Base field \(\Q(\sqrt{55}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, -w + 8]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 44x^{6} + 504x^{4} + 1584x^{2} + 1296\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{432}e^{7} - \frac{11}{108}e^{5} - \frac{7}{6}e^{3} - \frac{19}{6}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{432}e^{7} + \frac{11}{108}e^{5} + \frac{7}{6}e^{3} + \frac{25}{6}e$ |
| 5 | $[5, 5, -2w + 15]$ | $-\frac{1}{144}e^{6} - \frac{11}{36}e^{4} - \frac{13}{4}e^{2} - 6$ |
| 11 | $[11, 11, 3w - 22]$ | $\phantom{-}\frac{1}{48}e^{6} + \frac{5}{6}e^{4} + \frac{91}{12}e^{2} + 12$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{1}{288}e^{7} + \frac{19}{144}e^{5} + \frac{23}{24}e^{3} - \frac{1}{4}e$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{1}{144}e^{7} + \frac{11}{36}e^{5} + \frac{7}{2}e^{3} + \frac{19}{2}e$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{1}{108}e^{7} - \frac{79}{216}e^{5} - \frac{37}{12}e^{3} - \frac{8}{3}e$ |
| 17 | $[17, 17, w + 15]$ | $\phantom{-}\frac{19}{864}e^{7} + \frac{391}{432}e^{5} + \frac{209}{24}e^{3} + \frac{181}{12}e$ |
| 19 | $[19, 19, -w - 6]$ | $\phantom{-}\frac{1}{144}e^{6} + \frac{19}{72}e^{4} + \frac{23}{12}e^{2} + \frac{1}{2}$ |
| 19 | $[19, 19, w - 6]$ | $\phantom{-}\frac{1}{144}e^{6} + \frac{19}{72}e^{4} + \frac{23}{12}e^{2} + \frac{1}{2}$ |
| 23 | $[23, 23, w + 3]$ | $-\frac{11}{864}e^{7} - \frac{233}{432}e^{5} - \frac{43}{8}e^{3} - \frac{83}{12}e$ |
| 23 | $[23, 23, w + 20]$ | $\phantom{-}\frac{1}{216}e^{7} + \frac{11}{54}e^{5} + \frac{7}{3}e^{3} + \frac{25}{3}e$ |
| 47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{7}{216}e^{7} + \frac{299}{216}e^{5} + \frac{57}{4}e^{3} + \frac{79}{3}e$ |
| 47 | $[47, 47, w + 33]$ | $-\frac{17}{864}e^{7} - \frac{365}{432}e^{5} - \frac{71}{8}e^{3} - \frac{233}{12}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{144}e^{6} + \frac{11}{36}e^{4} + \frac{13}{4}e^{2} + 2$ |
| 67 | $[67, 67, w + 16]$ | $\phantom{-}\frac{1}{96}e^{7} + \frac{7}{16}e^{5} + \frac{101}{24}e^{3} + \frac{11}{4}e$ |
| 67 | $[67, 67, w + 51]$ | $\phantom{-}\frac{1}{96}e^{7} + \frac{7}{16}e^{5} + \frac{101}{24}e^{3} + \frac{11}{4}e$ |
| 73 | $[73, 73, w + 36]$ | $-\frac{7}{288}e^{7} - \frac{145}{144}e^{5} - \frac{79}{8}e^{3} - \frac{73}{4}e$ |
| 73 | $[73, 73, w + 37]$ | $-\frac{1}{72}e^{7} - \frac{19}{36}e^{5} - \frac{23}{6}e^{3} + e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |