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: | $[4, 2, 2]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $135$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - x^{19} + 13x^{18} - 26x^{17} + 164x^{16} + 269x^{15} + 1475x^{14} + 2122x^{13} + 12115x^{12} + 7255x^{11} + 24248x^{10} + 14804x^{9} + 45098x^{8} + 6802x^{7} + 80623x^{6} + 18722x^{5} + 129502x^{4} + 20595x^{3} + 3276x^{2} + 513x + 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 22]$ | $...$ |
| 41 | $[41, 41, w + 13]$ | $...$ |
| 41 | $[41, 41, w + 27]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 47 | $[47, 47, w + 2]$ | $...$ |
| 47 | $[47, 47, w + 44]$ | $...$ |
| 73 | $[73, 73, w + 33]$ | $...$ |
| 73 | $[73, 73, w + 39]$ | $...$ |
| 83 | $[83, 83, -4w - 37]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{511980115985128}{260788011026812317}e^{19} - \frac{512029264464316}{260788011026812317}e^{18} + \frac{6656380438036108}{260788011026812317}e^{17} - \frac{13312760876072216}{260788011026812317}e^{16} + \frac{83972799372147824}{260788011026812317}e^{15} + \frac{137700425989740635}{260788011026812317}e^{14} + \frac{12800731611607900}{4420135780115463}e^{13} + \frac{1086526099193278552}{260788011026812317}e^{12} + \frac{6203234538985188340}{260788011026812317}e^{11} + \frac{3714772313688612580}{260788011026812317}e^{10} + \frac{12420371459241419222}{260788011026812317}e^{9} + \frac{7580081231129734064}{260788011026812317}e^{8} + \frac{23091495768811722968}{260788011026812317}e^{7} + \frac{3482823056886277432}{260788011026812317}e^{6} + \frac{41281335388906548868}{260788011026812317}e^{5} + \frac{9506568529417369295}{260788011026812317}e^{4} + \frac{66308813806657850632}{260788011026812317}e^{3} + \frac{3515080900547529340}{86929337008937439}e^{2} + \frac{186378652265011024}{28976445669645813}e + \frac{9728556024822004}{9658815223215271}$ |
| $2$ | $[2, 2, w + 1]$ | $-\frac{316955106772}{9658815223215271}e^{19} + \frac{1030104097009}{28976445669645813}e^{18} - \frac{3644983727878}{9658815223215271}e^{17} + \frac{7988495105956}{9658815223215271}e^{16} - \frac{138192426552592}{28976445669645813}e^{15} - \frac{95007293254907}{9658815223215271}e^{14} - \frac{1128122463778241}{28976445669645813}e^{13} - \frac{1534855104543410}{28976445669645813}e^{12} - \frac{3075702287866552}{9658815223215271}e^{11} - \frac{3094432707415036}{28976445669645813}e^{10} - \frac{4746561201464086}{28976445669645813}e^{9} - \frac{1370830836788900}{9658815223215271}e^{8} - \frac{6927450052385525}{28976445669645813}e^{7} + \frac{17389917150645496}{28976445669645813}e^{6} - \frac{3915029478847744}{9658815223215271}e^{5} - \frac{11893502665289221}{28976445669645813}e^{4} - \frac{630502946146201}{9658815223215271}e^{3} - \frac{100078574963259}{9658815223215271}e^{2} + \frac{182116650602474620}{28976445669645813}e - \frac{2139446970711}{9658815223215271}$ |