Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $90$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 4x^{11} - 9x^{10} + 51x^{9} - x^{8} - 186x^{7} + 121x^{6} + 188x^{5} - 125x^{4} - 74x^{3} + 24x^{2} + 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{17}{13}e^{11} + \frac{55}{13}e^{10} + \frac{193}{13}e^{9} - \frac{725}{13}e^{8} - \frac{486}{13}e^{7} + \frac{2858}{13}e^{6} - \frac{280}{13}e^{5} - \frac{3617}{13}e^{4} + \frac{529}{13}e^{3} + \frac{1739}{13}e^{2} + \frac{61}{13}e - \frac{100}{13}$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{10}{13}e^{11} + \frac{41}{13}e^{10} + \frac{85}{13}e^{9} - \frac{515}{13}e^{8} + \frac{67}{13}e^{7} + \frac{1811}{13}e^{6} - \frac{1355}{13}e^{5} - \frac{1610}{13}e^{4} + \frac{1173}{13}e^{3} + 42e^{2} - \frac{94}{13}e + \frac{6}{13}$ |
| 7 | $[7, 7, w + 1]$ | $-3e^{11} + \frac{142}{13}e^{10} + \frac{391}{13}e^{9} - \frac{1824}{13}e^{8} - \frac{476}{13}e^{7} + \frac{6777}{13}e^{6} - \frac{2790}{13}e^{5} - \frac{7283}{13}e^{4} + 212e^{3} + \frac{3067}{13}e^{2} - \frac{111}{13}e - \frac{152}{13}$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}\frac{35}{13}e^{11} - \frac{133}{13}e^{10} - \frac{334}{13}e^{9} + \frac{1695}{13}e^{8} + \frac{220}{13}e^{7} - \frac{6179}{13}e^{6} + \frac{3195}{13}e^{5} + \frac{6245}{13}e^{4} - \frac{2981}{13}e^{3} - \frac{2453}{13}e^{2} + \frac{240}{13}e + \frac{93}{13}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{5}{13}e^{11} - \frac{33}{13}e^{10} - \frac{17}{13}e^{9} + \frac{422}{13}e^{8} - \frac{348}{13}e^{7} - \frac{1551}{13}e^{6} + \frac{1741}{13}e^{5} + \frac{1658}{13}e^{4} - \frac{1360}{13}e^{3} - \frac{916}{13}e^{2} + \frac{31}{13}e + \frac{47}{13}$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}\frac{1}{13}e^{11} - \frac{10}{13}e^{9} - \frac{27}{13}e^{8} + \frac{30}{13}e^{7} + \frac{329}{13}e^{6} - \frac{145}{13}e^{5} - \frac{1076}{13}e^{4} + \frac{573}{13}e^{3} + \frac{671}{13}e^{2} - \frac{140}{13}e + \frac{9}{13}$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{34}{13}e^{11} + \frac{119}{13}e^{10} + 28e^{9} - \frac{1557}{13}e^{8} - \frac{705}{13}e^{7} + \frac{6031}{13}e^{6} - \frac{1424}{13}e^{5} - \frac{7285}{13}e^{4} + \frac{1578}{13}e^{3} + \frac{3396}{13}e^{2} + \frac{94}{13}e - \frac{184}{13}$ |
| 29 | $[29, 29, w + 6]$ | $\phantom{-}\frac{54}{13}e^{11} - \frac{216}{13}e^{10} - \frac{493}{13}e^{9} + \frac{2761}{13}e^{8} + \frac{61}{13}e^{7} - \frac{10139}{13}e^{6} + \frac{5899}{13}e^{5} + \frac{10551}{13}e^{4} - \frac{5419}{13}e^{3} - \frac{4516}{13}e^{2} + \frac{496}{13}e + \frac{206}{13}$ |
| 29 | $[29, 29, w + 22]$ | $-\frac{49}{13}e^{11} + \frac{177}{13}e^{10} + \frac{482}{13}e^{9} - \frac{2246}{13}e^{8} - \frac{483}{13}e^{7} + \frac{8105}{13}e^{6} - \frac{3894}{13}e^{5} - \frac{7897}{13}e^{4} + \frac{3773}{13}e^{3} + \frac{2866}{13}e^{2} - 27e - \frac{109}{13}$ |
