Base field \(\Q(\sqrt{97}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 24\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, -12w + 65]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - x^{9} - 14x^{8} + 13x^{7} + 61x^{6} - 51x^{5} - 92x^{4} + 76x^{3} + 36x^{2} - 31x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 7w - 38]$ | $\phantom{-}\frac{25}{91}e^{9} + \frac{5}{91}e^{8} - \frac{365}{91}e^{7} - \frac{92}{91}e^{6} + \frac{1696}{91}e^{5} + \frac{74}{13}e^{4} - \frac{2776}{91}e^{3} - \frac{713}{91}e^{2} + \frac{1296}{91}e + \frac{132}{91}$ |
| 2 | $[2, 2, -7w - 31]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w + 9]$ | $-\frac{113}{91}e^{9} + \frac{25}{91}e^{8} + \frac{1584}{91}e^{7} - \frac{222}{91}e^{6} - \frac{6850}{91}e^{5} + \frac{40}{13}e^{4} + \frac{9864}{91}e^{3} - \frac{506}{91}e^{2} - \frac{3782}{91}e + \frac{268}{91}$ |
| 3 | $[3, 3, 2w - 11]$ | $\phantom{-}\frac{120}{91}e^{9} - \frac{25}{91}e^{8} - \frac{131}{7}e^{7} + \frac{215}{91}e^{6} + \frac{7515}{91}e^{5} - \frac{28}{13}e^{4} - \frac{11194}{91}e^{3} + \frac{226}{91}e^{2} + \frac{4405}{91}e - \frac{128}{91}$ |
| 11 | $[11, 11, -12w + 65]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -12w - 53]$ | $\phantom{-}\frac{222}{91}e^{9} - \frac{62}{91}e^{8} - \frac{3153}{91}e^{7} + \frac{627}{91}e^{6} + \frac{13985}{91}e^{5} - \frac{198}{13}e^{4} - \frac{21285}{91}e^{3} + \frac{1921}{91}e^{2} + \frac{8837}{91}e - \frac{843}{91}$ |
| 25 | $[25, 5, 5]$ | $-\frac{53}{91}e^{9} + \frac{23}{91}e^{8} + \frac{722}{91}e^{7} - \frac{237}{91}e^{6} - \frac{3026}{91}e^{5} + \frac{68}{13}e^{4} + \frac{4372}{91}e^{3} - \frac{36}{91}e^{2} - \frac{1947}{91}e - \frac{405}{91}$ |
| 31 | $[31, 31, 8w - 43]$ | $\phantom{-}\frac{58}{91}e^{9} + \frac{6}{91}e^{8} - \frac{823}{91}e^{7} - \frac{102}{91}e^{6} + \frac{3585}{91}e^{5} + \frac{64}{13}e^{4} - \frac{4993}{91}e^{3} + \frac{172}{91}e^{2} + \frac{1663}{91}e - \frac{592}{91}$ |
| 31 | $[31, 31, 8w + 35]$ | $\phantom{-}\frac{8}{91}e^{9} - \frac{32}{91}e^{8} - \frac{5}{7}e^{7} + \frac{348}{91}e^{6} - \frac{45}{91}e^{5} - \frac{118}{13}e^{4} + \frac{825}{91}e^{3} - \frac{173}{91}e^{2} - \frac{1132}{91}e + \frac{586}{91}$ |
| 43 | $[43, 43, 54w + 239]$ | $-\frac{75}{91}e^{9} + \frac{27}{91}e^{8} + \frac{81}{7}e^{7} - \frac{305}{91}e^{6} - \frac{4549}{91}e^{5} + \frac{141}{13}e^{4} + \frac{6382}{91}e^{3} - \frac{1893}{91}e^{2} - \frac{1809}{91}e + \frac{626}{91}$ |
