Base field 5.5.89417.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - x^{2} + 8x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, w^{3} + w^{2} - 4w - 1]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 6x^{10} - 6x^{9} + 90x^{8} - 64x^{7} - 430x^{6} + 534x^{5} + 734x^{4} - 1129x^{3} - 244x^{2} + 584x - 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{2} - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{4} - 5w^{2} + 4]$ | $\phantom{-}\frac{1}{328}e^{10} - \frac{23}{328}e^{9} + \frac{57}{328}e^{8} + \frac{351}{328}e^{7} - \frac{1029}{328}e^{6} - \frac{1797}{328}e^{5} + \frac{5171}{328}e^{4} + \frac{3765}{328}e^{3} - \frac{1059}{41}e^{2} - \frac{334}{41}e + \frac{298}{41}$ |
| 11 | $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $-\frac{39}{328}e^{10} + \frac{25}{41}e^{9} + \frac{401}{328}e^{8} - \frac{394}{41}e^{7} - \frac{49}{328}e^{6} + \frac{2062}{41}e^{5} - \frac{8313}{328}e^{4} - \frac{4235}{41}e^{3} + \frac{2638}{41}e^{2} + \frac{2776}{41}e - \frac{1372}{41}$ |
| 17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $\phantom{-}\frac{15}{164}e^{10} - \frac{29}{82}e^{9} - \frac{211}{164}e^{8} + \frac{439}{82}e^{7} + \frac{965}{164}e^{6} - \frac{2141}{82}e^{5} - \frac{1975}{164}e^{4} + \frac{3863}{82}e^{3} + \frac{1035}{82}e^{2} - \frac{918}{41}e - \frac{80}{41}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{21}{328}e^{10} - \frac{49}{82}e^{9} + \frac{49}{328}e^{8} + \frac{787}{82}e^{7} - \frac{4061}{328}e^{6} - \frac{2129}{41}e^{5} + \frac{24459}{328}e^{4} + \frac{4630}{41}e^{3} - \frac{11227}{82}e^{2} - \frac{3283}{41}e + \frac{2035}{41}$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ | $-\frac{57}{328}e^{10} + \frac{327}{328}e^{9} + \frac{441}{328}e^{8} - \frac{5165}{328}e^{7} + \frac{2401}{328}e^{6} + \frac{27153}{328}e^{5} - \frac{25869}{328}e^{4} - \frac{56427}{328}e^{3} + \frac{14249}{82}e^{2} + \frac{4811}{41}e - \frac{2964}{41}$ |
| 37 | $[37, 37, -w^{3} + 4w - 1]$ | $\phantom{-}\frac{9}{164}e^{10} - \frac{43}{164}e^{9} - \frac{51}{82}e^{8} + \frac{329}{82}e^{7} + \frac{169}{164}e^{6} - \frac{3299}{164}e^{5} + \frac{617}{82}e^{4} + \frac{1614}{41}e^{3} - \frac{2249}{82}e^{2} - \frac{1051}{41}e + \frac{772}{41}$ |
| 41 | $[41, 41, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{3} + 2w + 2]$ | $-\frac{5}{164}e^{10} - \frac{2}{41}e^{9} + \frac{83}{82}e^{8} + \frac{49}{164}e^{7} - \frac{1579}{164}e^{6} + \frac{63}{41}e^{5} + \frac{1357}{41}e^{4} - \frac{1441}{164}e^{3} - \frac{3133}{82}e^{2} + \frac{306}{41}e + \frac{300}{41}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{51}{328}e^{10} - \frac{271}{328}e^{9} - \frac{455}{328}e^{8} + \frac{4125}{328}e^{7} - \frac{819}{328}e^{6} - \frac{20553}{328}e^{5} + \frac{13867}{328}e^{4} + \frac{40315}{328}e^{3} - \frac{7363}{82}e^{2} - \frac{3381}{41}e + \frac{1586}{41}$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 2]$ | $\phantom{-}\frac{47}{328}e^{10} - \frac{261}{328}e^{9} - \frac{355}{328}e^{8} + \frac{3869}{328}e^{7} - \frac{1623}{328}e^{6} - \frac{18531}{328}e^{5} + \frac{16471}{328}e^{4} + \frac{34603}{328}e^{3} - \frac{8403}{82}e^{2} - \frac{2742}{41}e + \frac{1952}{41}$ |
