# Stored data for newform 63.6.e.e, downloaded from the LMFDB on 14 May 2024. {"label": "63.6.e.e", "space_label": "63.6.e", "level": 63, "weight": 6, "hecke_orbit": 5, "hecke_orbit_code": 18014673488052287, "dim": 8, "is_polredabs": true, "trace_hash": 1265780733270996975, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [41616, 37944, 53772, -16260, 9190, -90, 103, -3, 1]]], "qexp_display": "q+(1-\\beta _{1}+\\beta _{2})q^{2}+(-\\beta _{1}+18\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2268, "analytic_conductor": 10.10418064821778, "hecke_ring_index": 147, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [63, 3, [29, 10], [3, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [37, 46], "field_disc": 24043854579101902224, "field_disc_factorization": [[2, 4], [3, 4], [167, 2], [227, 2], [3593, 2]], "field_poly": [86436, 2058, 28567, -91, 9122, 83, 98, -1, 1], "hecke_ring_index_factorization": [[3, 1], [7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.522", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "245.225", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15118.166", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.3.c3", "trace_display": [3, 0, 0, 258], "traces": [0, 8, 3, 0, -69, 0, 0, 258, -246, 0, -283, 402, 0, 924, -1926, 0, -3273, 276, 0, -510, -9438, 0, 2750, 6900, 0, -2814, -15138, 0, -26221, -1080, 0, 6410, 15519, 0, 42288, 33108, 0, -15250, -41250, 0, 8547, -8616, 0, 58396, 70743, 0, -61800, -15060, 0, -64252, 14604, 0, 47476, 13692, 0, 146248, 15921, 0, -52309, 34830, 0, 5364, -32058, 0, -146974, 66864, 0, 5994, -58272, 0, -4307, -178536, 0, -59638, -185442, 0, 42616, 75660, 0, 44062, -33381, 0, -57596, 416892, 0, 72648, -136968, 0, -87597, -77520, 0, 104722, -316512, 0, 73722, -221376, 0, -377260, -382479, 0, 573116, 160428, 0, -147938, 1438848, 0, -463566, -37038, 0, -77542, -9603, 0, 507956, -319608, 0, -326628, -813987, 0, 400374, -333780, 0, 5874, -176574, 0, -591763, 1816200, 0, 146636, 58887, 0, 283496, -633390, 0, 207154, 1148424, 0, -332976, -444816, 0, 1043348, -413187, 0, 630954, -23712, 0, 333466, 1078296, 0, -1310416, 871608, 0, -411380, -669744, 0, -686465, -1402524, 0, -494988, -413511, 0, 1735258, -16128, 0, -638460, -925008, 0, -1078851, 247872, 0, 2050236, 585048, 0, -1258158, -1249704, 0, -516256, -866934, 0, 2002466, 812388, 0, -259308, 1813254, 0, -1262112, -805152, 0, 325236, -507396, 0, -1951216, 638460, 0, -767720, -155253, 0, -2085798, -4811184, 0, -903112, -225792, 0, 4910260, 2234622, 0, -1282096, -4446, 0, 1804876, 742560, 0, 446040, 1035825, 0, -491437, -158676, 0, -70966, 3992592, 0, 368747, -769584, 0, 837240, 588471, 0, 1210172, 1806126, 0, -227738, -3615888, 0, -666114, 1084392, 0, 132012, 2361399, 0, 3437064, -388800, 0, -1142258, -56808, 0, -3146948, -664956, 0, -1438546, 1090797, 0, 289527, -3708, 0, 3364440, -1318197, 0, 2728703, 2256996, 0, -1257514, 5560152, 0, 2311925, 2244384, 0, -5571108, -6269652, 0, 3935314, -1815504, 0, -1614612, -2901984, 0, -2421564, -6133788, 0, 1913022, 1389852, 0, 2780532, -3642576, 0, -2798958, 1420770, 0, -15885520, 2373156, 0, 2413748, 2107203, 0, 301094, 4683528, 0, 484440, -6188196, 0, 1341486, -1412208, 0, 5298654, 6169242, 0, 1913788, 2018940, 0, 922932, -8266500, 0, 655767, 600564, 0, 100288, -13955424, 0, 2165670, -3222948, 0, 6093556, 2223051, 0, -9389016, 11326560, 0, 840658, -482496, 0, -7814928, -154308, 0, 2938090, 6235371, 0, 1944134, -6313440, 0, -1091496, 5805747, 0, 1878432, 5590248, 