# Stored data for newform 35.6.a.a, downloaded from the LMFDB on 24 April 2024. {"label": "35.6.a.a", "space_label": "35.6.a", "level": 35, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663331, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2094923750690298601, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [8, 1]]], "qexp_display": "q-8q^{2}+q^{3}+2^{5}q^{4}+5^{2}q^{5}-8q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1260, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 5.613433693454322, "hecke_ring_index": 1, "level_radical": 35, "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": [35, 1, [22, 31], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [5, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.970", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.909", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.760", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [7, -1]], "trace_display": [-8, 1, 25, 49], "traces": [0, 1, -8, 1, 32, 25, -8, 49, 0, -242, -200, -453, 32, -969, -392, 25, -1024, 1637, 1936, -1550, 800, 49, 3624, -1654, 0, 625, 7752, -485, 1568, -4985, -200, 1192, 8192, -453, -13096, 1225, -7744, -11018, 12400, -969, 0, -1728, -392, -10814, -14496, -6050, 13232, 26237, -1024, 2401, -5000, 1637, -31008, 25936, 3880, -11325, 0, -1550, 39880, -4580, 800, -12488, -9536, -11858, -32768, -24225, 3624, -15848, 52384, -1654, -9800, 51792, 0, 4846, 88144, 625, -49600, -22197, 7752, 62765, -25600, 58321, 13824, -23644, 1568, 40925, 86512, -4985, 0, -147300, 48400, -47481, -52928, 1192, -209896, -38750, 8192, -8343, -19208, 109626, 20000, -11878, -13096, -132439, 0, 1225, -207488, 136842, -15520, 109485, 90600, -11018, -50176, -200934, 12400, -41350, -159520, 234498, 36640, 80213, 0, 44158, 99904, -1728, 38144, 15625, 94864, 330692, 0, -10814, 193800, 43982, -14496, -75950, 126784, -12125, 0, -99748, 13232, 258930, 39200, 26237, -414336, 438957, 247808, -124625, -38768, 2401, -352576, -498430, -5000, -245803, 0, -396154, 177576, 29800, -31008, -85478, -502120, 25936, 204800, -81046, -466568, 193026, -55296, -11325, 189152, -157783, 0, 567668, -327400, 375100, -346048, -265659, 39880, 30625, 463872, -4580, 1178400, 183660, -193600, -635048, 379848, -12488, 0, -275450, -9536, -741561, 839584, -23765, 310000, -226613, -32768, 46476, 66744, -24225, 76832, 204972, -877008, -953020, 0, -15848, 95024, -244265, 52384, -43200, 1059512, 400268, 992256, 702150, -9800, -223523, 829952, 51792, -1094736, -270350, 0, 58408, -875880, 4846, -362400, -1586253, 88144, 1014801, 401408, -151250, 1607472, 999797, -49600, -851120, 330800, -22197, 0, 1092696, -1875984, 655925, -146560, 62765, -641704, 765905, -25600, -1210938, -353264, 176176, -399616, 60025, 13824, 1501950, 0, -23644, -125000, 278262, -379456, 749262, -2645536, 40925, 1048576, -352998, 86512, -539882, -775200, 1206370, -351856, -1558094, 0, 648400, 607600, -147300, -507136, -1219630, 97000, 405792, -1676288, -47481, 797984, -283125, -52928, 652442, -2071440, -288464, 0, 118827, -209896, 1488011, 1657344, -38750, -3511656, -84672, -1982464, 1259912, 997000, -8343, 155072, 1895801, -19208, -114500, 0, 219705, 3987440, 1602726, 20000, -529886, 1966424, -11878, 1587200, -312200, 3169232, -821853, -710304, -132439, -238400, -2095998, 0, 394571, 683824, -296450, 2008480, 321422, -207488, 2258205, -819200, 136842, 648368, -2537350, 1866272, -605625, -1544208, 109485, 0, 1285613, 90600, -2232588, -756608, 2666356, 1262264, -396200, -50176, -3656558, -4541344, -200934, 1309600, -539976, -3000800, 117649, 0, -41350, 2125272, -1889618, -159520, -2693290, -245000, 469965, -3710976, -1574679, 36640, 1294800, -4713600, 80213, -1469280, 4055760, 0, -73599, 5080384, 44158, -1519392, 121150, 99904, -4906283, 1693696, 418176, 2203600, 1270864, 38144, -3453364, 5932488, 15625, 0, 4830465, 190120, -4234660, -1240000, 330692, 1812904, -1864604, 0, -554925, -371808, 2616988, -266976, -4815015, 193800, -2707598, 0, 43982, -1639776, 1569125, 3508032, 1213757, 7624160, -75950, -640000, 5904417, 126784, -1155048, -380096, 1458025, 1954120, 4991154, 0, 4842890, 345600, -99748, -4238048, -224420, -3202144, -591100, -7938048, 258930, -5617200, 270360, 39200, 3136477, 1788184, -6349354, 0, 1023125, -414336, -611912, 4378944, 438957, 2162800, -1877033, 496640, 3203566, -467264, -124625, 3503520, 2563700, -38768, -6272090, 0, -581042, 12690024, 724986, -352576, -3682500, -8118408, -498430, -1605632, -875985, 1210000, 782784, -6429888, -245803, -7998376, -1187025, 0, -832668, 6808960, -793945, -1323200, 5921152, 177576, 682776, 5104640, 29800, -8741568, -5416673, 7503936, -776552, -5247400, -85478, 0, 4898742, -502120, -968750, 2566816, -6276512, -6127240, 1985990, 204800, 10676442, 9687504, -81046, 1413056, -208575, -1409408, -1069738, 0, 193026, -480200, 4592457, -55296, -8160445, -12015600, 2740650, -1220608, 2537808, 189152, 1960655, 500000, -157783, -2226096, 3514831, 0, -296950, -5994096, 567668, 10582144, -1452110, -327400, 237454, -8388608, 751750, 2823984, -3310975, -346048, -11885361, 4319056, -265659, 0, -4242398, -9650960, -7560124, 1407424, 30625, 12464752, 1951304, 463872, -3700627, -5187200, 1108360, -2430400, 1674432, 1178400, 3421050, 0, 183660, 9757040, -1087653, -388000, 1240647, -3246336, -635048, 13410304, 2737125, 379848, -1850568, -3191936, 3022096, 2265000, 7726750, 0, 3075485, -5219536, -275450, 8285760, 7775552, 2307712, 10478766, -1254400, -741561, -950616, 8377156, 839584, -5023350, -11904088, 2857729, 0, -6155910, 310000, 7215132, 14046624, -226613, 677376, -1033750, 7929856, 13669927, -10079296, 46476, -3988000, -1158556, 66744, -11749008, 0, 5862450, -15166408, -10068648, 76832, -1847600, 916000, 204972, 11282432, 9806151, -1757640, 2005325, -15949760, -953020, -12821808, 8262575, 0, -3594918, 4239088, 3835216, -7865696, 1103950, 95024, -13296913, -12697600, -244265, 2497600, -25423653, -12676928, 2503266, 6574824, -43200, 0, 1882542, 1059512, 8214870, 953600, 802190, 16767984, -7217700, 992256, 390625, -3156568, 702150, -2735296, -18036466, 2371600, 16115487, 0, -223523, -2571376, 8267300, 829952, -2326569, -18065640, -12533664, 0, -8505438, -1094736, -13219079, -2593472, -270350, 20298800, 1891152, 0, 2074740, 4845000, 58408, 6176832, 4905866, -875880, 1099550, 1769472, -1172732, -10284904, 13636695, -362400, -2223448, 17860704, -1586253, 0, -1898750, -21330848, 8245190, -5049056, 1014801, 3169600, 5657064, 401408, 4884836, 29252464, -303125, 18165376, -19878473, 1607472, -408807, 0, 999797, 4319808, 4278696, 12003200, -2493700, -941192, -851120, 11073536, -25131984, 330800, 9489252, -8501088, 5371674, 15116944, 6473250, 0, -2828736, 21546320, 1092696, 980000, -5863853, -3759720, 17077900, 14843904, 655925, 12597432, -582022, -146560, -2666705, -10358400, -15189130, 0, -1971568, -641704, 10973925, 5877120, 765905, -32446080, -4466290, 6195200, -6489511, 588792, -1210938, -20321536, -3115625, -353264, -7477568, 0, -13995827, -969200, -17702518, -399616, -4397509, 39250264, 60025, -13549568, 7179144, -3345408, 28403555, -8814400, 1501950, -10166912, -19601184, 0, -12460750, 27626912, 5721848, -23729952, 6705258, -125000, -2603443, -26866688, 278262, -38643720, -6145075, -760480, -29886928, 33877280, 749262, 0, 12146982, -2645536, 5364765, -7251616, -9903850, 14916832, 4438020, 1048576, 4538450, 4439400, -352998, 1487232, 19332951, -20935904, 745000, 0, -539882, 38520120, 2678400, -775200, -23461776, 21660784, 2417725, -2458624, -2136950, -351856, 16639237, 6559104, -1558094, -12553000, -9845766, 0, 12100872, -9710056, 648400, -30496640, 18040917, 607600, 42949969, 5120000, 35646600, -47235336, -2195238, -507136, -2026150, 9240384, -1219630, 0, 23389065, -11664200, -22903698, -7816480, 405792, -39929232, 4825650, -1676288, 16761700, -38743120, 11490402, -1382400, -18074463, 797984, 11798936, 0, -283125, 1795360, 2576502, 12808576, -38433960, 4728800, 652442, 31752192, 3930437, -2071440, -3944575, 22468800, -578120, -2162880, -12422190, 0, 4339076, -25091816, 118827, -7152736, 14191700, 50794832, 2163742, -26558464, 1488011, -8185000, 18223772, 1657344, 7920666, 4895296, 9377500, 0, 14898342, -3511656, -13874020, -8651200, -84672, 15016264, 12549996, -3973120, -6641475, -25628528, 1259912, 1869056, -28432545, 997000, 15356712, 0, 2019006, -20509600, 765625, 155072, -28600198, 50176720, 1895801, 11596800, 40960752, 4648336, 13050436, -50760096, -114500, -5799888, 25359472, 0, 16203908, 29460000, -26419413, 32473632, -40667350, 3987440, 4591500, 0, 1602726, 7007880, -5942120, -4840000, 42457232, -6262272, -529886, 0, -15876200, 1966424, 19859482, 31993504, 2874476, 9496200, -19934448, 1587200, 10710732, 6661344, -312200, -27235840, 2155118, 6351560, -11069535, 0, -821853, -47369216, -50186448, -710304, -6886250, -5462208, 32050238, -40837120, -32568200, -238400, -3721550, 34966272, -2095998, 43333384, -18539025, 0, 31568977, 6212416, 394571, 20989600, -36799728, 683824, 2858112, 4689920, -594125, -39189936, 18845252, 2008480, -4695774, 7750000, 321422, 0, -12511964, 50212096, -5665325, 24508960, 2258205, -15887920, -4887652, -819200, -27208287, -85411536, -33115764, -38750016, 1161900, 648368, -34234418, 0, -2537350, 1668600, -26202748, 5637632, 12687570, 8557904, -605625, 12787712, -8011138, -1544208, 66726900, 1920800, -26495370, -36739656, -46012609, 0, 5124300, 65283560, 1285613, 48062400, 17886356, -21925200, -37582848, 9764864, -2232588, -20302464, -23825500, -756608, 22206617, -15685240, 5343730, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "35.6.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], [-8], [1], [32], [25], [-8], [49], [0], [-242], [-200], [-453], [32], [-969], [-392], [25], [-1024], [1637], [1936], [-1550], [800], [49], [3624], [-1654], [0], [625], [7752], [-485], [1568], [-4985], [-200], [1192], [8192], [-453], [-13096], [1225], [-7744], [-11018], [12400], [-969], [0], [-1728], [-392], [-10814], [-14496], [-6050], [13232], [26237], [-1024], [2401], [-5000], [1637], [-31008], [25936], [3880], [-11325], [0], [-1550], [39880], [-4580], [800], [-12488], [-9536], [-11858], [-32768], [-24225], [3624], [-15848], [52384], [-1654], [-9800], [51792], [0], [4846], [88144], [625], [-49600], [-22197], [7752], [62765], [-25600], [58321], [13824], [-23644], [1568], [40925], [86512], [-4985], [0], [-147300], [48400], [-47481], [-52928], [1192], [-209896], [-38750], [8192], [-8343], [-19208], [109626], [20000]]}