Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11,11,-w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $186$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 4x^{9} + 15x^{8} - 18x^{7} + 32x^{6} - 18x^{5} + 48x^{4} - 19x^{3} + 16x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{66172}{253039}e^{9} - \frac{269683}{253039}e^{8} + \frac{1002555}{253039}e^{7} - \frac{1227804}{253039}e^{6} + \frac{2076897}{253039}e^{5} - \frac{1252941}{253039}e^{4} + \frac{3181044}{253039}e^{3} - \frac{1590021}{253039}e^{2} + \frac{1047181}{253039}e + \frac{195723}{253039}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{18955}{253039}e^{9} + \frac{56850}{253039}e^{8} - \frac{209208}{253039}e^{7} + \frac{74881}{253039}e^{6} - \frac{352470}{253039}e^{5} + \frac{27288}{253039}e^{4} - \frac{985121}{253039}e^{3} - \frac{65946}{253039}e^{2} - \frac{15918}{253039}e + \frac{387694}{253039}$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{128701}{253039}e^{9} + \frac{556407}{253039}e^{8} - \frac{2088064}{253039}e^{7} + \frac{2926763}{253039}e^{6} - \frac{4816134}{253039}e^{5} + \frac{3748892}{253039}e^{4} - \frac{6840322}{253039}e^{3} + \frac{4435591}{253039}e^{2} - \frac{2524239}{253039}e + \frac{295669}{253039}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{31271}{253039}e^{9} - \frac{75366}{253039}e^{8} + \frac{297590}{253039}e^{7} + \frac{68150}{253039}e^{6} + \frac{517877}{253039}e^{5} + \frac{500267}{253039}e^{4} + \frac{1418700}{253039}e^{3} + \frac{1089459}{253039}e^{2} + \frac{699247}{253039}e + \frac{141826}{253039}$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{169556}{253039}e^{9} + \frac{713982}{253039}e^{8} - \frac{2667940}{253039}e^{7} + \frac{3510536}{253039}e^{6} - \frac{5793099}{253039}e^{5} + \frac{3824528}{253039}e^{4} - \frac{8198496}{253039}e^{3} + \frac{4252804}{253039}e^{2} - \frac{2568360}{253039}e - \frac{473780}{253039}$ |
| 11 | $[11, 11, w + 9]$ | $\phantom{-}\frac{52212}{253039}e^{9} - \frac{222808}{253039}e^{8} + \frac{830055}{253039}e^{7} - \frac{1112316}{253039}e^{6} + \frac{1786272}{253039}e^{5} - \frac{1230441}{253039}e^{4} + \frac{2528676}{253039}e^{3} - \frac{1644396}{253039}e^{2} + \frac{781017}{253039}e - \frac{109528}{253039}$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{418965}{253039}e^{9} + \frac{1607187}{253039}e^{8} - \frac{6056150}{253039}e^{7} + \frac{6701134}{253039}e^{6} - \frac{12849204}{253039}e^{5} + \frac{6125755}{253039}e^{4} - \frac{20000724}{253039}e^{3} + \frac{5544645}{253039}e^{2} - \frac{6968297}{253039}e - \frac{1320826}{253039}$ |
| 17 | $[17, 17, w + 14]$ | $-\frac{192603}{253039}e^{9} + \frac{845113}{253039}e^{8} - \frac{3221353}{253039}e^{7} + \frac{4699869}{253039}e^{6} - \frac{7921914}{253039}e^{5} + \frac{6185065}{253039}e^{4} - \frac{11287062}{253039}e^{3} + \frac{7299105}{253039}e^{2} - \frac{5105102}{253039}e + \frac{486907}{253039}$ |