| 43 | $[43, 43, -54w + 293]$ | $-\frac{296}{91}e^{9} + \frac{36}{91}e^{8} + \frac{4190}{91}e^{7} - \frac{150}{91}e^{6} - \frac{18467}{91}e^{5} - \frac{174}{13}e^{4} + \frac{27701}{91}e^{3} + \frac{1494}{91}e^{2} - \frac{11484}{91}e + \frac{10}{7}$ |
| 47 | $[47, 47, 2w - 13]$ | $\phantom{-}\frac{53}{13}e^{9} - \frac{14}{13}e^{8} - \frac{744}{13}e^{7} + \frac{132}{13}e^{6} + \frac{3226}{13}e^{5} - \frac{237}{13}e^{4} - \frac{4685}{13}e^{3} + \frac{394}{13}e^{2} + \frac{1814}{13}e - 14$ |
| 47 | $[47, 47, -2w - 11]$ | $-\frac{222}{91}e^{9} + \frac{62}{91}e^{8} + \frac{3153}{91}e^{7} - \frac{627}{91}e^{6} - \frac{13985}{91}e^{5} + \frac{198}{13}e^{4} + \frac{21376}{91}e^{3} - \frac{2012}{91}e^{2} - \frac{9474}{91}e + \frac{661}{91}$ |
| 49 | $[49, 7, -7]$ | $-\frac{141}{91}e^{9} + \frac{3}{7}e^{8} + \frac{2046}{91}e^{7} - \frac{418}{91}e^{6} - \frac{9391}{91}e^{5} + \frac{152}{13}e^{4} + \frac{15051}{91}e^{3} - \frac{1458}{91}e^{2} - \frac{6400}{91}e + \frac{716}{91}$ |
| 53 | $[53, 53, 4w + 19]$ | $\phantom{-}\frac{2}{13}e^{9} + \frac{2}{13}e^{8} - \frac{36}{13}e^{7} - \frac{21}{13}e^{6} + \frac{220}{13}e^{5} + \frac{41}{13}e^{4} - \frac{503}{13}e^{3} + \frac{66}{13}e^{2} + \frac{329}{13}e - \frac{89}{13}$ |
| 53 | $[53, 53, 4w - 23]$ | $-\frac{433}{91}e^{9} + \frac{73}{91}e^{8} + \frac{6144}{91}e^{7} - \frac{618}{91}e^{6} - \frac{2083}{7}e^{5} + \frac{92}{13}e^{4} + \frac{40165}{91}e^{3} - \frac{2441}{91}e^{2} - \frac{16028}{91}e + \frac{1328}{91}$ |
| 61 | $[61, 61, 2w - 7]$ | $\phantom{-}\frac{15}{91}e^{9} + \frac{4}{7}e^{8} - \frac{177}{91}e^{7} - \frac{730}{91}e^{6} + \frac{515}{91}e^{5} + \frac{438}{13}e^{4} - \frac{120}{91}e^{3} - \frac{3512}{91}e^{2} + \frac{464}{91}e + \frac{495}{91}$ |
| 61 | $[61, 61, -2w - 5]$ | $-\frac{233}{91}e^{9} + \frac{43}{91}e^{8} + \frac{3294}{91}e^{7} - \frac{25}{7}e^{6} - \frac{14470}{91}e^{5} + \frac{1}{13}e^{4} + \frac{21625}{91}e^{3} - \frac{424}{91}e^{2} - \frac{9125}{91}e + \frac{74}{91}$ |
| 73 | $[73, 73, 22w + 97]$ | $-\frac{125}{91}e^{9} + \frac{45}{91}e^{8} + \frac{135}{7}e^{7} - \frac{387}{91}e^{6} - \frac{7703}{91}e^{5} + \frac{40}{13}e^{4} + \frac{11941}{91}e^{3} + \frac{576}{91}e^{2} - \frac{5927}{91}e + \frac{103}{91}$ |
| 73 | $[73, 73, -22w + 119]$ | $-\frac{12}{7}e^{9} + \frac{85}{91}e^{8} + \frac{2216}{91}e^{7} - \frac{983}{91}e^{6} - \frac{9983}{91}e^{5} + \frac{431}{13}e^{4} + \frac{16242}{91}e^{3} - \frac{3441}{91}e^{2} - \frac{7655}{91}e + \frac{725}{91}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -12w + 65]$ | $-1$ |