Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, -w + 5]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 25x^{8} + 207x^{6} - 626x^{4} + 544x^{2} - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}\frac{15}{1048}e^{8} - \frac{323}{1048}e^{6} + \frac{2125}{1048}e^{4} - \frac{1885}{524}e^{2} - \frac{46}{131}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{5}{262}e^{9} + \frac{259}{524}e^{7} - \frac{2159}{524}e^{5} + \frac{5963}{524}e^{3} - \frac{1231}{262}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{53}{2096}e^{9} + \frac{1281}{2096}e^{7} - \frac{10303}{2096}e^{5} + \frac{15219}{1048}e^{3} - \frac{3095}{262}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{17}{524}e^{9} + \frac{401}{524}e^{7} - \frac{3107}{524}e^{5} + \frac{4407}{262}e^{3} - \frac{1852}{131}e$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}\frac{55}{1048}e^{9} - \frac{1359}{1048}e^{7} + \frac{10761}{1048}e^{5} - \frac{14335}{524}e^{3} + \frac{2233}{131}e$ |
| 17 | $[17, 17, -3w + 17]$ | $-\frac{9}{1048}e^{8} + \frac{89}{1048}e^{6} + \frac{297}{1048}e^{4} - \frac{1751}{524}e^{2} + \frac{866}{131}$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{7}{2096}e^{9} - \frac{11}{2096}e^{7} - \frac{1803}{2096}e^{5} + \frac{7679}{1048}e^{3} - \frac{4065}{262}e$ |
| 29 | $[29, 29, w + 18]$ | $-\frac{35}{1048}e^{9} + \frac{841}{1048}e^{7} - \frac{6443}{1048}e^{5} + \frac{1962}{131}e^{3} - \frac{1139}{262}e$ |
| 37 | $[37, 37, w + 16]$ | $-\frac{75}{2096}e^{9} + \frac{1615}{2096}e^{7} - \frac{10625}{2096}e^{5} + \frac{9949}{1048}e^{3} + \frac{361}{262}e$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{99}{2096}e^{9} + \frac{2551}{2096}e^{7} - \frac{22409}{2096}e^{5} + \frac{37069}{1048}e^{3} - \frac{8159}{262}e$ |
| 47 | $[47, 47, -w - 9]$ | $\phantom{-}\frac{9}{524}e^{8} - \frac{89}{524}e^{6} - \frac{297}{524}e^{4} + \frac{1227}{262}e^{2} + \frac{364}{131}$ |
| 47 | $[47, 47, w - 9]$ | $-\frac{9}{131}e^{8} + \frac{220}{131}e^{6} - \frac{1668}{131}e^{4} + \frac{3834}{131}e^{2} - \frac{932}{131}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{35}{1048}e^{8} - \frac{579}{1048}e^{6} + \frac{1989}{1048}e^{4} + \frac{1453}{524}e^{2} - \frac{806}{131}$ |
| 61 | $[61, 61, w + 20]$ | $-\frac{1}{1048}e^{9} + \frac{39}{1048}e^{7} - \frac{229}{1048}e^{5} - \frac{483}{262}e^{3} + \frac{3089}{262}e$ |
| 61 | $[61, 61, w + 41]$ | $-\frac{103}{1048}e^{9} + \frac{2445}{1048}e^{7} - \frac{18871}{1048}e^{5} + \frac{6369}{131}e^{3} - \frac{8023}{262}e$ |
| 89 | $[89, 89, 2w - 15]$ | $-\frac{29}{1048}e^{8} + \frac{869}{1048}e^{6} - \frac{8475}{1048}e^{4} + \frac{13513}{524}e^{2} - \frac{1518}{131}$ |
| 89 | $[89, 89, -2w - 15]$ | $-\frac{17}{1048}e^{8} + \frac{401}{1048}e^{6} - \frac{2583}{1048}e^{4} + \frac{1525}{524}e^{2} + \frac{1170}{131}$ |
| 103 | $[103, 103, -14w + 81]$ | $-\frac{77}{524}e^{8} + \frac{1693}{524}e^{6} - \frac{11607}{524}e^{4} + \frac{12733}{262}e^{2} - \frac{3056}{131}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |