Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,-w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $150$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 30x^{8} + 327x^{6} - 1539x^{4} + 2840x^{2} - 1510\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}\frac{39}{1093}e^{8} - \frac{833}{1093}e^{6} + \frac{5527}{1093}e^{4} - \frac{11113}{1093}e^{2} + \frac{3494}{1093}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{39}{1093}e^{8} - \frac{833}{1093}e^{6} + \frac{5527}{1093}e^{4} - \frac{12206}{1093}e^{2} + \frac{10052}{1093}$ |
| 5 | $[5, 5, w + 3]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{28}{1093}e^{9} - \frac{542}{1093}e^{7} + \frac{2763}{1093}e^{5} - \frac{804}{1093}e^{3} - \frac{6796}{1093}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{11}{1093}e^{9} - \frac{291}{1093}e^{7} + \frac{2764}{1093}e^{5} - \frac{10309}{1093}e^{3} + \frac{9197}{1093}e$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{14}{1093}e^{8} + \frac{271}{1093}e^{6} - \frac{1928}{1093}e^{4} + \frac{6960}{1093}e^{2} - \frac{9718}{1093}$ |
| 13 | $[13, 13, w + 12]$ | $\phantom{-}\frac{64}{1093}e^{8} - \frac{1395}{1093}e^{6} + \frac{10219}{1093}e^{4} - \frac{28382}{1093}e^{2} + \frac{23502}{1093}$ |
| 43 | $[43, 43, -w - 6]$ | $\phantom{-}\frac{31}{1093}e^{9} - \frac{522}{1093}e^{7} + \frac{1927}{1093}e^{5} + \frac{3638}{1093}e^{3} - \frac{13926}{1093}e$ |
| 43 | $[43, 43, w - 6]$ | $\phantom{-}\frac{50}{1093}e^{9} - \frac{1124}{1093}e^{7} + \frac{8291}{1093}e^{5} - \frac{22515}{1093}e^{3} + \frac{19249}{1093}e$ |
| 47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{28}{1093}e^{9} - \frac{542}{1093}e^{7} + \frac{2763}{1093}e^{5} - \frac{804}{1093}e^{3} - \frac{5703}{1093}e$ |
| 47 | $[47, 47, w + 28]$ | $\phantom{-}\frac{36}{1093}e^{9} - \frac{853}{1093}e^{7} + \frac{6363}{1093}e^{5} - \frac{14462}{1093}e^{3} - \frac{306}{1093}e$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{8}{1093}e^{9} + \frac{311}{1093}e^{7} - \frac{3600}{1093}e^{5} + \frac{15844}{1093}e^{3} - \frac{26164}{1093}e$ |
| 59 | $[59, 59, w + 43]$ | $\phantom{-}\frac{14}{1093}e^{9} - \frac{271}{1093}e^{7} + \frac{1928}{1093}e^{5} - \frac{6960}{1093}e^{3} + \frac{11904}{1093}e$ |
| 71 | $[71, 71, w + 24]$ | $\phantom{-}\frac{80}{1093}e^{9} - \frac{2017}{1093}e^{7} + \frac{17419}{1093}e^{5} - \frac{57884}{1093}e^{3} + \frac{55063}{1093}e$ |
| 71 | $[71, 71, w + 47]$ | $\phantom{-}\frac{92}{1093}e^{9} - \frac{1937}{1093}e^{7} + \frac{12982}{1093}e^{5} - \frac{30279}{1093}e^{3} + \frac{24357}{1093}e$ |
| 73 | $[73, 73, 3w - 28]$ | $-\frac{59}{1093}e^{8} + \frac{1064}{1093}e^{6} - \frac{5783}{1093}e^{4} + \frac{11375}{1093}e^{2} - \frac{12068}{1093}$ |
| 73 | $[73, 73, 12w - 107]$ | $\phantom{-}\frac{12}{1093}e^{8} + \frac{80}{1093}e^{6} - \frac{4437}{1093}e^{4} + \frac{26512}{1093}e^{2} - \frac{24148}{1093}$ |
| 79 | $[79, 79, -w]$ | $\phantom{-}\frac{50}{1093}e^{9} - \frac{1124}{1093}e^{7} + \frac{8291}{1093}e^{5} - \frac{23608}{1093}e^{3} + \frac{26900}{1093}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 2]$ | $1$ |