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: | $[6,6,w - 7]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + 18x^{6} + 81x^{4} + 53x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{5}{106}e^{7} + \frac{47}{53}e^{5} + \frac{459}{106}e^{3} + \frac{399}{106}e$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{5}{106}e^{7} + \frac{47}{53}e^{5} + \frac{459}{106}e^{3} + \frac{399}{106}e$ |
5 | $[5, 5, -2w + 15]$ | $-\frac{7}{53}e^{6} - \frac{121}{53}e^{4} - \frac{473}{53}e^{2} - \frac{71}{53}$ |
11 | $[11, 11, 3w - 22]$ | $\phantom{-}\frac{10}{53}e^{6} + \frac{188}{53}e^{4} + \frac{865}{53}e^{2} + \frac{321}{53}$ |
13 | $[13, 13, w + 4]$ | $-\frac{12}{53}e^{7} - \frac{215}{53}e^{5} - \frac{932}{53}e^{3} - \frac{417}{53}e$ |
13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{67}{106}e^{7} + \frac{598}{53}e^{5} + \frac{5239}{106}e^{3} + \frac{2739}{106}e$ |
17 | $[17, 17, w + 2]$ | $-\frac{12}{53}e^{7} - \frac{215}{53}e^{5} - \frac{932}{53}e^{3} - \frac{258}{53}e$ |
17 | $[17, 17, w + 15]$ | $\phantom{-}\frac{29}{106}e^{7} + \frac{262}{53}e^{5} + \frac{2429}{106}e^{3} + \frac{2081}{106}e$ |
19 | $[19, 19, -w - 6]$ | $-\frac{2}{53}e^{6} - \frac{27}{53}e^{4} - \frac{67}{53}e^{2} + \frac{63}{53}$ |
19 | $[19, 19, w - 6]$ | $\phantom{-}\frac{2}{53}e^{6} + \frac{27}{53}e^{4} + \frac{14}{53}e^{2} - \frac{116}{53}$ |
23 | $[23, 23, w + 3]$ | $\phantom{-}\frac{5}{53}e^{7} + \frac{94}{53}e^{5} + \frac{512}{53}e^{3} + \frac{876}{53}e$ |
23 | $[23, 23, w + 20]$ | $\phantom{-}\frac{19}{53}e^{7} + \frac{336}{53}e^{5} + \frac{1458}{53}e^{3} + \frac{859}{53}e$ |
47 | $[47, 47, w + 14]$ | $\phantom{-}\frac{60}{53}e^{7} + \frac{1075}{53}e^{5} + \frac{4713}{53}e^{3} + \frac{2297}{53}e$ |
47 | $[47, 47, w + 33]$ | $\phantom{-}\frac{77}{106}e^{7} + \frac{692}{53}e^{5} + \frac{6157}{106}e^{3} + \frac{3113}{106}e$ |
49 | $[49, 7, -7]$ | $\phantom{-}\frac{14}{53}e^{6} + \frac{242}{53}e^{4} + \frac{999}{53}e^{2} + \frac{301}{53}$ |
67 | $[67, 67, w + 16]$ | $-\frac{99}{106}e^{7} - \frac{867}{53}e^{5} - \frac{7371}{106}e^{3} - \frac{3533}{106}e$ |
67 | $[67, 67, w + 51]$ | $-\frac{44}{53}e^{7} - \frac{806}{53}e^{5} - \frac{3753}{53}e^{3} - \frac{2642}{53}e$ |
73 | $[73, 73, w + 36]$ | $-\frac{1}{106}e^{7} - \frac{20}{53}e^{5} - \frac{431}{106}e^{3} - \frac{1373}{106}e$ |
73 | $[73, 73, w + 37]$ | $-\frac{70}{53}e^{7} - \frac{1263}{53}e^{5} - \frac{5684}{53}e^{3} - \frac{3519}{53}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w + 1]$ | $-\frac{5}{106}e^{7} - \frac{47}{53}e^{5} - \frac{459}{106}e^{3} - \frac{399}{106}e$ |
$3$ | $[3,3,-w + 1]$ | $-\frac{5}{106}e^{7} - \frac{47}{53}e^{5} - \frac{459}{106}e^{3} - \frac{399}{106}e$ |