Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, w^{2} - 2w - 2]$ |
| Dimension: | $16$ |
| 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:
| \(x^{16} - 24x^{14} + 2x^{13} + 231x^{12} - 35x^{11} - 1140x^{10} + 233x^{9} + 3059x^{8} - 739x^{7} - 4357x^{6} + 1145x^{5} + 2958x^{4} - 787x^{3} - 713x^{2} + 186x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{344}{66325}e^{15} + \frac{5322}{66325}e^{14} + \frac{251}{13265}e^{13} - \frac{106872}{66325}e^{12} - \frac{96947}{66325}e^{11} + \frac{118732}{9475}e^{10} + \frac{834327}{66325}e^{9} - \frac{3153522}{66325}e^{8} - \frac{575203}{13265}e^{7} + \frac{6041839}{66325}e^{6} + \frac{4218099}{66325}e^{5} - \frac{5409658}{66325}e^{4} - \frac{2132652}{66325}e^{3} + \frac{1697471}{66325}e^{2} + \frac{31051}{66325}e - \frac{96678}{66325}$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $-\frac{1448}{66325}e^{15} - \frac{682}{9475}e^{14} + \frac{5598}{13265}e^{13} + \frac{100824}{66325}e^{12} - \frac{201626}{66325}e^{11} - \frac{833333}{66325}e^{10} + \frac{91663}{9475}e^{9} + \frac{3389499}{66325}e^{8} - \frac{139779}{13265}e^{7} - \frac{6965813}{66325}e^{6} - \frac{639658}{66325}e^{5} + \frac{6587586}{66325}e^{4} + \frac{1789859}{66325}e^{3} - \frac{2223457}{66325}e^{2} - \frac{944892}{66325}e + \frac{147376}{66325}$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $\phantom{-}\frac{7439}{66325}e^{15} + \frac{7547}{66325}e^{14} - \frac{33846}{13265}e^{13} - \frac{148912}{66325}e^{12} + \frac{1532683}{66325}e^{11} + \frac{1140719}{66325}e^{10} - \frac{7025923}{66325}e^{9} - \frac{609381}{9475}e^{8} + \frac{3420727}{13265}e^{7} + \frac{8009184}{66325}e^{6} - \frac{21111866}{66325}e^{5} - \frac{6909463}{66325}e^{4} + \frac{11295163}{66325}e^{3} + \frac{2130456}{66325}e^{2} - \frac{1722144}{66325}e - \frac{73908}{66325}$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $-\frac{223}{9475}e^{15} - \frac{1333}{66325}e^{14} + \frac{7253}{13265}e^{13} + \frac{22098}{66325}e^{12} - \frac{350097}{66325}e^{11} - \frac{129431}{66325}e^{10} + \frac{1823072}{66325}e^{9} + \frac{299153}{66325}e^{8} - \frac{1098568}{13265}e^{7} - \frac{136616}{66325}e^{6} + \frac{9287879}{66325}e^{5} - \frac{341508}{66325}e^{4} - \frac{1074716}{9475}e^{3} + \frac{372846}{66325}e^{2} + \frac{1887656}{66325}e - \frac{118128}{66325}$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $-1$ |
| 19 | $[19, 19, -w + 2]$ | $-\frac{1859}{66325}e^{15} - \frac{6362}{66325}e^{14} + \frac{1538}{2653}e^{13} + \frac{134907}{66325}e^{12} - \frac{317378}{66325}e^{11} - \frac{1119564}{66325}e^{10} + \frac{193194}{9475}e^{9} + \frac{651996}{9475}e^{8} - \frac{651017}{13265}e^{7} - \frac{1331147}{9475}e^{6} + \frac{4680566}{66325}e^{5} + \frac{8383958}{66325}e^{4} - \frac{606654}{9475}e^{3} - \frac{1948746}{66325}e^{2} + \frac{1937714}{66325}e - \frac{40296}{9475}$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $-\frac{12879}{66325}e^{15} - \frac{14102}{66325}e^{14} + \frac{56724}{13265}e^{13} + \frac{265602}{66325}e^{12} - \frac{354064}{9475}e^{11} - \frac{1896284}{66325}e^{10} + \frac{10952843}{66325}e^{9} + \frac{6343902}{66325}e^{8} - \frac{5167992}{13265}e^{7} - \frac{9880949}{66325}e^{6} + \frac{31509791}{66325}e^{5} + \frac{5994378}{66325}e^{4} - \frac{17613718}{66325}e^{3} - \frac{710611}{66325}e^{2} + \frac{3491884}{66325}e - \frac{31602}{66325}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $-\frac{121}{2653}e^{15} - \frac{698}{13265}e^{14} + \frac{13897}{13265}e^{13} + \frac{13856}{13265}e^{12} - \frac{126013}{13265}e^{11} - \frac{3048}{379}e^{10} + \frac{568297}{13265}e^{9} + \frac{58101}{1895}e^{8} - \frac{261727}{2653}e^{7} - \frac{163957}{2653}e^{6} + \frac{1375792}{13265}e^{5} + \frac{121489}{1895}e^{4} - \frac{83868}{2653}e^{3} - \frac{345721}{13265}e^{2} - \frac{6179}{2653}e - \frac{25422}{13265}$ |
| 27 | $[27, 3, 3]$ | $-\frac{8536}{66325}e^{15} - \frac{5183}{66325}e^{14} + \frac{38053}{13265}e^{13} + \frac{12764}{9475}e^{12} - \frac{1682097}{66325}e^{11} - \frac{579881}{66325}e^{10} + \frac{7496147}{66325}e^{9} + \frac{254429}{9475}e^{8} - \frac{3534563}{13265}e^{7} - \frac{2771416}{66325}e^{6} + \frac{21091054}{66325}e^{5} + \frac{2460492}{66325}e^{4} - \frac{10973262}{66325}e^{3} - \frac{1507679}{66325}e^{2} + \frac{1727156}{66325}e + \frac{222622}{66325}$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $-\frac{1144}{13265}e^{15} - \frac{1816}{13265}e^{14} + \frac{22991}{13265}e^{13} + \frac{6610}{2653}e^{12} - \frac{178342}{13265}e^{11} - \frac{224979}{13265}e^{10} + \frac{676014}{13265}e^{9} + \frac{713078}{13265}e^{8} - \frac{264594}{2653}e^{7} - \frac{156792}{1895}e^{6} + \frac{1316157}{13265}e^{5} + \frac{840887}{13265}e^{4} - \frac{553268}{13265}e^{3} - \frac{263419}{13265}e^{2} - \frac{6221}{13265}e - \frac{36618}{13265}$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $\phantom{-}\frac{3428}{66325}e^{15} + \frac{1649}{66325}e^{14} - \frac{17361}{13265}e^{13} - \frac{44909}{66325}e^{12} + \frac{877196}{66325}e^{11} + \frac{475288}{66325}e^{10} - \frac{4519766}{66325}e^{9} - \frac{2457979}{66325}e^{8} + \frac{359457}{1895}e^{7} + \frac{6389518}{66325}e^{6} - \frac{2644036}{9475}e^{5} - \frac{7666081}{66325}e^{4} + \frac{13092326}{66325}e^{3} + \frac{3201447}{66325}e^{2} - \frac{459309}{9475}e + \frac{146754}{66325}$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $-\frac{2211}{66325}e^{15} - \frac{5638}{66325}e^{14} + \frac{9857}{13265}e^{13} + \frac{129683}{66325}e^{12} - \frac{430152}{66325}e^{11} - \frac{1176981}{66325}e^{10} + \frac{1862367}{66325}e^{9} + \frac{5312348}{66325}e^{8} - \frac{842428}{13265}e^{7} - \frac{12294741}{66325}e^{6} + \frac{4935949}{66325}e^{5} + \frac{13417247}{66325}e^{4} - \frac{2972387}{66325}e^{3} - \frac{5470739}{66325}e^{2} + \frac{109408}{9475}e + \frac{466002}{66325}$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $\phantom{-}\frac{7646}{66325}e^{15} + \frac{11708}{66325}e^{14} - \frac{33024}{13265}e^{13} - \frac{227368}{66325}e^{12} + \frac{1421787}{66325}e^{11} + \frac{1699566}{66325}e^{10} - \frac{6277472}{66325}e^{9} - \frac{6150313}{66325}e^{8} + \frac{437204}{1895}e^{7} + \frac{1597493}{9475}e^{6} - \frac{2952432}{9475}e^{5} - \frac{9638357}{66325}e^{4} + \frac{14187132}{66325}e^{3} + \frac{3150759}{66325}e^{2} - \frac{3361116}{66325}e - \frac{202562}{66325}$ |
