# Stored data for newform 21.10.a.b, downloaded from the LMFDB on 16 April 2024. {"label": "21.10.a.b", "space_label": "21.10.a", "level": 21, "weight": 10, "hecke_orbit": 2, "hecke_orbit_code": 4503599795142677, "dim": 2, "is_polredabs": true, "nf_label": "2.2.2353.1", "trace_hash": 1527079248668558550, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-568, -9, 1]]], "qexp_display": "q+(5-\\beta )q^{2}-3^{4}q^{3}+(101-9\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2100, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 10.815752559441336, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [21, 1, [8, 10], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 2353, "field_disc_factorization": [[13, 1], [181, 1]], "field_poly": [-588, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.100", "prec": 17}, {"__RealLiteral__": 0, "data": "9.309", "prec": 17}, {"__RealLiteral__": 0, "data": "1.896", "prec": 17}, {"__RealLiteral__": 0, "data": "60.290", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "9.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [7, 1]], "trace_display": [9, -162, 1170, -4802], "traces": [0, 2, 9, -162, 193, 1170, -729, -4802, 6849, 13122, -77090, -145746, -15633, 86528, -21609, -94770, -509183, -229842, 59049, -221224, -628290, 388962, -1302932, -2035782, -554769, 2543050, 516438, -1062882, -463393, 9756252, 6244290, 204000, -9175743, 11805426, 25627554, -2809170, 1266273, -13959816, -656676, -7008768, 34889790, -42362550, 1750329, -4763912, -19888164, 7676370, -15930600, -48278484, 41243823, 11529602, -84911625, 18617202, 9493510, -108980352, -4782969, -39966160, -16444449, 17919144, 72176782, -188376804, 50891490, 19722092, 228951936, -31505922, 130572161, 41724540, 105537492, 70274396, 217776834, 164898342, 185093090, -382044186, 44936289, 191785896, 4142502, -205987050, -18298628, 349936146, -41831478, -72592148, -61430850, 86093442, 114611450, 187994232, 37534833, -2000786580, 1230207804, -790256412, -256454052, 42930954, -505787490, -207753728, -257379192, -16524000, -1045824480, -153134280, 743235183, 1726854096, 51883209, -956239506, -621793825, -123998274, -2075831874, 1587088984, 248666886, 227542770, -3044400138, 69238350, -102568113, -387755460, 5443069320, 1130745096, 1222548383, 125091900, 53190756, -717061800, 1195941150, 567710208, 1742124420, 551850642, -2826072990, 6260944126, -4440417930, 3431366550, 2071991424, 5947402500, -141776649, -1633169364, 1217548737, 385876872, -3300915020, 739717488, 1610941284, 531158824, -12598897500, -621785970, -10785285054, -6863499288, 1290378600, -1601917368, 1508524290, 3910557204, 2554143288, -6375439044, -3340749663, 3728252060, -1690613190, -933897762, -744467178, -11035837440, 6877841625, 2994434992, -884643588, -1507993362, 3128339732, -15843035520, -768974310, 17224096100, 1751264928, 8827408512, 850898750, 4887912582, 387420489, 9309119780, -1340799750, 3237258960, -16236128292, 5823414108, 1332000369, -17451728658, 16057957500, -1451450664, 10805091164, -18631634346, -5846319342, -6105863050, 38963445084, 15258521124, 26676667834, 2709083250, -4122210690, 28222852328, -1239967638, -1597489452, -4432942584, -12853809540, -18545106816, 2085262416, -12116015424, 2551979682, 8618563720, -34523551170, -10576345041, -20369406152, 35917151778, -3379687740, 1112606593, 50205162528, -8548536852, -25537350984, 44841930975, -5692226076, -77767360066, -23424761052, -17639923554, -46149096500, 10457625672, -13356765702, -22394088314, 15934898952, -14992540290, 34224851984, -33502500954, 30945579066, -12971288900, -90402067080, -3639839409, -489804000, 95273544654, -15534657576, 46749518920, -7064405244, -335542662, -69840185608, 22030958943, 16684951050, 39237320386, -21783119508, 1482188868, -9889628600, 76641430320, -28344827826, 22807666974, 48341009304, 3388349718, 29757078000, 5130018756, 5879963988, -61531757154, 37112872554, 4975898850, 88733077936, 122482841517, -6973568802, -38859324218, 6744817170, -9283527450, -9534441280, -84814128000, -15227532792, 26528599500, -142656973956, -3040321473, 152076811236, -125092492704, 162063712980, 42614477825, 67620116250, -99646832124, 33517518216, -27371660940, 64010769372, 116007884428, -42324665814, 20772778212, 115025692860, 1576679076, -3477407274, -109454711324, -127305604782, 40968786690, -181199375176, -18030331710, 