Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, w]$ |
| Dimension: | $46$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{46} + 127x^{44} + 7397x^{42} + 262345x^{40} + 6345015x^{38} + 111075637x^{36} + 1458219976x^{34} + 14679876062x^{32} + 114936230326x^{30} + 705905153573x^{28} + 3415846048959x^{26} + 13035825942781x^{24} + 39152791377987x^{22} + 92075956198229x^{20} + 168115354521546x^{18} + 235329307289617x^{16} + 248004286821795x^{14} + 191637891061098x^{12} + 104357376205867x^{10} + 37610974330406x^{8} + 8052634898325x^{6} + 829788817732x^{4} + 25809135396x^{2} + 60372900\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w]$ | $...$ |
| 11 | $[11, 11, w + 10]$ | $...$ |
| 13 | $[13, 13, w + 6]$ | $...$ |
| 17 | $[17, 17, -w - 8]$ | $...$ |
| 31 | $[31, 31, w + 14]$ | $...$ |
| 31 | $[31, 31, w + 16]$ | $...$ |
| 37 | $[37, 37, w + 15]$ | $...$ |
| 37 | $[37, 37, w + 21]$ | $...$ |
| 41 | $[41, 41, w + 18]$ | $...$ |
| 41 | $[41, 41, w + 22]$ | $...$ |
| 43 | $[43, 43, -w - 3]$ | $...$ |
| 43 | $[43, 43, w - 4]$ | $...$ |
| 53 | $[53, 53, -w - 1]$ | $...$ |
| 53 | $[53, 53, w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w]$ | $\frac{8902013401941473660543799204416829128802925510287926140202483819}{1221898521318443419135200872918994849727870084547325079080611009604930}e^{45} + \frac{559480622275499959583777665644724225271176540700321906138004591709}{610949260659221709567600436459497424863935042273662539540305504802465}e^{43} + \frac{32195397789970216801402679881513373132299141783855977326391727395599}{610949260659221709567600436459497424863935042273662539540305504802465}e^{41} + \frac{225153235838581010014284662259984037963405166891388253585123966204694}{122189852131844341913520087291899484972787008454732507908061100960493}e^{39} + \frac{1785029107415086970428478036646173838817252463377918478603937459879293}{40729950710614780637840029097299828324262336151577502636020366986831}e^{37} + \frac{459524308154534844923171790713190164679600511468747151427120200183897059}{610949260659221709567600436459497424863935042273662539540305504802465}e^{35} + \frac{11784059733256213985874695603912659507327760627336964143358195069936067379}{1221898521318443419135200872918994849727870084547325079080611009604930}e^{33} + \frac{57665995110454476662852957941548736813094898653469124028521822059646215899}{610949260659221709567600436459497424863935042273662539540305504802465}e^{31} + \frac{436472905188887454740137259439706472386538330869259879539125965370124653172}{610949260659221709567600436459497424863935042273662539540305504802465}e^{29} + \frac{5146971668887865405207858840510578774435519716486763612573537483776727566967}{1221898521318443419135200872918994849727870084547325079080611009604930}e^{27} + \frac{3950659744669610960020572448292889942675477718524976188077430436204027373936}{203649753553073903189200145486499141621311680757887513180101834934155}e^{25} + \frac{42585140369082013152291192066310938029170969850738507748021963332213870605432}{610949260659221709567600436459497424863935042273662539540305504802465}e^{23} + \frac{5657176351776464621794959118790055088407657204785465307159034434008763994444}{29092821936153414741314306498071305945901668679698216168585976419165}e^{21} + \frac{255085906574169706092685735092069962637510454515806918957440658952526867730063}{610949260659221709567600436459497424863935042273662539540305504802465}e^{19} + \frac{277340427592229604668647743518346369551532804964404591997329181960381051790923}{407299507106147806378400290972998283242623361515775026360203669868310}e^{17} + \frac{1011088841890969345997631896942340276870944074019685269990166641987380976145923}{1221898521318443419135200872918994849727870084547325079080611009604930}e^{15} + \frac{1413656536507883259478432496895768285281999997786535619564651143266081892350}{1939521462410227649420953766538087063060111245313214411239065094611}e^{13} + \frac{181902252595545432059355111421337857766244969385885480184275676401756018627489}{407299507106147806378400290972998283242623361515775026360203669868310}e^{11} + \frac{217982965410880765768662434405232578410243960174095505730221295666932872260063}{1221898521318443419135200872918994849727870084547325079080611009604930}e^{9} + \frac{50749032113672740590838587543293937627318345257342775953367019025228938392019}{1221898521318443419135200872918994849727870084547325079080611009604930}e^{7} + \frac{368438430650961393293879335580638724581254249717972668006230968830044573273}{81459901421229561275680058194599656648524672303155005272040733973662}e^{5} + \frac{25001216743707518439519181964594912153384073541302128119922772630528630329}{174556931616920488447885838988427835675410012078189297011515858514990}e^{3} + \frac{64288388350676053930841042334118775925711438813175023416842998044136229}{203649753553073903189200145486499141621311680757887513180101834934155}e$ |