Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, w]$ |
| 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:
| \(x^{8} + 57x^{6} + 1048x^{4} + 6441x^{2} + 3721\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{13}{39894}e^{7} + \frac{2}{183}e^{5} + \frac{163}{19947}e^{3} - \frac{49735}{39894}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{199}{106384}e^{7} + \frac{5}{61}e^{5} + \frac{12771}{13298}e^{3} + \frac{234999}{106384}e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{95}{106384}e^{7} - \frac{3}{61}e^{5} - \frac{12445}{13298}e^{3} - \frac{739263}{106384}e$ |
| 13 | $[13, 13, w + 2]$ | $-\frac{281}{79788}e^{7} - \frac{31}{183}e^{5} - \frac{47026}{19947}e^{3} - \frac{651653}{79788}e$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{119}{39894}e^{7} - \frac{23}{183}e^{5} - \frac{29111}{19947}e^{3} - \frac{175877}{39894}e$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{35}{79788}e^{7} + \frac{2}{183}e^{5} + \frac{17426}{19947}e^{3} + \frac{678097}{79788}e$ |
| 17 | $[17, 17, w + 9]$ | $-\frac{769}{319152}e^{7} - \frac{23}{183}e^{5} - \frac{74143}{39894}e^{3} - \frac{2223745}{319152}e$ |
| 19 | $[19, 19, w + 7]$ | $-\frac{11}{654}e^{6} - \frac{2}{3}e^{4} - \frac{1949}{327}e^{2} + \frac{2005}{654}$ |
| 19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{79}{5232}e^{6} + \frac{2}{3}e^{4} + \frac{4681}{654}e^{2} + \frac{39823}{5232}$ |
| 29 | $[29, 29, -w - 1]$ | $\phantom{-}\frac{25}{2616}e^{6} + \frac{1}{3}e^{4} + \frac{877}{327}e^{2} + \frac{13993}{2616}$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{35}{5232}e^{6} - \frac{1}{3}e^{4} - \frac{3059}{654}e^{2} - \frac{53075}{5232}$ |
| 37 | $[37, 37, w + 17]$ | $\phantom{-}\frac{129}{106384}e^{7} + \frac{6}{61}e^{5} + \frac{30197}{13298}e^{3} + \frac{1538001}{106384}e$ |
| 37 | $[37, 37, w + 20]$ | $-\frac{69}{53192}e^{7} - \frac{5}{61}e^{5} - \frac{9039}{6649}e^{3} - \frac{253621}{53192}e$ |
| 71 | $[71, 71, 2w - 7]$ | $-\frac{35}{5232}e^{6} - \frac{1}{3}e^{4} - \frac{3059}{654}e^{2} - \frac{53075}{5232}$ |
| 71 | $[71, 71, -2w - 7]$ | $\phantom{-}\frac{25}{2616}e^{6} + \frac{1}{3}e^{4} + \frac{877}{327}e^{2} + \frac{13993}{2616}$ |
| 83 | $[83, 83, w + 14]$ | $\phantom{-}\frac{479}{319152}e^{7} + \frac{1}{183}e^{5} - \frac{70231}{39894}e^{3} - \frac{6998305}{319152}e$ |
| 83 | $[83, 83, w + 69]$ | $\phantom{-}\frac{277}{79788}e^{7} + \frac{26}{183}e^{5} + \frac{19382}{19947}e^{3} - \frac{515543}{79788}e$ |
| 101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{91}{5232}e^{6} + \frac{2}{3}e^{4} + \frac{4291}{654}e^{2} + \frac{64747}{5232}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{13}{39894}e^{7} - \frac{2}{183}e^{5} - \frac{163}{19947}e^{3} + \frac{49735}{39894}e$ |
| $5$ | $[5, 5, -w + 5]$ | $-1$ |