# Stored data for newform 50.6.a.f, downloaded from the LMFDB on 19 April 2024. {"label": "50.6.a.f", "space_label": "50.6.a", "level": 50, "weight": 6, "hecke_orbit": 6, "hecke_orbit_code": 22517998237515826, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 135703492093216403, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-11, 1]]], "qexp_display": "q+4q^{2}+11q^{3}+2^{4}q^{4}+44q^{6}+142q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1800, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 8.019190990649031, "hecke_ring_index": 1, "level_radical": 10, "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": [50, 1, [27], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "1.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.112", "prec": 17}, {"__RealLiteral__": 0, "data": "1.969", "prec": 17}, {"__RealLiteral__": 0, "data": "0.362", "prec": 17}, {"__RealLiteral__": 0, "data": "4.888", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [5, 1]], "trace_display": [4, 11, 0, 142], "traces": [0, 1, 4, 11, 16, 0, 44, 142, 64, -122, 0, 777, 176, -884, 568, 0, 256, 27, -488, 1145, 0, 1562, 3108, -1854, 704, 0, -3536, -4015, 2272, -4920, 0, 1802, 1024, 8547, 108, 0, -1952, -13178, 4580, -9724, 0, -15123, 6248, -7844, 12432, 0, -7416, 6732, 2816, 3357, 0, 297, -14144, -3414, -16060, 0, 9088, 12595, -19680, 33960, 0, 47402, 7208, -17324, 4096, 0, 34188, 13177, 432, -20394, 0, -7548, -7808, 59821, -52712, 0, 18320, 110334, -38896, 75830, 0, -14519, -60492, -46299, 24992, 0, -31376, -54120, 49728, -30585, 0, -125528, -29664, 19822, 26928, 0, 11264, -104018, 13428, -94794, 0, -23898, 1188, 22636, -56576, 0, -13656, -60633, -64240, -7090, 0, -144958, 36352, 128841, 50380, 0, -78720, 107848, 135840, 3834, 0, 442678, 189608, -166353, 28832, 0, -69296, -141338, 16384, -86284, 0, 80052, 136752, 162590, 52708, 0, 1728, -32253, -81576, 394865, 0, 74052, -30192, -686868, -31232, 0, 239284, 36927, -210848, -491400, 0, 200402, 73280, -3294, 441336, 0, -155584, 22942, 303320, -37554, 0, -263268, -58076, 336241, -241968, 0, -185196, -59748, 99968, 410163, 0, -139690, -125504, 60696, -216480, 0, 198912, 373560, -122340, -7995, 0, -454798, -502112, 521422, -118656, 0, 79288, 20979, 107712, -570130, 0, -428298, 45056, 835531, -416072, 0, 53712, -678318, -379176, -31900, 0, 144947, -95592, -698640, 4752, 0, 90544, 226188, -226304, 889665, 0, -423673, -54624, -83028, -242532, 0, -256960, 255884, -28360, 658031, 0, -23868, -579832, -398204, 145408, 0, 515364, 1257612, 201520, 203780, 0, 1213674, -314880, -823974, 431392, 0, 543360, 834130, 15336, -555960, 0, 523577, 1770712, 815936, 758432, 0, -665412, -1012180, 115328, -509289, 0, 113127, -277184, -1440558, -565352, 0, 65536, -872958, -345136, -1871276, 0, 600240, 320208, 1646466, 547008, 0, 650360, -336435, 210832, 1788720, 0, 1121402, 6912, -1380808, -129012, 0, -326304, 598312, 1579460, -219844, 0, -1530498, 296208, 1797001, -120768, 0, -2747472, -2147466, -124928, -1419128, 0, -1144198, 957136, -754494, 147708, 0, -843392, -3119655, -1965600, 1638936, 0, -1113848, 801608, -262878, 293120, 0, -13176, 1966267, 1765344, 248996, 0, -599298, -622336, 721366, 91768, 0, 1213280, -102348, -150216, -3822840, 0, -666963, -1053072, 