Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[20,10,-8w + 58]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + x^{10} - 22x^{9} - 22x^{8} + 170x^{7} + 169x^{6} - 548x^{5} - 546x^{4} + 655x^{3} + 689x^{2} - 162x - 196\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $-\frac{9457}{65106}e^{10} + \frac{535}{65106}e^{9} + \frac{103111}{32553}e^{8} - \frac{2417}{10851}e^{7} - \frac{784735}{32553}e^{6} + \frac{15815}{7234}e^{5} + \frac{2448829}{32553}e^{4} - \frac{228011}{32553}e^{3} - \frac{5415755}{65106}e^{2} - \frac{715}{65106}e + \frac{682360}{32553}$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, 4w + 25]$ | $\phantom{-}\frac{3167}{10851}e^{10} - \frac{42}{3617}e^{9} - \frac{70162}{10851}e^{8} + \frac{2834}{10851}e^{7} + \frac{181725}{3617}e^{6} - \frac{7895}{3617}e^{5} - \frac{1753186}{10851}e^{4} + \frac{51211}{10851}e^{3} + \frac{2058347}{10851}e^{2} + \frac{112363}{10851}e - \frac{200300}{3617}$ |
| 5 | $[5, 5, -4w + 29]$ | $-1$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}\frac{1469}{32553}e^{10} + \frac{556}{32553}e^{9} - \frac{32863}{32553}e^{8} - \frac{994}{3617}e^{7} + \frac{254869}{32553}e^{6} + \frac{3996}{3617}e^{5} - \frac{786634}{32553}e^{4} + \frac{1433}{32553}e^{3} + \frac{777709}{32553}e^{2} - \frac{88768}{32553}e - \frac{126610}{32553}$ |
| 11 | $[11, 11, -w - 7]$ | $-\frac{8570}{32553}e^{10} + \frac{494}{32553}e^{9} + \frac{188329}{32553}e^{8} - \frac{2077}{10851}e^{7} - \frac{1455886}{32553}e^{6} + \frac{1859}{3617}e^{5} + \frac{4698637}{32553}e^{4} + \frac{84217}{32553}e^{3} - \frac{5664148}{32553}e^{2} - \frac{472628}{32553}e + \frac{1734130}{32553}$ |
| 13 | $[13, 13, 3w + 19]$ | $-\frac{2455}{65106}e^{10} - \frac{3581}{65106}e^{9} + \frac{30175}{32553}e^{8} + \frac{11405}{10851}e^{7} - \frac{268033}{32553}e^{6} - \frac{47647}{7234}e^{5} + \frac{1030177}{32553}e^{4} + \frac{515599}{32553}e^{3} - \frac{3089513}{65106}e^{2} - \frac{841795}{65106}e + \frac{572071}{32553}$ |
| 13 | $[13, 13, 3w - 22]$ | $...$ |
| 29 | $[29, 29, 6w + 37]$ | $...$ |
| 29 | $[29, 29, 6w - 43]$ | $...$ |
| 37 | $[37, 37, 2w - 13]$ | $...$ |
| 37 | $[37, 37, 2w + 11]$ | $-\frac{7745}{7234}e^{10} + \frac{725}{7234}e^{9} + \frac{84934}{3617}e^{8} - \frac{6919}{3617}e^{7} - \frac{653488}{3617}e^{6} + \frac{94515}{7234}e^{5} + \frac{2088828}{3617}e^{4} - \frac{104001}{3617}e^{3} - \frac{4938839}{7234}e^{2} - \frac{160793}{7234}e + \frac{748745}{3617}$ |
| 43 | $[43, 43, -w - 1]$ | $\phantom{-}\frac{2003}{3617}e^{10} - \frac{343}{10851}e^{9} - \frac{43839}{3617}e^{8} + \frac{6911}{10851}e^{7} + \frac{1008452}{10851}e^{6} - \frac{17674}{3617}e^{5} - \frac{1069872}{3617}e^{4} + \frac{123935}{10851}e^{3} + \frac{3801811}{10851}e^{2} + \frac{146930}{10851}e - \frac{1163162}{10851}$ |
| 43 | $[43, 43, w - 2]$ | $-\frac{17593}{65106}e^{10} - \frac{875}{65106}e^{9} + \frac{186604}{32553}e^{8} + \frac{1205}{3617}e^{7} - \frac{1379512}{32553}e^{6} - \frac{16333}{7234}e^{5} + \frac{4234060}{32553}e^{4} + \frac{179524}{32553}e^{3} - \frac{9764801}{65106}e^{2} - \frac{534079}{65106}e + \frac{1435294}{32553}$ |
| 49 | $[49, 7, -7]$ | $-\frac{794}{10851}e^{10} - \frac{367}{10851}e^{9} + \frac{18745}{10851}e^{8} + \frac{1565}{3617}e^{7} - \frac{155722}{10851}e^{6} - \frac{1954}{3617}e^{5} + \frac{530047}{10851}e^{4} - \frac{61973}{10851}e^{3} - \frac{626206}{10851}e^{2} + \frac{45010}{10851}e + \frac{138178}{10851}$ |
| 59 | $[59, 59, 5w - 37]$ | $-\frac{566}{3617}e^{10} + \frac{682}{10851}e^{9} + \frac{12433}{3617}e^{8} - \frac{11780}{10851}e^{7} - \frac{290306}{10851}e^{6} + \frac{19883}{3617}e^{5} + \frac{322184}{3617}e^{4} - \frac{60629}{10851}e^{3} - \frac{1291489}{10851}e^{2} - \frac{125174}{10851}e + \frac{495992}{10851}$ |
| 59 | $[59, 59, 5w + 32]$ | $-\frac{29582}{32553}e^{10} - \frac{1483}{32553}e^{9} + \frac{647242}{32553}e^{8} + \frac{10621}{10851}e^{7} - \frac{4961167}{32553}e^{6} - \frac{22238}{3617}e^{5} + \frac{15766480}{32553}e^{4} + \frac{603463}{32553}e^{3} - \frac{18454039}{32553}e^{2} - \frac{1547480}{32553}e + \frac{5549110}{32553}$ |
| 67 | $[67, 67, 21w + 131]$ | $...$ |
| 67 | $[67, 67, 21w - 152]$ | $-\frac{4523}{10851}e^{10} - \frac{109}{10851}e^{9} + \frac{97993}{10851}e^{8} + \frac{1066}{3617}e^{7} - \frac{743434}{10851}e^{6} - \frac{8179}{3617}e^{5} + \frac{2348263}{10851}e^{4} + \frac{73783}{10851}e^{3} - \frac{2783188}{10851}e^{2} - \frac{147002}{10851}e + \frac{873580}{10851}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,2]$ | $1$ |
| $5$ | $[5,5,-4w + 29]$ | $1$ |