| 41 | $[41, 41, w + 13]$ | $\phantom{-}\frac{40}{13}e^{11} - \frac{172}{13}e^{10} - \frac{345}{13}e^{9} + 170e^{8} - \frac{202}{13}e^{7} - \frac{8213}{13}e^{6} + 399e^{5} + \frac{8899}{13}e^{4} - \frac{4497}{13}e^{3} - \frac{4116}{13}e^{2} + \frac{73}{13}e + \frac{255}{13}$ |
| 41 | $[41, 41, w + 27]$ | $\phantom{-}\frac{9}{13}e^{11} - \frac{28}{13}e^{10} - \frac{114}{13}e^{9} + \frac{399}{13}e^{8} + \frac{384}{13}e^{7} - \frac{1815}{13}e^{6} - \frac{112}{13}e^{5} + \frac{2972}{13}e^{4} - \frac{615}{13}e^{3} - \frac{1438}{13}e^{2} + 10e + \frac{63}{13}$ |
| 43 | $[43, 43, w + 16]$ | $-\frac{61}{13}e^{11} + \frac{233}{13}e^{10} + 46e^{9} - \frac{3024}{13}e^{8} - \frac{564}{13}e^{7} + \frac{11499}{13}e^{6} - \frac{5086}{13}e^{5} - \frac{13225}{13}e^{4} + \frac{5165}{13}e^{3} + \frac{5998}{13}e^{2} - \frac{203}{13}e - \frac{298}{13}$ |
| 43 | $[43, 43, w + 26]$ | $\phantom{-}\frac{5}{13}e^{11} - \frac{28}{13}e^{10} - \frac{35}{13}e^{9} + 29e^{8} - \frac{139}{13}e^{7} - \frac{1545}{13}e^{6} + 89e^{5} + \frac{2128}{13}e^{4} - \frac{1373}{13}e^{3} - \frac{1132}{13}e^{2} + \frac{352}{13}e + \frac{92}{13}$ |
| 47 | $[47, 47, w + 2]$ | $-\frac{3}{13}e^{11} + \frac{8}{13}e^{10} + \frac{9}{13}e^{9} - \frac{43}{13}e^{8} + 18e^{7} - \frac{356}{13}e^{6} - \frac{1204}{13}e^{5} + \frac{2095}{13}e^{4} + \frac{1232}{13}e^{3} - \frac{1719}{13}e^{2} - \frac{629}{13}e + \frac{110}{13}$ |
| 47 | $[47, 47, w + 44]$ | $\phantom{-}\frac{20}{13}e^{11} - \frac{64}{13}e^{10} - \frac{214}{13}e^{9} + \frac{803}{13}e^{8} + \frac{426}{13}e^{7} - \frac{2823}{13}e^{6} + \frac{683}{13}e^{5} + \frac{2507}{13}e^{4} - \frac{461}{13}e^{3} - \frac{775}{13}e^{2} - \frac{76}{13}e + \frac{33}{13}$ |
| 73 | $[73, 73, w + 33]$ | $\phantom{-}\frac{32}{13}e^{11} - \frac{107}{13}e^{10} - \frac{330}{13}e^{9} + \frac{1347}{13}e^{8} + 38e^{7} - \frac{4761}{13}e^{6} + \frac{2031}{13}e^{5} + \frac{4221}{13}e^{4} - \frac{2464}{13}e^{3} - \frac{995}{13}e^{2} + \frac{660}{13}e - \frac{25}{13}$ |
| 73 | $[73, 73, w + 39]$ | $-\frac{56}{13}e^{11} + \frac{181}{13}e^{10} + \frac{639}{13}e^{9} - 184e^{8} - \frac{1636}{13}e^{7} + \frac{9465}{13}e^{6} - 65e^{5} - \frac{11975}{13}e^{4} + \frac{1816}{13}e^{3} + \frac{5388}{13}e^{2} + \frac{163}{13}e - \frac{253}{13}$ |
| 83 | $[83, 83, -4w - 37]$ | $-\frac{40}{13}e^{11} + \frac{111}{13}e^{10} + \frac{484}{13}e^{9} - \frac{1440}{13}e^{8} - 117e^{7} + \frac{5480}{13}e^{6} + \frac{695}{13}e^{5} - \frac{6248}{13}e^{4} + \frac{51}{13}e^{3} + \frac{2417}{13}e^{2} - \frac{32}{13}e - \frac{141}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |