Base field 4.4.19525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, \frac{2}{3}w^{2} - \frac{2}{3}w - 5]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 11x^{9} + 13x^{8} + 200x^{7} - 504x^{6} - 1059x^{5} + 3342x^{4} + 1360x^{3} - 5392x^{2} + 128x + 512\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ | $\phantom{-}1$ |
| 5 | $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ | $-\frac{911}{256104}e^{9} + \frac{1835}{85368}e^{8} + \frac{26785}{256104}e^{7} - \frac{39929}{64026}e^{6} - \frac{32450}{32013}e^{5} + \frac{1373509}{256104}e^{4} + \frac{501913}{128052}e^{3} - \frac{445016}{32013}e^{2} - \frac{50297}{10671}e + \frac{164974}{32013}$ |
| 16 | $[16, 2, 2]$ | $-\frac{865}{2048832}e^{9} + \frac{4741}{682944}e^{8} - \frac{54313}{2048832}e^{7} - \frac{26785}{512208}e^{6} + \frac{85937}{256104}e^{5} - \frac{145789}{2048832}e^{4} - \frac{161629}{1024416}e^{3} + \frac{62663}{256104}e^{2} - \frac{146029}{42684}e + \frac{53371}{32013}$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ | $-e + 2$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ | $-e + 2$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ | $\phantom{-}\frac{847}{512208}e^{9} - \frac{3713}{170736}e^{8} + \frac{22021}{512208}e^{7} + \frac{111485}{256104}e^{6} - \frac{46645}{32013}e^{5} - \frac{1416173}{512208}e^{4} + \frac{1394423}{128052}e^{3} + \frac{661841}{128052}e^{2} - \frac{211472}{10671}e + \frac{79976}{32013}$ |
| 29 | $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $\phantom{-}\frac{847}{512208}e^{9} - \frac{3713}{170736}e^{8} + \frac{22021}{512208}e^{7} + \frac{111485}{256104}e^{6} - \frac{46645}{32013}e^{5} - \frac{1416173}{512208}e^{4} + \frac{1394423}{128052}e^{3} + \frac{661841}{128052}e^{2} - \frac{211472}{10671}e + \frac{79976}{32013}$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ | $\phantom{-}\frac{4873}{512208}e^{9} - \frac{7147}{85368}e^{8} - \frac{11143}{256104}e^{7} + \frac{854437}{512208}e^{6} - \frac{40666}{32013}e^{5} - \frac{5196299}{512208}e^{4} + \frac{4562123}{512208}e^{3} + \frac{4083091}{256104}e^{2} - \frac{206573}{21342}e + \frac{140546}{32013}$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ | $\phantom{-}\frac{4873}{512208}e^{9} - \frac{7147}{85368}e^{8} - \frac{11143}{256104}e^{7} + \frac{854437}{512208}e^{6} - \frac{40666}{32013}e^{5} - \frac{5196299}{512208}e^{4} + \frac{4562123}{512208}e^{3} + \frac{4083091}{256104}e^{2} - \frac{206573}{21342}e + \frac{140546}{32013}$ |
| 49 | $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ | $-\frac{6203}{1024416}e^{9} + \frac{19507}{341472}e^{8} + \frac{8785}{1024416}e^{7} - \frac{148993}{128052}e^{6} + \frac{142717}{128052}e^{5} + \frac{8180593}{1024416}e^{4} - \frac{3731669}{512208}e^{3} - \frac{1253647}{64026}e^{2} + \frac{219005}{21342}e + \frac{255766}{32013}$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ | $-\frac{6203}{1024416}e^{9} + \frac{19507}{341472}e^{8} + \frac{8785}{1024416}e^{7} - \frac{148993}{128052}e^{6} + \frac{142717}{128052}e^{5} + \frac{8180593}{1024416}e^{4} - \frac{3731669}{512208}e^{3} - \frac{1253647}{64026}e^{2} + \frac{219005}{21342}e + \frac{255766}{32013}$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ | $\phantom{-}\frac{325}{170736}e^{9} + \frac{43}{170736}e^{8} - \frac{8399}{56912}e^{7} + \frac{5359}{28456}e^{6} + \frac{26365}{10671}e^{5} - \frac{443615}{170736}e^{4} - \frac{52676}{3557}e^{3} + \frac{110019}{14228}e^{2} + \frac{293782}{10671}e - \frac{38966}{10671}$ |
| 59 | $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ | $\phantom{-}\frac{325}{170736}e^{9} + \frac{43}{170736}e^{8} - \frac{8399}{56912}e^{7} + \frac{5359}{28456}e^{6} + \frac{26365}{10671}e^{5} - \frac{443615}{170736}e^{4} - \frac{52676}{3557}e^{3} + \frac{110019}{14228}e^{2} + \frac{293782}{10671}e - \frac{38966}{10671}$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ | $-\frac{1181}{341472}e^{9} + \frac{3027}{113824}e^{8} + \frac{11929}{341472}e^{7} - \frac{86155}{170736}e^{6} + \frac{6649}{42684}e^{5} + \frac{737335}{341472}e^{4} - \frac{138409}{85368}e^{3} + \frac{310499}{85368}e^{2} - \frac{2072}{3557}e - \frac{89420}{10671}$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ | $-\frac{589}{42684}e^{9} + \frac{6897}{56912}e^{8} + \frac{3241}{56912}e^{7} - \frac{136043}{56912}e^{6} + \frac{91967}{42684}e^{5} + \frac{194733}{14228}e^{4} - \frac{880591}{56912}e^{3} - \frac{509083}{28456}e^{2} + \frac{186800}{10671}e + \frac{7046}{3557}$ |
| 61 | $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ | $-\frac{589}{42684}e^{9} + \frac{6897}{56912}e^{8} + \frac{3241}{56912}e^{7} - \frac{136043}{56912}e^{6} + \frac{91967}{42684}e^{5} + \frac{194733}{14228}e^{4} - \frac{880591}{56912}e^{3} - \frac{509083}{28456}e^{2} + \frac{186800}{10671}e + \frac{7046}{3557}$ |
| 61 | $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ | $-\frac{1181}{341472}e^{9} + \frac{3027}{113824}e^{8} + \frac{11929}{341472}e^{7} - \frac{86155}{170736}e^{6} + \frac{6649}{42684}e^{5} + \frac{737335}{341472}e^{4} - \frac{138409}{85368}e^{3} + \frac{310499}{85368}e^{2} - \frac{2072}{3557}e - \frac{89420}{10671}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ | $-1$ |
| $5$ | $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ | $-1$ |