# Stored data for newform 11.8.a.a, downloaded from the LMFDB on 19 April 2024. {"label": "11.8.a.a", "space_label": "11.8.a", "level": 11, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 134217739, "dim": 2, "is_polredabs": true, "nf_label": "2.2.60.1", "trace_hash": 1563723191452801501, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-44, 8, 1]]], "qexp_display": "q+(-4+\\beta )q^{2}+(-3-6\\beta )q^{3}+(-52+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 704, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 3.4362352803253393, "hecke_ring_index": 2, "level_radical": 11, "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": [11, 1, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [11], "conrey_indexes": [1], "field_disc": 60, "field_disc_factorization": [[2, 2], [3, 1], [5, 1]], "field_poly": [-15, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.915", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.365", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "64.582", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[11, -1]], "trace_display": [-8, -6, -470, -1228], "traces": [0, 2, -8, -6, -104, -470, -696, -1228, 480, -36, 4280, 2662, 6072, 344, 14752, -12990, -6368, -8468, 4464, -35280, 5240, -55356, -10648, -61486, 105120, 2200, 60784, -12690, -14864, 179040, 213960, -57166, 186752, -7986, -406048, 485380, -32688, -877698, -216720, -373992, -468000, -283616, 633984, 275484, -138424, 94860, 760744, 1662512, -1317216, -86214, -1136800, 2664924, -515168, 1616484, 1625400, -625570, -1751040, 2252880, -2092320, -2454130, -620520, -6019176, 2653864, 376344, 1068416, 1162360, -926376, -174698, 3959696, -2904342, -5727520, -1151466, -648000, 885944, 3061032, 6761400, 4697280, -1634468, 1185648, 3801460, 5950880, -9331038, 9398864, -2282916, -421968, -6808420, 429264, 7719840, 638880, -13481970, -1437840, 4885904, -921128, -14379702, -8480288, 1134000, -6562176, -68078, -11738664, -47916, 8909600, -4900156, -6291456, 25479424, -9117120, 21259860, 1500624, 26038812, -11937240, -9446140, 5696680, 5331654, 22172992, 1667154, 4762800, 24745210, 1699200, 2231568, -7832840, -30874088, -27093600, 3543122, 20608704, -48735552, -16428968, 13641750, -4334976, 46963072, -49482240, -10013652, -18844240, -27115836, 8081832, -7680960, -46412008, 34474950, 63075840, -6247678, 32207928, -47867860, 5048240, 5993904, 58952664, 457864, 8132544, -69597600, -26971856, 72759762, 49238376, 40384940, -24453600, -32626916, 44493120, -15684696, 19634912, 61938010, 21930144, -22752758, 23661680, -52648812, -23880320, 79966004, 27720792, -94265896, -51367168, -17289690, -11876496, -91566648, -74344320, -93238986, 120453280, -12247200, -26574768, 72986724, -91205280, -93846800, -8475808, 113258550, 78136680, 8184390, 3534480, -159114106, -56017376, 38865528, -90947040, 197263830, 70822968, -11270908, -71808704, 136912140, 37220400, 4205534, 124620672, -29774776, 21264632, 81681720, 101151288, 196125292, 5941584, -163289760, 167472000, 283188894, -208866176, -222775680, -173521968, 231937760, -236922976, 19639548, 114273664, -46957680, -248418240, -102282936, -147789648, -322626402, 31605312, -34114740, -236092320, 233966324, 69253360, 137910648, 6974440, -229335056, 295993944, 111774074, -32639488, -40647600, -28858536, 82355772, -227344320, -47706570, -293742040, -73678836, 246641280, 470603664, -9302112, -427295120, 268809640, -244609500, 351944672, 375736380, 342032160, 153355664, -14172488, 113366304, 340741152, -221410110, 272250768, -191429280, -372649440, 132897708, 25653000, -281610746, 3066912, -81837866, 4744592, -538892340, 82452992, -216334148, -63713232, 502026252, 53115680, -52764480, 