| 47 | $[47, 47, -2w + 7]$ | $\phantom{-}\frac{6239}{66325}e^{15} - \frac{838}{66325}e^{14} - \frac{28543}{13265}e^{13} + \frac{36733}{66325}e^{12} + \frac{1298448}{66325}e^{11} - \frac{454306}{66325}e^{10} - \frac{5985908}{66325}e^{9} + \frac{2425673}{66325}e^{8} + \frac{2952952}{13265}e^{7} - \frac{6161266}{66325}e^{6} - \frac{18907076}{66325}e^{5} + \frac{7286472}{66325}e^{4} + \frac{1564309}{9475}e^{3} - \frac{3388289}{66325}e^{2} - \frac{1535194}{66325}e + \frac{115002}{66325}$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $\phantom{-}\frac{1184}{9475}e^{15} + \frac{8794}{66325}e^{14} - \frac{35863}{13265}e^{13} - \frac{155219}{66325}e^{12} + \frac{1544156}{66325}e^{11} + \frac{1000473}{66325}e^{10} - \frac{6776471}{66325}e^{9} - \frac{2770944}{66325}e^{8} + \frac{3218259}{13265}e^{7} + \frac{2595028}{66325}e^{6} - \frac{19946527}{66325}e^{5} + \frac{1376959}{66325}e^{4} + \frac{10767796}{66325}e^{3} - \frac{2938108}{66325}e^{2} - \frac{1523023}{66325}e + \frac{67842}{9475}$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}\frac{3183}{66325}e^{15} + \frac{1172}{9475}e^{14} - \frac{14088}{13265}e^{13} - \frac{150229}{66325}e^{12} + \frac{653746}{66325}e^{11} + \frac{1007243}{66325}e^{10} - \frac{3320711}{66325}e^{9} - \frac{2957679}{66325}e^{8} + \frac{1974304}{13265}e^{7} + \frac{3357023}{66325}e^{6} - \frac{16321482}{66325}e^{5} - \frac{10481}{66325}e^{4} + \frac{12293261}{66325}e^{3} - \frac{319129}{9475}e^{2} - \frac{2553618}{66325}e + \frac{881404}{66325}$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $-\frac{5624}{66325}e^{15} - \frac{21}{9475}e^{14} + \frac{23537}{13265}e^{13} - \frac{26443}{66325}e^{12} - \frac{956048}{66325}e^{11} + \frac{467921}{66325}e^{10} + \frac{3816023}{66325}e^{9} - \frac{2889973}{66325}e^{8} - \frac{226206}{1895}e^{7} + \frac{7692431}{66325}e^{6} + \frac{1250048}{9475}e^{5} - \frac{8216647}{66325}e^{4} - \frac{5748758}{66325}e^{3} + \frac{2282839}{66325}e^{2} + \frac{2449654}{66325}e + \frac{209298}{66325}$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $\phantom{-}\frac{5553}{66325}e^{15} + \frac{1219}{66325}e^{14} - \frac{28702}{13265}e^{13} - \frac{24699}{66325}e^{12} + \frac{1509241}{66325}e^{11} + \frac{203263}{66325}e^{10} - \frac{8246471}{66325}e^{9} - \frac{846884}{66325}e^{8} + \frac{4938364}{13265}e^{7} + \frac{1826668}{66325}e^{6} - \frac{38974157}{66325}e^{5} - \frac{1903701}{66325}e^{4} + \frac{28024726}{66325}e^{3} + \frac{76791}{9475}e^{2} - \frac{6080388}{66325}e + \frac{552934}{66325}$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{1774}{13265}e^{15} + \frac{22}{379}e^{14} - \frac{37622}{13265}e^{13} - \frac{10418}{13265}e^{12} + \frac{43688}{1895}e^{11} + \frac{27934}{13265}e^{10} - \frac{236398}{2653}e^{9} + \frac{184581}{13265}e^{8} + \frac{429591}{2653}e^{7} - \frac{1210376}{13265}e^{6} - \frac{1415788}{13265}e^{5} + \frac{338792}{1895}e^{4} - \frac{19886}{1895}e^{3} - \frac{1603033}{13265}e^{2} + \frac{20233}{1895}e + \frac{214584}{13265}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^{2} - 2w - 2]$ | $1$ |