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: | $[5,5,-w + 2]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} - 5x^{21} + 36x^{20} - 103x^{19} + 511x^{18} - 1215x^{17} + 4844x^{16} - 9038x^{15} + 28947x^{14} - 46917x^{13} + 124683x^{12} - 168537x^{11} + 331409x^{10} - 409870x^{9} + 601146x^{8} - 525015x^{7} + 430872x^{6} - 164288x^{5} + 59225x^{4} + 9128x^{3} + 3472x^{2} + 60x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, w + 1]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 14]$ | $...$ |
| 19 | $[19, 19, w]$ | $...$ |
| 19 | $[19, 19, w + 18]$ | $...$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 37 | $[37, 37, w - 5]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -w - 10]$ | $...$ |
| 53 | $[53, 53, w - 11]$ | $...$ |
| 61 | $[61, 61, w + 15]$ | $...$ |
| 61 | $[61, 61, w + 45]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 2]$ | $\frac{1462741918431119970858626762623400054858}{87719020534428139166148321778356704549671}e^{21} - \frac{7322155050544795282436105902576288718877}{87719020534428139166148321778356704549671}e^{20} + \frac{52703789310128957331858064984011018908150}{87719020534428139166148321778356704549671}e^{19} - \frac{150982352735046598147434726561218169795093}{87719020534428139166148321778356704549671}e^{18} + \frac{748441676603356676303170925975047794625593}{87719020534428139166148321778356704549671}e^{17} - \frac{1781898759077683257480401357565006217407848}{87719020534428139166148321778356704549671}e^{16} + \frac{7097401845279938516686097526802858582635455}{87719020534428139166148321778356704549671}e^{15} - \frac{13265451337941923839316278812054324521661415}{87719020534428139166148321778356704549671}e^{14} + \frac{42434014541010940906510392509333498463774173}{87719020534428139166148321778356704549671}e^{13} - \frac{68905371856671238382330280294695472164283352}{87719020534428139166148321778356704549671}e^{12} + \frac{182871548872298005806578705378120611542666509}{87719020534428139166148321778356704549671}e^{11} - \frac{247758255221115153110217028152432365603215265}{87719020534428139166148321778356704549671}e^{10} + \frac{486614633067996548661486768934760863770070385}{87719020534428139166148321778356704549671}e^{9} - \frac{603006320992524284031393041139993452992482341}{87719020534428139166148321778356704549671}e^{8} + \frac{883972307357957549666844438164892966509487477}{87719020534428139166148321778356704549671}e^{7} - \frac{774706985223152109562005870641890121853304881}{87719020534428139166148321778356704549671}e^{6} + \frac{636979574603198238442091633291884989221598207}{87719020534428139166148321778356704549671}e^{5} - \frac{246318232026478405814523293763535628468504998}{87719020534428139166148321778356704549671}e^{4} + \frac{89923125950601071342440344067137886279666535}{87719020534428139166148321778356704549671}e^{3} + \frac{11823973827947634825293064815143401114039139}{87719020534428139166148321778356704549671}e^{2} + \frac{5255399803384627772284612426534470311877190}{87719020534428139166148321778356704549671}e + \frac{90817881856354367313173573387070138696133}{87719020534428139166148321778356704549671}$ |