30915, -232304, 0, 1344964, -77990, -967872, 955944, 0, 1310477, -740784, 1607716, -238992, 0, 399872, 804397, 1640652, 1417251, 0, 1400154, -558760, -1909900, -502016, 0, 242784, 2883207, -865920, 1273550, 0, 3549260, 795648, -2830614, 1494240, 0, -489360, 42174, -31980, -981090, 0, -1165074, -1819192, 4869458, -2008448, 0, 2085688, 4191052, -474624, 1845006, 0, -484788, 317152, -3234554, 83916, 0, 430848, 4349280, -2280520, 1390355, 0, -1554718, -1713192, -1141974, 180224, 0, 3342124, 956968, -1664288, 3462990, 0, -50058, 214848, 880572, -2713272, 0, -1516704, -5940068, -127600, 1788490, 0, -2274123, 579788, -1592968, -382368, 0, -2794560, -10239306, 19008, -4295515, 0, -354783, 362176, 4822320, 904752, 0, -905216, 4343515, 3558660, 1797045, 0, -257548, -1694692, -821304, -218496, 0, -332112, 6731084, -970128, -7555548, 0, 2229102, -1027840, 4205851, 1023536, 0, -113440, -2122830, 2632124, 352640, 0, -409554, -95472, -1283619, -2319328, 0, -1592816, -5405400, 581632, -2103975, 0, -11750571, 2061456, 2204422, 5030448, 0, 806080, -825233, 815120, -108405, 0, 4501452, 4854696, 1442116, -1259520, 0, -3295896, -393348, 1725568, 1871134, 0, 252362, 2173440, -6094788, 3336520, 0, 61344, 416508, -2223840, -9176970, 0, 11649352, 2094308, -2895948, 7082848, 0, 3263744, -6605978, 3033728, 3698651, 0, 38052, -2661648, -132840, -4048720, 0, 461312, -1071816, -2037156, 6856700, 0, -657228, 452508, -8200164, -1108736, 0, -5762232, 4511793, -2261408, 4065810, 0, 8494582, 262144, -4597175, -3491832, 0, -1380544, 5230764, -7485104, 667656, 0, 5284077, 2400960, -2533829, 1280832, 0, 6585864, 48654, 2188032, -2999027, 0, -4143120, 2601440, 13368732, -1345740, 0, 843328, -87945, 7154880, 2608389, 0, 498752, 4485608, -5002778, 27648, 0, -5523232, -3002693, -516048, -5783044, 0, -5633400, -1305216, 10767860, 2393248, 0, 6317840, 12737292, -879376, 6934096, 0, 230769, -6121992, 5970816, 1184832, 0, 7188004, -2061698, -483072, -9269055, 0, -3895348, -10989888, -4711278, -8589864, 0, -499712, -7294163, -5676512, 9190841, 0, -6574458, -4576792, -2652678, 3828544, 0, -3017976, 8728197, 590832, 2063290, 0, -7461498, -3373568, 13096281, -12478620, 0, -7862400, -350900, 6555744, -13016850, 0, -9939973, -4455392, -1607594, 3206432, 0, -1051512, -15643808, 1172480, -7685040, 0, -5951088, -52704, -9337934, 7865068, 0, 7061376, 5066802, 995984, 13767020, 0, 7443810, -2397192, -4343070, -2489344, 0, 2885464, 9786315, 367072, -355806, 0, 2070602, 4853120, -4660403, -409392, 0, -600864, -2967588, -15291360, 920856, 0, -17911398, -2667852, 17141356, -4212288, 0, 123660, 8487732, -929216, 26386920, 0, 2814724, 5379856, 2454786, -311960, 0, -3871488, -7298162, 3823776, -5915565, 0, 4330952, 5241908, -262548, -2963136, 0, 6430864, 9121680, -955968, -4380244, 0, 36831354, 1599488, 9139846, 3217588, 0, 6562608, -4572288, 5669004, -14770556, 0, 13833732, 5600616, -15322149, -2235040, 0, -7639600, 2241580, -2008064, 3017976, 0, 7025477, 971136, -13460748, 11532828, 0, -3463680, -408321, 5094200, -9063714, 0, 7911252, 14197040, -15088810, 3182592, 0, -11322456, -3393516, 5976960, -15448540, 0, -9251260, -1957440, -3340908, 168696, 0, -127920, -6115560, -3924360, 23054370, 0, 3214312, -4660296, 5759347, -7276768, 0, 