19, w + 15]$ | $-\frac{1}{144}e^{7} - \frac{53}{96}e^{5} - \frac{97}{24}e^{3} - \frac{109}{18}e$ |
| 29 | $[29, 29, -2w + 21]$ | $-\frac{13}{576}e^{6} - \frac{41}{24}e^{4} - \frac{20}{3}e^{2} + \frac{13}{9}$ |
| 29 | $[29, 29, 5w - 54]$ | $\phantom{-}\frac{1}{192}e^{6} + \frac{3}{8}e^{4} - \frac{19}{3}$ |
| 47 | $[47, 47, w + 18]$ | $-\frac{1}{128}e^{7} - \frac{21}{32}e^{5} - \frac{29}{4}e^{3} - 19e$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{1}{128}e^{7} - \frac{9}{16}e^{5} - \frac{1}{8}e^{3} + \frac{19}{2}e$ |
| 59 | $[59, 59, w + 27]$ | $\phantom{-}\frac{1}{64}e^{7} + \frac{19}{16}e^{5} + 5e^{3}$ |
| 59 | $[59, 59, w + 31]$ | $\phantom{-}\frac{1}{64}e^{7} + \frac{5}{4}e^{5} + \frac{39}{4}e^{3} + 19e$ |
| 71 | $[71, 71, w + 21]$ | $-\frac{1}{128}e^{7} - \frac{17}{32}e^{5} + \frac{9}{4}e^{3} + 19e$ |
| 71 | $[71, 71, w + 49]$ | $-\frac{1}{128}e^{7} - \frac{11}{16}e^{5} - \frac{77}{8}e^{3} - \frac{57}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |