# Stored data for newform 21.34.c.a, downloaded from the LMFDB on 24 April 2024.
{"label": "21.34.c.a", "space_label": "21.34.c", "level": 21, "weight": 34, "hecke_orbit": 1, "hecke_orbit_code": 138009378837, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 95618615361096539, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+3^{14}\\zeta_{6}q^{3}+2^{33}q^{4}+(-794875726270+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 21, "char_orbit_label": "c", "char_is_real": true, "Nk2": 24276, "analytic_conductor": 144.8639406501157, "hecke_ring_index": 18, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.763", "prec": 17}, "analytic_rank_proved": true, "char_values": [21, 2, [8, 10], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [20], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [[2, 1], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "1.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.146", "prec": 17}, {"__RealLiteral__": 0, "data": "22.462", "prec": 20}, {"__RealLiteral__": 0, "data": "1.957", "prec": 17}, {"__RealLiteral__": 0, "data": "300.468", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "33.2.1.d2", "trace_display": [0, 0, 0, -1589751452540], "traces": [0, 2, 0, 0, 17179869184, 0, 0, -1589751452540, 0, -11118121133111046, 0, 0, 0, 0, 0, 0, 147573952589676412928, 0, 0, 0, 0, 13110842834938946928762, 0, 0, 0, -232830643653869628906250, 0, 0, -13655860994855592263680, 0, 0, 0, 0, 0, 0, 0, -95503933319356810612703232, 124030829910378084618743060, 0, -707425274537547627758191848, 0, 0, 0, -1199686962559540252871192080, 0, 0, 0, 0, 0, -15459460129734036008401737214, 0, 0, 0, 0, 0, 0, 0, 298025335416653562830805109260, 0, 0, 0, 0, 0, 8837524610439478033809378420, 1267650600228229401496703205376, 0, 0, -3939428047415281684497821887520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76459787822348661165292343420168, 0, 61806308765265224723841283607058, 0, 0, 112621282398117406431424863535104, 0, 0, 0, 0, 0, 0, 834218433212018067697767395941656, 0, -1092097645354187766006964872724260, 0, 0, 0, 0, 0, 0, -2000000000000000000000000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 399339129691796051810556068320508, 0, 0, -117302952743253586030432417218560, 0, 0, 0, 0, 0, 0, 0, 0, 46450308839775616282003535592618262, 0, 0, 0, 0, 0, -205290446010210029419295827915595480, 0, 0, 0, 0, 0, -351440975205885322256170902266111220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -820372540492004450672852207187001344, 0, 0, -20842981440867842342217361403955480, 1065416716321624968865244142653931520, 0, 0, -2786119637459368467983920684222197496, 0, 0, 0, 0, -6076736837005177170527631566507606016, 0, 0, 0, 0, 0, 0, -11251246164929205459930357088167676400, 0, 0, 0, 0, 0, -33499887603121322270820805249185147718, 0, 0, -10305232539261603677754680168268431360, 0, 0, 185071426972281187772750854492187500, 0, 0, 0, 0, 0, 0, 0, -44251977306482256590029682226036892440, 0, 0, 0, 0, 0, -72883969398016121633441434013998652526, 0, 0, 0, -142498819144411196385342150166796292100, 0, 0, -132795751342047203668343685127432306688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 347448321169083438588061839910086626336, 0, 0, 0, 0, 0, 1287836354472163378437774286634218016220, 0, -343948876866280030113532821456819586512, 0, 0, 0, 0, 0, 1294319649821967585012316703796386718750, 0, 0, 2560018137987915172240378251242813521920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18962795260288438193187842554370360252880, 0, 0, 0, 0, 75913758358865396685043325223976304640, 0, 0, 0, 10889035741470030830827987437816582766592, 0, 0, -98589096004882619021614905872022186200, 0, 0, 0, 0, 0, 0, 0, 0, -33839429257187544331091870380262781091840, 0, 0, 0, 0, 562315178879787308999008357120993446960, 0, 0, 0, -77220833329108863166385409836016165756620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80508994221855886358699614108912342410274, 0, -104140199816847022305149303577855340356144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 953602045661164856618288257350671941600, 0, 0, 0, 0, 0, 0, 0, -283621860895436794556636879434994120997108, 0, 0, 0, 0, 0, 0, -656784576312173115228631730537644693651456, 0, 0, 0, 0, 0, 0, 0, 530912149666584561909977889173950049550336, 0, 0, 0, 0, 0, 0, 1190069726200350376924401460814551283681216, 0, -689494895591938103078968654033829960920380, 0, 0, 967409449466989425182619711129069255917568, 1989868907141766550345218838420835322289220, 0, 0, 0, 0, 0, 36867057692211428144331740303439232767340, 0, 