| 53 | $[53, 53, w^{4} - w^{3} - 5w^{2} + 2w + 5]$ | $-\frac{3}{41}e^{10} + \frac{101}{328}e^{9} + \frac{177}{164}e^{8} - \frac{1659}{328}e^{7} - \frac{427}{82}e^{6} + \frac{8975}{328}e^{5} + \frac{1785}{164}e^{4} - \frac{18241}{328}e^{3} - \frac{455}{41}e^{2} + \frac{1415}{41}e - \frac{18}{41}$ |
| 59 | $[59, 59, w^{4} - w^{3} - 4w^{2} + 3w - 1]$ | $\phantom{-}\frac{5}{164}e^{10} + \frac{2}{41}e^{9} - \frac{83}{82}e^{8} - \frac{45}{82}e^{7} + \frac{1661}{164}e^{6} + \frac{101}{41}e^{5} - \frac{1603}{41}e^{4} - \frac{981}{82}e^{3} + \frac{2325}{41}e^{2} + \frac{1170}{41}e - \frac{792}{41}$ |
| 67 | $[67, 67, -w^{4} + 3w^{2} + 2w + 2]$ | $\phantom{-}\frac{11}{164}e^{10} - \frac{55}{328}e^{9} - \frac{193}{164}e^{8} + \frac{875}{328}e^{7} + \frac{1145}{164}e^{6} - \frac{4561}{328}e^{5} - \frac{2569}{164}e^{4} + \frac{8661}{328}e^{3} + \frac{677}{82}e^{2} - \frac{460}{41}e + \frac{406}{41}$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{69}{164}e^{10} - \frac{673}{328}e^{9} - \frac{741}{164}e^{8} + \frac{10349}{328}e^{7} + \frac{749}{164}e^{6} - \frac{52047}{328}e^{5} + \frac{10185}{164}e^{4} + \frac{100755}{328}e^{3} - \frac{13443}{82}e^{2} - \frac{7429}{41}e + \frac{3650}{41}$ |
| 81 | $[81, 3, -w^{4} + 6w^{2} + w - 8]$ | $-\frac{15}{164}e^{10} + \frac{157}{328}e^{9} + \frac{85}{82}e^{8} - \frac{2617}{328}e^{7} - \frac{145}{164}e^{6} + \frac{14427}{328}e^{5} - \frac{1657}{82}e^{4} - \frac{29679}{328}e^{3} + \frac{2455}{41}e^{2} + \frac{2148}{41}e - \frac{1478}{41}$ |
| 83 | $[83, 83, w^{4} + w^{3} - 5w^{2} - 4w + 1]$ | $\phantom{-}\frac{25}{164}e^{10} - \frac{207}{328}e^{9} - \frac{297}{164}e^{8} + \frac{2913}{328}e^{7} + \frac{843}{164}e^{6} - \frac{12237}{328}e^{5} - \frac{39}{164}e^{4} + \frac{15435}{328}e^{3} - \frac{347}{41}e^{2} + \frac{28}{41}e + \frac{304}{41}$ |
| 89 | $[89, 89, -w^{4} + 5w^{2} + w - 1]$ | $\phantom{-}\frac{11}{164}e^{10} + \frac{27}{328}e^{9} - \frac{357}{164}e^{8} - \frac{273}{328}e^{7} + \frac{3605}{164}e^{6} + \frac{769}{328}e^{5} - \frac{14213}{164}e^{4} - \frac{2819}{328}e^{3} + \frac{10435}{82}e^{2} + \frac{852}{41}e - \frac{1644}{41}$ |
| 97 | $[97, 97, -w^{4} + 2w^{3} + 5w^{2} - 5w - 5]$ | $\phantom{-}\frac{51}{328}e^{10} - \frac{37}{82}e^{9} - \frac{865}{328}e^{8} + \frac{285}{41}e^{7} + \frac{5249}{328}e^{6} - \frac{1416}{41}e^{5} - \frac{14259}{328}e^{4} + \frac{5169}{82}e^{3} + \frac{1915}{41}e^{2} - \frac{1208}{41}e - \frac{382}{41}$ |
| 101 | $[101, 101, 2w^{2} - w - 2]$ | $\phantom{-}\frac{49}{328}e^{10} - \frac{23}{41}e^{9} - \frac{651}{328}e^{8} + \frac{1363}{164}e^{7} + \frac{2223}{328}e^{6} - \frac{3143}{82}e^{5} + \frac{327}{328}e^{4} + \frac{9935}{164}e^{3} - \frac{2307}{82}e^{2} - \frac{909}{41}e + \frac{908}{41}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, w^{3} + w^{2} - 4w - 1]$ | $-1$ |