62382144, -129094636, 139914720, -220542540, 76860000, -104806890, 385970696, -368235260, -523168200, 54915304, -789529408, 204184848, 503181592, 2928200, -13698696, -1295908468, -219672320, 88336188, 676819200, 485536284, -616989216, 309950264, -374898168, -253940400, 80903504, 851821024, 32649984, 827922886, 816636000, -125749686, 141355552, -428230656, -223751448, 223733350, -144083040, -16890390, 5739520, 256090808, -372328800, -43588776, 278546864, 1385501268, -551819520, 1345146360, 52366464, -325363808, -19783984, 733593408, -886273240, -358888536, -43830720, 127619374, 561582392, -145032840, -508616080, -1420256078, -395238672, 238302240, -677164160, -892679796, -938462336, 1461216960, 562040856, -583925600, 26544544, -160474380, -1291199040, -1170862048, 284780760, 77191514, 286776912, -392796, 700272912, -901161970, 941964864, -158930108, 394338984, 128138058, -391718960, -76087946, -20774880, 73397560, -160501440, 1094331570, 72894384, 2034232, 81175680, -623429700, 1078803200, 813480840, 248566912, 226420374, 483400680, 1357530510, 507392040, -1278067656, -67792200, 1266615640, 179409600, -98325398, -59418776, -10629366, 37723072, -676758440, 2021845248, -1185620158, 1151240224, 302623488, -1736599320, -339263256, 641311224, -13706836, -540449888, -522245250, 669878400, -682056000, -1576912320, 361378130, -393019200, -1296470496, -1251791336, -1066561726, 20759040, 646040780, 946560544, 50164488, -164398504, -902646390, -702592080, -1626925076, 1767669600, 357834708, 5650832, -115992700, -43507728, -1393083028, 918479040, -253774080, -2100572800, 738207044, -928531896, 1246421048, 2082542512, 2000726730, 2616941760, -1168216038, -6917760, 1726638180, -3210224240, -2850402246, -244887808, 59588300, -220634352, 116322060, 550287104, 2610466140, -288454320, -1954983400, 201517680, 361099964, 1752613344, -95813856, -791094720, 4125933200, 1541992968, 3411398064, -2440102704, -497783352, 107207760, 3364633044, 2962936800, 1172167274, -2706194816, -3020680800, 239448880, -450520560, -800298192, 3033390800, -622908000, -433454868, 578488544, -4167056306, -2815810488, 3652438950, -3723416216, -1124830500, -2402961664, 1674380390, 187646400, -377492896, 90827352, -790354452, 1189642752, -1877662640, -1497908160, 1553835912, 4479114600, -5718900780, 271338680, -3804976296, 843832704, 138140534, -3124216320, 3645313170, -3973272096, 1618725342, -113034816, -3755821028, 4134301280, -2755169886, 2023114080, 366669204, -506690160, 3324888000, -222133984, 257699448, -3246772560, -1536358360, 137477760, -383939736, 147610144, 3471691908, -184242344, 435844730, -509219136, 4499502562, -931338240, 2385911928, 3621810840, -1932369776, 1915780224, 4286947200, -392333760, 126258660, 4683187744, 5163437724, 353283408, 2521694200, -1351131000, -1729337976, 758951384, 1948343284, 509103360, -3417799340, 1012550264, 151418718, -3982854784, -9705917370, 4326941760, -2465072176, 5676808192, -4471724880, 830197232, -8687770240, 1350852624, 2212803472, -6050226528, -2408007852, 2379796800, 8146205994, 622555200, -415523216, 1778673072, -3938955600, -4657823456, -8648742356, -1753214496, -2710894796, 949809360, -591202620, 30320640, 4232177248, 5200110360, -3403909620, 6930470880, 185774670, -310688080, -114750834, 1289449800, -10940390656, -857517616, 4652593518, -4457881088, 2849218900, -2466243552, -5109628208, -3500647784, -16502832, -1513080800, 945443520, -3744444960, 853040200, 4783126192, 5093472510, 5778278800, 8615900572, -520476912, 840544848, -8572265920, 3547013844, 3069594864, 7005833464, 4432425792, -835579590, 6116156224, 4941781812, -8319678240, 1992612960, 482252400, 5932033624, -685688608, 