0, 0, 0, 0, 0, 0, 3932619947466395914604333356494579977976504, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4827137911821492214143489618164181814845682, 0, 0, 7165881776731955669846049955568991288164352, 0, 0, 0, 0, 0, 0, 0, -9381047341669685583286429273142998251601920, 10253557515781075410558900835418582070753100, 0, 0, 0, 0, 0, -7326314665693656695632259457539413984599568, 0, 0, 0, 0, 0, 0, 0, 6669132485775512347327875649235280517857840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -236893104936172853808119288351869202260200, -17179869184000000000000000000000000000000000, 0, 0, -69488132692282947694021000089666856359872880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -59197667596587763152212373434202598517176380, 0, 0, 0, 14116107872216146996920326994175301231013076, 0, 0, 0, 0, 0, 52183342190141167832180044926363935422888680, 0, 0, 0, 0, 0, 0, 0, 0, 3430297004078733204056519802021847012212736, 0, 0, 0, 0, 85940075187441809311980382917737461386332922, 0, 0, 0, 0, 0, 0, -1007624691513015273270859385383884968427520, 0, 0, 0, 0, 0, 0, 0, 0, 308889143114522004485774915042992755114416660, 0, 0, 0, 0, 0, -92083656107585618328350030677514388154033880, 0, 0, 0, 0, 0, 3131355730277630025261835173075562249150400, 0, 385553497899972458118583400929428324828674376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 399005114711871951818900597453334828604719104, 0, 0, 753870407268411148936021998159448720046431400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1237881893173864687505203822142473418250590272, 0, 0, 0, 0, 0, 0, 0, 0, -1763431503590211516894146904493452869930844160, 0, 0, 405595479115430311714539301328661491016777264, 0, -1656740889949201929222797650103044787871442980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1526302988051779909148113802075386047363281250, 0, 0, 0, 1730009883483877267835495414005768536093457966, 0, 0, -3018854989967248651633349918839519957997322240, 0, 0, 0, 0, 0, 0, 0, 0, -1097012821438624495987564327403373943477956956, 0, 3932433161767959634380937304532584873433536280, 0, 0, 0, -3896955584872285292908806644630787005478735440, 0, 0, 0, 0, 0, 60776029375739493780923895992976294765413360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -49128334567858062451538100491369273048013660, 0, 0, 0, 11763217023902414212711780381864358999292281824, 0, 0, 0, 0, -7046946463899189730252690849819173857576091648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -179039847279324681435815214706802863279964160, 29274079960787976065825891630117156462406870600, 0, 0, 9151859906426177317706483647508389048447139840, 0, 0, 0, 0, 20252722185162220283003343000223929244632805620, 0, 0, 0, 0, 0, 21899519113169113525258174695021403044740772960, -23932585451262728197609124785184562885146181632, 0, 0, 0, 0, 0, 0, 0, 0, -16313528099239326738612039234363688367654903060, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52198771962671437060203985284974833547945705472, 27105054312137610850186320021748542785644531250, 0, 0, 0, 0, 0, -38756654430816910460373993222657533460016821416, 0, 0, 0, 0, 0, -1326199965934448700907249771413300927093006240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 868081909008666891890735021085074280948310200, -96647468635232719211331044262563917404622028800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -123850693337178197996430712108670607113256046812, 0, 0, 0, 160982077820914672703828214331633943390954188700, 0, 0, -287761843350163813346903627243270680195478061056, 0, 0, 122805443136574788603164459751564131278448073168, 0, 0, 0, 0, 0, 0, 0, 39031163995288172760998088883489817180548031160, -88521273467607247568939348067305379280841605120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1589751452540000000000000000000000000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 432722274336299423118519020701490773644763208492, 0, 425044591410420626497306869465312196388889987864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 334455938933674883018160901547556839525123364876, 0, 577676976805593567827093421387976426325067733920, 0, 0, 0, 0, 0, -343585013821340887357640753177080848468071681334, 0, 0, -380121590629350921716915929660201865438539284480, 0, 0, 0, 0, 0, 0, 360666446665387121773159870981139138489801364448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -421636731280875862027068739793509190018933395096, 0, 0, 0, 0, -626068529934288099392778118042932437574475579392, 649088397559594708114169117769433657133823858380, 0, 0, 0, 0, 