16828051968, -175496519622, -132324240150, 20847714552, 9397932320, -339660421596, 1338444000, -83770385790, 170839534896, 84711782880, 20049025064, 1592815176, 12403876680, -65943917624, 101712482550, -60202049823, 393448605554, -368420848380, -139875181776, -4475508534, -72279465714, -4202539929, -291487833000, -72916017642, 77455399986, -39172032138, -88807187196, 50365299825, 11438152712, 239177051640, 10043860194, 55348963324, 328579137900, 168142381794, 312567052160, 47751481764, -128554207704, 53705982720, -202359596004, -20142017766, 513932268436, 284850660582, -18430964370, 11696224064, -80415668160, 246596411178, -726517858396, 361145162430, -5608306350, 38249370600, 33101894088, 8308017153, 99616137400, 237853213236, 31408192260, -259536649350, 115916640084, -440888614920, -155821180832, -135597477636, -91590352776, 642585407896, 945169781400, -99026419023, -198856587700, -67538358225, -10132443900, 32477569020, -140284756800, -4308451236, -27682574402, -485681044644, 58082005800, -423951217066, -228314743326, -96871233150, -504184123252, 203872811625, -45984526848, 717525199964, -358998712290, -141112078020, -522629797560, 242494143930, -44699902002, -550049357500, 20263978566, 228911912190, -620807782854, 468441004158, -507136474206, -22793917510, 290950229700, 359673852330, 683163891600, 537728260104, -277940690550, 556160759700, 261661825152, -167831305344, -649116315668, -1859182297992, -481739602500, 145384569792, 425148040512, 11483908569, -664904738448, 68991553800, 132286718484, 675976409584, 434278534392, -98621447697, 95958750160, -212346704718, -31256026632, 419958195378, -20940157476, 267374116620, 80541858600, 39483122049, -59917116528, -550175704730, -187921478160, -130486244004, 845812929876, -513276508728, -43023864744, -370802704225, -306167702112, 1020510697500, 33453521088, -706850143938, 50364663570, -173296453582, 980464750668, 873608089374, -282457301072, 1715280079500, 555943442328, 182995614152, 452292706404, -104520666600, 1305723789240, -406573923834, 129755306808, 118589600848, 700904779452, -122190467490, 60191875264, 253256658516, -316755133524, 584542492326, -2475854790750, -206885606328, -47352742892, -112864252500, 516410562564, 521569248200, -835788408210, 270600722703, 597438816860, -549713598336, -301988416860, 835747596126, 223232279256, 136939668390, -1232030849904, -2245458004920, 75645718722, 1107106059852, -1602803530638, 60301841418, -1828728889780, -1245110872464, 893902832640, -313503758561, 1807887591252, -557105171625, 2919202497400, 360141029874, -242549234352, -3436576379508, -100180620540, 71656130628, -1064291259628, -2175148871154, 122147462322, 649617412080, 1130862001518, -253395518292, -175564255420, -2565032474466, 1283285877120, -196441176678, 2194616020212, 62286919110, -168728824796, 1637179914240, -1395151784100, -1616278879548, -341244415224, -141852459168, -309042187400, -522882178434, -715020089472, 1565823665424, 1629345782772, -68922798750, -596725618632, -847475974350, -395920919142, 1452958444709, -960031938060, -31381059609, 2342100588920, 1765976058054, -754038702180, -444408509090, 937112733234, 108604779750, -480460825116, -42300340056, -262217975760, -706622096256, 917288090586, 1315126391652, -2413504771456, 571811935500, -471696542748, -1636924414028, 1665401150592, -107892029889, 5332116758020, 1836317145600, 1413590021298, -1217289918720, -3387938958990, -1300694557500, -460477936296, 2835370567233, 117567503784, 2243958093602, 696346288560, -875212384284, 3973912180632, -9946147302, 1509162382026, 1451138980980, 699094588086, 473551866702, -3561989271688, 1085495139180, 494574907050, -3883414807112, 5144261173632, -3156039051804, -1491148978090, 3511070758260, -1235940211044, 43935005828, -1799807127300, -2160810094554, 970304738000, 5083829274852, -219435743250, -1325410653258, -840196686546, 333899065890, -5238155897024, 2259662547456, -2286051038568, -958776865470, -7018128039780, 100437378678, 279528874412, -1963824636726, 129396645612, 5603472300500, -1071015735600, 359068349304, 174293747348, -952220402010, 1041158572740, -3146651166972, -6125555066472, 1502153652096, -70928184704, 147495470850, -168906255696, -2034770575222, 3702215970324, 981397249344, -2634029717020, 3027938439780, -206710354242, -2910813611832, -3313198055304, -698103661320, -2904496001324, -950519845080, 2796407644770, -275182091450, -2034119023650, 