7397198598, -9877016416, -4906754600, -786187008, -4518326238, 413551016, -4875444312, -686889600, -320958696, 464529864, 2151540204, 3679982400, -531935280, 5010799344, 12855868072, -4321808424, -6223538160, 307710200, -5329287876, 1959835872, -3861972136, 2163407400, 11824377080, -3438251120, -1102050720, -2846802512, 6792991120, 1239120000, -12011728076, 589579584, -1692844236, 512286032, -832633670, -3092548512, -2765642228, -6277259520, -9686707200, -11788616640, -662112256, 898582752, 6422329504, -3745181968, 12999025920, -2330634240, -8992716828, -11701950432, -2056032710, 1887393080, 7145334270, -3238030656, 10263051180, 614836608, -1773286250, -697080856, 2998583280, -2581427464, 5364993492, 1696700160, 2681607074, -4840042560, -7754040792, 9379193432, -7184384320, 7584409584, -6274092168, -2784877920, 1977211188, 12053952000, -6984787266, -6210534816, 9496203214, 790554352, 277851420, 3430415520, -5561109058, -818151840, -3266447030, 2210062400, 9920078148, 7705978912, -162446666, 3948101520, 5450597460, 16241759744, -859357872, 13986774592, -1576628900, -825912120, -13646559406, 8346170344, 2721115248, 2561307840, 2727748800, -1886160816, -11407953120, 2089415136, 19322597298, 14466048280, -8011523256, -1729821696, 6614831644, -10711913728, -14815575000, 4677362952, -15670777428, -1046157912, 1763170132, -15430521600, -9361462356, 3532292984, -3365075776, 1194963840, 11032021930, -1402144960, -25586610210, 1964766144, 4404713328, -12701318280, -848772506, -6714039888, 500913864, -7171636048, 3026071900, 10780997760, -29096460256, -6621001440, 11133333648, -747294400, 19339734884, -3377490480, 16823777040, 1422061696, -13268839440, 9328885704, -15725581816, -13380923640, 6147019750, -19583379240, 1330804440, -6818575200, 12161562338, 15541597344, 1547101160, -145151160, 9335753100, 11741846480, -11587023390, -2266424640, -26714799296, 13017896792, -5026263792, 13840935112, 13132848000, -1233006456, 16467155082, 6570733440, 20401404714, 9275765360, -6779778456, -19439466336, 2656993464, 9275716072, -15752792070, -1449943936, -232523038, -1971863712, 16239171820, -2677367160, 7522593120, 4418686464, 27034157944, -5420144160, -6144875300, -1294674656, -715201272, 5270355376, -4855464648, -3062709000, 9653252174, -8690363648, 3049781838, 8056087680, 10628109260, 1114678800, 21770244772, -16410780440, -3865679202, -5907787200, -8593573656, -12298614576, 8380371560, 9661065832, 3478457160, -11762321336, -9564478840, 1715280384, -16739752040, -7623329120, 859838604, -5071403168, -5431593756, 366825888, -22859762600, -3123202080, 22746650364, -14113636200, -19641454560, -1240527840, -1532601246, 17852497664, -19193980320, -22152507744, 14758325330, 8468605728, -1577673568, -16519731184, 31432495908, -4108144400, -2843205996, -862488000, -2831722272, 18274507312, 255792420, 6368507520, 4390513922, 3641833440, -329415968, -9197580800, 1114192260, -20766806576, 1179191464, -16359611928, -31163977340, -6345269072, 11806480500, 32637048960, 16166932080, -16943362920, -27251488036, -2222376960, 3662392488, 4074233592, 15142104760, -377664576, -9425576160, 7408220400, -1401001632, 6199022080, 15044450524, 12216200424, -31593485406, 26095843200, 8999423400, -1475965760, -25538379688, 115352784, 2279115050, 1732130160, 6290771484, -10851870208, 44663214396, 8023996320, 28198288680, 6252079680, 32186192670, -528828800, -1753113830, 29282428800, -2690288938, 30541266544, -31527048852, -5429140128, 22338822510, 4007225664, -2175476908, 9639050304, -45065594472, -12211692800, 25053599214, 14764674024, 7535551564, -41130586176, 1482818400, -13843248000, -40106530288, 1578097488, 4376496150, 2007976080, 