| 19 | $[19, 19, w]$ | $-\frac{18970}{253039}e^{9} + \frac{75117}{253039}e^{8} - \frac{266309}{253039}e^{7} + \frac{254090}{253039}e^{6} - \frac{313902}{253039}e^{5} - \frac{75281}{253039}e^{4} - \frac{426091}{253039}e^{3} + \frac{287362}{253039}e^{2} + \frac{444559}{253039}e + \frac{18955}{253039}$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}\frac{58430}{253039}e^{9} - \frac{305134}{253039}e^{8} + \frac{1102650}{253039}e^{7} - \frac{1884156}{253039}e^{6} + \frac{2347301}{253039}e^{5} - \frac{2454180}{253039}e^{4} + \frac{2913216}{253039}e^{3} - \frac{3431508}{253039}e^{2} + \frac{672488}{253039}e + \frac{111954}{253039}$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{40957}{253039}e^{9} - \frac{180575}{253039}e^{8} + \frac{664516}{253039}e^{7} - \frac{840846}{253039}e^{6} + \frac{1119565}{253039}e^{5} - \frac{86676}{253039}e^{4} + \frac{1352355}{253039}e^{3} + \frac{209467}{253039}e^{2} + \frac{50561}{253039}e + \frac{1556209}{253039}$ |
| 37 | $[37, 37, w - 5]$ | $\phantom{-}\frac{205096}{253039}e^{9} - \frac{724925}{253039}e^{8} + \frac{2667724}{253039}e^{7} - \frac{2167410}{253039}e^{6} + \frac{4494535}{253039}e^{5} - \frac{347964}{253039}e^{4} + \frac{7401438}{253039}e^{3} + \frac{840913}{253039}e^{2} + \frac{202979}{253039}e + \frac{2420029}{253039}$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{193569}{253039}e^{9} - \frac{705705}{253039}e^{8} + \frac{2698210}{253039}e^{7} - \frac{2728646}{253039}e^{6} + \frac{5893605}{253039}e^{5} - \frac{2211227}{253039}e^{4} + \frac{9192756}{253039}e^{3} - \frac{1256302}{253039}e^{2} + \frac{3335281}{253039}e + \frac{638198}{253039}$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{53586}{253039}e^{9} - \frac{175400}{253039}e^{8} + \frac{645472}{253039}e^{7} - \frac{422424}{253039}e^{6} + \frac{1087480}{253039}e^{5} - \frac{84192}{253039}e^{4} + \frac{1423250}{253039}e^{3} + \frac{203464}{253039}e^{2} + \frac{49112}{253039}e - \frac{1151202}{253039}$ |
| 53 | $[53, 53, -w - 10]$ | $-\frac{270003}{253039}e^{9} + \frac{972325}{253039}e^{8} - \frac{3578156}{253039}e^{7} + \frac{3042530}{253039}e^{6} - \frac{6028415}{253039}e^{5} + \frac{466716}{253039}e^{4} - \frac{10071667}{253039}e^{3} - \frac{1127897}{253039}e^{2} - \frac{272251}{253039}e - \frac{3401677}{253039}$ |
| 53 | $[53, 53, w - 11]$ | $\phantom{-}\frac{50743}{253039}e^{9} - \frac{154525}{253039}e^{8} + \frac{568652}{253039}e^{7} - \frac{245486}{253039}e^{6} + \frac{958055}{253039}e^{5} - \frac{74172}{253039}e^{4} + \frac{2282538}{253039}e^{3} + \frac{179249}{253039}e^{2} + \frac{43267}{253039}e + \frac{115033}{253039}$ |
| 61 | $[61, 61, w + 15]$ | $-\frac{495727}{253039}e^{9} + \frac{2121422}{253039}e^{8} - \frac{7897927}{253039}e^{7} + \frac{10714421}{253039}e^{6} - \frac{17302656}{253039}e^{5} + \frac{12900994}{253039}e^{4} - \frac{24512623}{253039}e^{3} + \frac{15930025}{253039}e^{2} - \frac{5290402}{253039}e + \frac{1061238}{253039}$ |
| 61 | $[61, 61, w + 45]$ | $-\frac{425183}{253039}e^{9} + \frac{1689513}{253039}e^{8} - \frac{6328745}{253039}e^{7} + \frac{7472974}{253039}e^{6} - \frac{13410233}{253039}e^{5} + \frac{7349494}{253039}e^{4} - \frac{20385264}{253039}e^{3} + \frac{7078718}{253039}e^{2} - \frac{6859768}{253039}e - \frac{1289269}{253039}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-w + 2]$ | $-\frac{52212}{253039}e^{9} + \frac{222808}{253039}e^{8} - \frac{830055}{253039}e^{7} + \frac{1112316}{253039}e^{6} - \frac{1786272}{253039}e^{5} + \frac{1230441}{253039}e^{4} - \frac{2528676}{253039}e^{3} + \frac{1644396}{253039}e^{2} - \frac{781017}{253039}e + \frac{109528}{253039}$ |