Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, 12w^{2} + w + 7]$ |
| Dimension: | $52$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $104$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{52} + 74x^{50} + 2555x^{48} + 54700x^{46} + 813991x^{44} + 8945812x^{42} + 75310425x^{40} + 497171675x^{38} + 2613654770x^{36} + 11050193844x^{34} + 37791247981x^{32} + 104810882723x^{30} + 235647425039x^{28} + 428179824323x^{26} + 625109668917x^{24} + 726767106368x^{22} + 664612519782x^{20} + 470197502029x^{18} + 251823835549x^{16} + 99272720320x^{14} + 27797959975x^{12} + 5291146579x^{10} + 649067038x^{8} + 47845060x^{6} + 1926008x^{4} + 38173x^{2} + 289\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 11 | $[11, 11, 10w + 4]$ | $...$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $...$ |
| 17 | $[17, 17, w + 1]$ | $...$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $...$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $...$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $...$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $...$ |
| 27 | $[27, 3, -3]$ | $...$ |
| 29 | $[29, 29, w + 7]$ | $...$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $...$ |
| 43 | $[43, 43, w^{2} - 11]$ | $...$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $...$ |
| 79 | $[79, 79, w^{2} + 37]$ | $...$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, 12w^{2} + w + 7]$ | $\frac{2496284135478002687921125231696170479}{93301813190991462576810774550529455392}e^{51} + \frac{184668025794012798985435591835707682369}{93301813190991462576810774550529455392}e^{49} + \frac{1062295530847744548979144147334354178659}{15550302198498577096135129091754909232}e^{47} + \frac{68200014920746930401475229791921619781607}{46650906595495731288405387275264727696}e^{45} + \frac{676266113090834556438850472672522979729461}{31100604396997154192270258183509818464}e^{43} + \frac{1061148699897491732961232458627518327666283}{4442943485285307741752894026215688352}e^{41} + \frac{5513974118654607218055886156689427493223401}{2744170976205631252259140427956748688}e^{39} + \frac{412223055185498811698150652036430717011978101}{31100604396997154192270258183509818464}e^{37} + \frac{6495105675998263613512542882003823128776490697}{93301813190991462576810774550529455392}e^{35} + \frac{27429188145847573984324628003553341066843534033}{93301813190991462576810774550529455392}e^{33} + \frac{11709527155496247086412885459662094282381110635}{11662726648873932822101346818816181924}e^{31} + \frac{259356084018750060631929099092755577171661637165}{93301813190991462576810774550529455392}e^{29} + \frac{290927992855449491502201005866433695601333117221}{46650906595495731288405387275264727696}e^{27} + \frac{1054355302275063058177472576806452278378386715567}{93301813190991462576810774550529455392}e^{25} + \frac{766910630625318644647752214644895238263521629683}{46650906595495731288405387275264727696}e^{23} + \frac{126779945556262499447754495033721872735683481277}{6664415227927961612629341039323532528}e^{21} + \frac{100805408399056844909679080165937540562957478477}{5831363324436966411050673409408090962}e^{19} + \frac{53862324280951353201058523836566252267354407583}{4442943485285307741752894026215688352}e^{17} + \frac{5864983335323731569226743919600573368649611259}{914723658735210417419713475985582896}e^{15} + \frac{16534000437019296765109013972332971673987302011}{6664415227927961612629341039323532528}e^{13} + \frac{62975219033733753721406078223575559492621752555}{93301813190991462576810774550529455392}e^{11} + \frac{2860149302305213237730749887473969391779192737}{23325453297747865644202693637632363848}e^{9} + \frac{5446840948606589568488156699359417492468777}{392024425172233036037020061136678384}e^{7} + \frac{13768214950714680947205634552906951264470367}{15550302198498577096135129091754909232}e^{5} + \frac{1235342662241618814897094304647319417725985}{46650906595495731288405387275264727696}e^{3} + \frac{26277773451438384282643169599975793362789}{93301813190991462576810774550529455392}e$ |