19477832, -16290488, -8033792, 12503413, 0, -211788, 8342752, -12827924, 16764208, 0, -1898496, 10238529, 7380024, -12453460, 0, -11133980, -1939152, 26324706, 1268608, 0, -12938216, 5648478, 335664, -8609886, 0, -17499448, 1723392, 1244397, 17397120, 0, -9122080, -3463808, 5561420, -15846138, 0, -12617523, -6218872, -1006780, -6852768, 0, -4567896, -30020640, 720896, 5708045, 0, -9602538, 13368496, -12082704, 3827872, 0, -6657152, -20584036, 13851960, -17315835, 0, -5864796, -200232, 19753800, 859392, 0, 3522288, 13763572, -10853088, 18111126, 0, 18295422, -6066816, -41903368, -23760272, 0, -510400, 8777382, 7153960, 181764, 0, 3731370, -9096492, 46480917, 2319152, 0, -6371872, 19675920, -1529472, -10204590, 0, -1173748, -11178240, 12335422, -40957224, 0, 76032, -8981380, -17182060, 15314416, 0, -19806198, -1419132, 30672196, 1448704, 0, 19289280, -25551963, 3619008, -9194020, 0, 6581432, -3620864, 90639, 17374060, 0, 14234640, -7235030, 7188180, -15690960, 0, 3695251, -1030192, -16835478, -6778768, 0, -3285216, 62860276, -873984, 19767011, 0, 24432012, -1328448, -1601114, 26924336, 0, -3880512, 16461267, -30222192, 19673585, 0, -23622126, 8916408, -36806784, -4111360, 0, 16823404, -15610408, 4094144, 58919910, 0, -11648468, -453760, 12690196, -8491320, 0, 10528496, 26959612, 1410560, -8299434, 0, 34733502, -1638216, -21618749, -381888, 0, -5134476, -4481628, -9277312, -20069996, 0, -11281263, -6371264, 7708140, -21621600, 0, 2326528, 18028296, -8415900, -8865840, 0, -92178, -47002284, -12252328, 8245824, 0, 8817688, 33663892, 20121792, 2915556, 0, -1031748, 3224320, -35974323, -3300932, 0, 3260480, 11367384, -433620, 4101470, 0, 21628937, 18005808, 6672432, 19418784, 0, 5768464, -2761592, -5038080, 7716030, 0, 3843765, -13183584, -6592278, -1573392, 0, 6902272, -43845803, 7484536, 7935026, 0, -10021548, 1009448, 28038042, 8693760, 0, -24379152, -27952968, 13346080, -52881764, 0, -1125828, 245376, 23181111, 1666032, 0, -8895360, -42051240, -36707880, -4579926, 0, -25381947, 46597408, 7397226, 8377232, 0, -11583792, 1584352, 28331392, 340065, 0, 34455177, 13054976, 56070830, -26423912, 0, 12134912, 29359887, 14794604, -23764545, 0, 864980, 152208, -8939574, -10646592, 0, -531360, 10515384, -16194880, 14542776, 0, -17889898, 1845248, 14415247, -4287264, 0, -8148624, -33051668, 27426800, 52909670, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "50.6.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], [1], [4], [11], [16], [0], [44], [142], [64], [-122], [0], [777], [176], [-884], [568], [0], [256], [27], [-488], [1145], [0], [1562], [3108], [-1854], [704], [0], [-3536], [-4015], [2272], [-4920], [0], [1802], [1024], [8547], [108], [0], [-1952], [-13178], [4580], [-9724], [0], [-15123], [6248], [-7844], [12432], [0], [-7416], [6732], [2816], [3357], [0], [297], [-14144], [-3414], [-16060], [0], [9088], [12595], [-19680], [33960], [0], [47402], [7208], [-17324], [4096], [0], [34188], [13177], [432], [-20394], [0], [-7548], [-7808], [59821], [-52712], [0], [18320], [110334], [-38896], [75830], [0], [-14519], [-60492], [-46299], [24992], [0], [-31376], [-54120], [49728], [-30585], [0], [-125528], [-29664], [19822], [26928], [0], [11264], [-104018], [13428], [-94794], [0]]}