0, -317424980741796107943634303258819535635345160, 0, 0, 0, 0, 0, 0, 0, 0, -1224055535887729579302555897473422039327126323200, 0, 0, 0, 0, 813074358821005869885222290275616493943900945860, 0, 0, 0, 0, 0, 0, -1140706818123681698887574716220886699357604151296, 0, 0, 0, 0, 0, 0, 0, 0, -2815670635359218909822866290681409560222275106720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2236268394616755102434338447979394821171189594820, 0, 0, 0, 0, 0, -4637470795962661884091417050041435143432992566088, 0, 0, 0, 1317514851127325906739212417222291214384057225880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6071036955116603673209048155644129904521559087980, 0, 0, 0, 3632151260188029144928048843086335633910708875578, 0, 0, 2984558352942635710061900036878819281280184614912, 0, 0, -36922222974482444055994397484890235858115142740, 0, 6846653147719176084284067743423682709161581226972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11062430050115610105518224264247392588397795082240, 0, 0, 0, 0, 0, 0, 0, -2954498355273207389031037270359294400482565423104, -14080876579274645914256072654123420838663121496900, 0, 0, 0, 0, 0, 15701519134104349998849828858216625800547161463280, 0, 0, 0, 0, 0, 163180392368657920969900837566389897424529259600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11118121133111046000000000000000000000000000000000, 0, 0, -7864453608621708505830954705050836687950889302480, 0, 0, 0, -23223145929522397801795729598867595264280769149360, 0, 0, 0, 0, 21990388359649821815989263279515110863345958256640, 0, 0, 0, 0, 0, 0, 16253654027389093442631230359148386996342158359912, 0, -32474070995483879201981766284570488055298031056276, 0, 0, 0, -14439088980478477270661743823438882827758789062500, 0, 0, 0, 0, 0, 558703800815630316613413681856032689612191498800, 0, 0, 0, 0, 0, 0, 0, -44264069390790063342438351506248871428434880539552, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21884824398915738300326312097356517727522622398656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -74466322428018823245631549421352202915426137944218, 0, 0, 0, 0, 0, -71381144678019516110135077076596780019143494501080, 0, 0, 0, 0, 0, 69807776580380262636756953477595023840692950577860, 0, 82355141003796321777416375465691089630126953125000, 0, 0, 0, 0, 0, -2219950408552265236678330760022493410629141565684, 0, 0, 0, 0, 0, 0, 162889170967365299133318227511635598315715779624960, 0, 0, -42674296744646480469834460821319451191232740237144, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 21, 3, 1, 2, 0], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "21.34.c.a", "char_is_minimal": true, "conrey_index": 20, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 4782969], [8589934592, 0], [0, 0], [0, 0], [-794875726270, -5640229503943], [0, 0], [-5559060566555523, 0], [0, 0], [0, 0], [0, 41085390865563648], [0, 304331380942850972], [0, 0], [0, 0], [73786976294838206464, 0], [0, 0], [0, 0], [0, -128209247178222747890], [0, 0], [6555421417469473464381, -3801865957601895630], [0, 0], [0, 0], [0, 0], [-116415321826934814453125, 0], [0, 0], [0, -26588814358957503287787], [-6827930497427796131840, -48449202522738976096256], [0, 0], [0, 0], [0, 469815818712928115170390], [0, 0], [0, 0], [0, 0], [0, 0], [-47751966659678405306351616, 0], [62015414955189042309371530, 0], [0, 0], [-353712637268773813879095924, 0], [0, 0], [0, 0], [0, 0], [-599843481279770126435596040, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 352920820221946001532911616], [-7729730064867018004200868607, 8966563046552347907365220], [0, 0], [0, 0], [0, 2614186656592125139483623424], [0, 0], [0, 0], [0, 0], [0, 0], [149012667708326781415402554630, 0], [0, 0], [0, 0], [0, 0], [0, 19037014717826077851908034660], [0, 0], [4418762305219739016904689210, 31354377421692550026456927189], [633825300114114700748351602688, 0], [0, 0], [0, 0], [-1969714023707640842248910943760, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 147965361767551410234239840568], [0, 0], [0, -556810875423252582550048828125], [0, -1101309047350493971181606010880], [0, 0], [0, 0], [-38229893911174330582646171710084, 0], [0, 0], [30903154382632612361920641803529, 0], [0, 0], [0, 0], [56310641199058703215712431767552, -32657779903351728636910632960], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [417109216606009033848883697970828, -241905627453700703732875434440], [0, 0], [-546048822677093883003482436362130, 0], [0, 0], [0, 0], [0, 0], [0, 44800676428536808019786697263816], [0, 0], [0, 0], [-1000000000000000000000000000000000, 0]]}