36262930848, 1193044224, -44525572176, 11941257600, -9855054540, -7987582376, -24835224018, 1996387312, 5059743260, 35523122400, -24433442456, -6924456000, 756948924, 3722085360, -1797994500, -5182108896, 734363352, -3967119200, -18502568352, 7920621280, -30257583286, 1765100592, 11200260824, 14636236352, -7887061650, -4459061896, 23461999532, -45683845920, -13042382048, -36477187800, -12419611578, 20398307512, -23868936000, -10541094240, -2624424450, 32127160320, 10166363256, 4174372360, -32929693920, 1913227200, -36049602216, 12509887984, -2360580552, 3684225120, 23474310910, 14462989968, -6965147208, -16435026864, -8136601992, 21945068960, -16972719576, 18391968000, -3038561196, -41239594368, 34412748120, -31825564920, 12870464904, 18999869760, 71031674540, 34763508000, 31255914624, 6787507584, 27953590248, -561639408, 3262276200, 20844149464, -5318819712, 5246369280, -11594828220, -34963372680, 37553871600, -7744531008, 29118174408, 3927379512, -9062007020, 591200640, -15958856768, 43089801152, 736762038, 2818379840, 21975406884, 17799958344, 44173482688, -24943262240, -52759628100, 571350384, 41290077822, 24600719280, -11983363072, 6204744000, -17928246486, -41220132480, -48441990956, 2317409568, -25687684490, -5587675440, 10275107040, -40342027280, 43047726452, -35700193920, -4377960444, -25820453616, 4418681544, -14062756928, 23546301160, -40818734112, 77051920352, 850349280, -60035351040, -6758267720, 11207643914, -5449016448, -4322922280, -37592032888, 2505616800, 12728448384, 98628352362, 25443631968, -17944502070, -10376037480, 1302907320, 17169202304, -89739224286, -23138199360, -30286403620, -50702765760, -52307372256, 19218729600, -1900356612, -1913765040, 20105820464, 14878534784, -52161192942, -59687898816, 43679493600, -13989674736, 70740198412, -64582608160, -332756910, -8598540000], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "11.8.a.a", "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], [-4, 1], [-3, -6], [-52, -8], [-235, 20], [-348, 21], [-614, 82], [240, -148], [-18, 36], [2140, -315], [1331, 0], [3036, 336], [172, 518], [7376, -942], [-6495, 1350], [-3184, 1856], [-4234, -3666], [2232, -162], [-17640, -2982], [2620, 840], [-27678, 3438], [-5324, 1331], [-30743, 4290], [52560, -996], [1100, -9400], [30392, -1900], [-6345, 13122], [-7432, 648], [89520, -11468], [106980, -11895], [-28583, 20210], [93376, 8336], [-3993, -7986], [-203024, 10430], [242690, -31550], [-16344, -1728], [-438849, -3748], [-108360, -5712], [-186996, -2586], [-234000, 39580], [-141808, 68870], [316992, -41430], [137742, 12760], [-69212, -10648], [47430, -8820], [380372, -47903], [831256, -15252], [-658608, 13536], [-43107, -100696], [-568400, 38700], [1332462, 36402], [-257584, -28312], [808242, 66388], [812700, -58833], [-312785, 26620], [-875520, 110552], [1126440, 114786], [-1046160, 135392], [-1227065, -147078], [-310260, -18240], [-3009588, -28900], [1326932, -109423], [188172, -23580], [534208, -177536], [581180, -118290], [-463188, 27951], [-87349, -392590], [1979848, 224504], [-1452171, 171588], [-2863760, 368890], [-575733, 452890], [-324000, 11304], [442972, -195234], [1530516, -423857], [3380700, 21600], [2348640, 296184], [-817234, 109142], [592824, -176652], [1900730, 323896], [2975440, -499840], [-4665519, -80028], [4699432, -417288], [-1141458, -175068], [-210984, 42648], [-3404210, 776830], [214632, 86702], [3859920, -502716], [319440, -196988], [-6740985, 201740], [-718920, 82710], [2442952, -303948], [-460564, 22864], [-7189851, 110868], [-4240144, 892264], [567000, 347970], [-3281088, -585264], [-34039, 174936], [-5869332, 359677], [-23958, 47916], [4454800, 480000]]}