856683948321, -3446410196164, -4357492593813, 1649921898312, -3107005520060, -451374151032, -2909289294018, 9346418895996, 1614389446602, 273754706940, 5839058651870, -616119137244, -90121134033, 43108925568, 7960235320440, -4066618164768, 3361803529110, -957552037362, 692431485012, 4803888578580, -970555185882, 2068525429704, -821846761008, 280939028526, -3632196408975, 2503471087020, -2953728937404, 461070312156, 2320281824312, -2938949192790, 6299156165346, 4267350334576, 989361741564, 1897405645212, -1983063219020, -2178206032392, 1428833807874, 701568361820, -120987713988, 3738076816500, 615746178852, -11655418153104, -847067679432, 1303335612992, -403856144640, 1081898021862, 4161802559448, -103077220554, 1813921153434, -1471234246250, 2685731620698, -1290726815112, 3528205326838, 3121761470724, 1214395763490, 441744414268, -1027815408576, -2772213010704, 1683851707998, 7286622061680, 2713702577274, 498816700928, -8486229294936, -2506591904346, -6566925834690, -4914711749736, 1050674400900, -1717883568248, 617967439992, 7322567433480, -2839100166792, 1985115516228, 294826992129, 12303181816992, -3558882734550, 39674124000, 2661989626804, 925994525652, -7717157116974, -7454806170760, 9908792710650, 1258307263656, 2511024576480, -6255436049514, -3786711032520, -2021587022092, -6702253355268, 572216824764, 7049574623484, 367675406280, 27178955622, -10093487675124, 6109379861112, 5657055034248, -6195812309960, 1053834028884, -1784507674383, -811389587680, 8713794290274, -1351481035050, -1585142028873, -1308190311738, -3178222951266, -4146176684496, -16249755059460, 1764432680148, -17314800073728, -6581188009926, -120057298308, 6107607014340, -124571584809, 801059916600, -2380622464420, -4990756712760, -6207955855920, -11677088905952, -4858932476970, 2295931053906, -7166420858596, 22334503880520, -1847421024894, 11785761774900, 8432986692294, -3915621753624, 1492926973825, 1199939406444, -274456327158, 1563408129504, -7277781566628, -2410323318000, 7189527973570, 297719855874, -415531519236, 10203218085468, 15879695523120, -476277083028, -9784287400902, -1519757031744, 4984072329474, -1121820905920, -4798735555500, -3006142676874, -31244453656, -1566221931072, -403047806850, -3810600650584, -2868592793211, -7187379312816, 5796448767790, 10089706553100, -9921110162877, 4665338543464, -597049193286, 564859072962, -8081872786260, 28912261767048, 3147605261658, 11380583352960, 7636757275872, -546330190770, 9851084048904, 1982216695392, 751965723450, -7675058252652, 4285633503060, 772289743680, 7309604731338, 24795619913862, 6869944368000, -7190211446340, 1785691891494, 1233430156152, -16615865986632, -166241278350, -2148816559500, 2241117079856, 14670119867328, 11555214890436, 3756221735188, -14047402122000, 246266039313, 2161147117468, -5741871482772, -12318221710116, -4014783834360, -3866125367142, 10132491909024, 931000859460, 4150468820736, -13127160751380, -5030871082512, -7870233484152, -3451772703825, -470716168820, -13068809437320, -5477229416250, -3051807086974, 12697430441958, 8071393402044, -18416588258400, -4641253777998, -2714918975496, 38628376692342, 4773716343000, 2217104536140, 25490367797628, -25998444651312, -5184872319132, -2935338667583, -4437859750740, -9396638638668, -28741642432816, -2140092241002, 3428297930934, 3359105335040, -300345651900, -1682595035172, 364106515136, -10622631938058, -9317081121660, -6049580233656, -20091275533386, -127711005156, -13228871186160, -4391297784225, 281669989194, -12032125816830, -12571506252108, 8865831617244, 1721665381800, 10029161376000, 10311753987342, 28528880848062, 17559633402900, -3318471721890, -23030118893648, -2871454701150, 14677149389256, 4048917277704, -8271517124520, 1460456868510, 887419711648, -16234114420710, -1363072209408, 12853171311500, -13545591832728, 14215218089382, -967025336748, 4191589259208, 10718263452150, -4182840732420, -33437959819362, -1688664878712, 16903117591000, -11858405303160, -761232517920, 5209729281926, -1324993391442, 27512494149276, -39739905855520, 1959660748944, -108413964000, -5398441711716, 3228795112644, 6785401248990, 19257406900750, -29112202926666, -13838002326576, 4195901637748, -10978870716450, -6861654413280, -15032526846526, 35077972424742, -1623971030184, 33833106539550, 13824273595860, -129018029256, -13201664710532, 10661443449930, -1004714011080, 5218179782700, -5294046115062, 5341457327544, 42211528425184, -368392522680, -8238711086550, 17287706248752, 31681405602306, 4876366035663, 12908114283220, 33765953682834, -31869337049874, -4974851409024, 4147146324504, 29842088718780, 1645517182088, -37709785156770, 11329889723856, 1408448106912, -14279713402500, 362516191254, -5082885843796, -25279562494296, 5854636722834, -5968350198200, 23916811057254, 340405734249, -10530040008704, 9568347845004, 23610514473000, 16681965675852, 14603596708284, 5906197429002, 3921239642964, 5495765584140, -6273887398866, -15117048246224, 5101551137232, 3172934603178, 40941629950000, -2923334517537, 7193382162876, 11755773860658, 6475249253952, -4079589285825, -45354357578556, 4598317085400, -926490369672, -14074525351950, -7390303195860, -19373341182840, 19315280639512, -32149042108020, -813552675714, 7925496963020, 19564557367230, -4483266029244, -4304547383736, -45274249655910, -26614910169900, -20130159041986, -1776061688688, -13619532925314, 13339848553912, -32406156291600, -25317931224960, -32284978593898, -16067238713604, -3867870022884, -23234416140000, -14109104960064, 10412890824024, -46895401931746, -17505045306990, -4350184600320, -1275312336424, 939125930922, 16391127276324, 51265461456732, 132019497033840, 1631503439046, -19875094037268, 30249952897500, -41628513743316, 16401015596160, -1848827223918, -23072903507142, 41364090591600, 40523759766468, 1492908113970, -91205451506992, -16419311488386, -947394149184, 8021630834568, 9698201489700, 6513669120960, 25895469414654, -19727826064380, -19974309305418, -78389544723880, 16170733851840, 58847946530076, -18985087221424, 16479261790488, -29252758156830, -8659986710078, -675116490204, 454272814350, -2658231404734, -3468196206540, -3098199018600, 16625597059004, -13925119196763, -2681253421128, -58962087876900, -12548230693416, -672949389393, 3846203600568, 21018718888776, -8068907129400, 7982162459206, 3291203631888, -19266110272116, -17694420608392, -3621966820290, -2544063573060, 46771349425628, -27846564592968, 21022468597350, 83696945606300, 124648519931388, -9389247846804, -914631772184, -2352824528040, 35711977808520, -62147185069784, -18154996327296, 12621515647392, -6132498034488, 12945739725360, 10983395688516, 19623093086996, -36663969711852, 7418818574856, 20454896767500], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "21.10.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [5, -1], [-81, 0], [101, -9], [550, 70], [-405, 81], [-2401, 0], [3237, 375], [6561, 0], [-38410, -270], [-73148, 550], [-8181, 729], [43318, -108], [-12005, 2401], [-44550, -5670], [-256027, 2871], [-103590, -22662], [32805, -6561], [-110468, -288], [-314890, 1490], [194481, 0], [-689140, 75348], [-1020768, 5754], [-262197, -30375], [1230575, 81900], [280094, -43750], [-531441, 0], [-242501, 21609], [4890142, -24032], [3111210, 21870], [198912, -193824], [-4625627, 75511], [5924988, -44550], [12807306, 12942], [-1320550, -168070], [662661, -59049], [-6951450, -56916], [-382996, 109316], [-3508758, 8748], [17215350, 459090], [-21051550, -259450], [972405, -194481], [-1850020, -1063872], [-10298548, 708932], [3608550, 459270], [-8487192, 1043784], [-24491376, 704268], [20738187, -232551], [5764801, 0], [-42004325, -902975], [8390790, 1835622], [4946654, -399798], [-55575594, 2170836], [-2657205, 531441], [-17593400, -4779360], [-7772037, -900375], [8947908, 23328], [38581526, -4986270], [-93087756, -2201292], [25506090, -120690], [7936198, 3849696], [114963072, -974208], [-15752961, 0], [63557221, 3457719], [19379620, 2965300], [55820340, -6103188], [29648404, 10977588], [109464714, -1152594], [82682208, -466074], [92222410, 648270], [-189205968, -3632250], [21237957, 2460375], [94807674, 2170548], [-1290642, 6723786], [-99676575, -6633900], [-9633172, 967716], [175628348, -1320550], [-22687614, 3543750], [-35412976, -1766196], [-22644490, -16141870], [43046721, 0], [47298850, 20013750], [86737404, 14519424], [19642581, -1750329], [-989742420, -21301740], [616306636, -2405468], [-396101502, 1946592], [-115505076, -25443900], [32720674, -22510394], [-252008010, -1771470], [-104006518, 259308], [-133547736, 9716280], [-16111872, 15699744], [-536566464, 27308448], [-72611480, -7911320], [374675787, -6116391], [875388930, -23923764], [28824005, -5764801], [-479924028, 3608550], [-309126725, -3540375]]}