0, 3482352, 1939188, 0, -6647978, 4115088, 0, 2716752, -4593126, 0, -6566573, -6636060, 0, 2998404, -15380892, 0, 19208992, -3675372, 0, -2149446, 5375850, 0, 4488132, 4916424, 0, 1865150, 9057024, 0, -5455800, 12910722, 0, -9280238, 8010408, 0, 406578, -1868520, 0, -16766164, 7089348, 0, -5823316, -3400644, 0, 2229578, -18996294, 0, 7859285, 9040092, 0, 15307680, 14848215, 0, -3023422, -9178026, 0, 1256018, -23435304, 0, 5104856, -2545848, 0, 3202618, 6731526, 0, -13671212, 11209872, 0, 5529736, 2608872, 0, 3798576, 9763836, 0, -4948188, 3816444, 0, 15015800, -8302488, 0, 66244, 13367286, 0, -1613595, 2967456, 0, -11274380, -13461138, 0, 2501530, -7470972, 0, -2810796, 807135, 0, -2055094, -15021936, 0, -2008060, -10617486, 0, 13488192, -11143314, 0, -10741052, -7038567, 0, -12989403, -4647312, 0, 1934144, -3887664, 0, 11710002, 11373156, 0, 3006648, 19064334, 0, 268464, 13120656, 0, -31032180, 1350897, 0, -4049676, -13074972, 0, 25391236, 6154452, 0, -10742133, 7620792, 0, 14394460, -18012576, 0, -9508908, -14075568, 0, -20235590, 28371162, 0, 11816396, -10858308, 0, 19965030, -13477086, 0, 8527010, -16010220, 0, -14396268, -6522534, 0, -5321842, -13894440, 0, 9903486, 2667009, 0, -19004203, 15631344, 0, -22616968, 23345880, 0, -5383489, 17412864, 0, -7959400, 25596594, 0, 9650974, -19513524, 0, 2842080, -45868920, 0, 20292588, -10624620, 0, 14339070, 62249706, 0, 21254900, -3731580, 0, -7620916, -5640177, 0, 23288556, -34925976, 0, -10438316, -33945570, 0, -28637430, 20365152, 0, 7724398, 28917279, 0, -1772688, 51094536, 0, 11333544, 8855994, 0, -960080, -17043804, 0, 25134174, 39166380, 0, -19848634, 5390040, 0, 15488292, -15394629, 0, 38788282, -6320598, 0, -27432944, 28254432, 0, -22313700, -25723224, 0, 13732450, -20630988, 0, -21919588, 16816320, 0, 5410908, -15512019, 0, -12258514, 8604864, 0, 1214580, -13587798, 0, 19075915, 61111980, 0, -11508308, 4881189, 0, 6837824, 9801744, 0, -9360804, -38494068, 0, 26274528, -32765124, 0, 37077944, -24342090, 0, 11279661, -16806684, 0, 9287638, 18487464, 0, -6079564, -2818500, 0, -40526832, 6940758, 0, -29812389, -63951408, 0, -18750402, -13642647, 0, 2077848, 40174176, 0, -25506024, 8030943, 0, -36986636, 26399232, 0, -29928824, 11876853, 0, -10075437, -32270118, 0, 33608538, -35106846, 0, 17847603, 31508964, 0, -20188316, -9669072, 0, -16268832, 4713036, 0, -14094306, -95925804, 0, -6203264, 21811776, 0, 25115692, -6269952, 0, 4042710, 41460240, 0, 17442474, -13841190, 0, 95544594, -4656828, 0, -18259692, 20633454, 0, 10265354, 5355456, 0, 108053616, 20075763, 0, -62328783, 8133516, 0, -21212104, -3121056, 0, -6108477, 4736586, 0, 28741368, 8831115, 0, -15826782, -11152572, 0, 28512802, -54708276, 0, -119261192, 26221392, 0, -23506368, 20861982, 0, -78408576, -89691288, 0, -41329286, -5925237, 0, 14262104, 65664396, 0, -10988344, -10314906, 0, 51223974, -414984, 0, -27474392, 45210780, 0, 36787546, -35910816, 0, 60954354, 59870910, 0, 70611448, 59665200, 0, 52785748, 57581112, 0, 8463798, -25467000, 0, 22179710, -66778398, 0, 88983552, -11844876, 0, 5942558, 20893272, 0, -38334087, -4161840, 0, -11867460, 5926926, 0, -20920320, 11623224, 0, -37408254, -13554822, 0, -90840364, 5325276, 0, 22782712, -15940362, 0, 14333148, -9296316, 0, -87188440, 130851072, 0, 21785334, -26024388, 0, -93087536, -17973108, 0, 7167615, 23617116, 0, 69932810, -3428274, 0, 122002956, -43763124, 0, -2053224, 22675104, 0, 76152243, -74016432, 0, -6020892, 68657694, 0, -28182878, -12979092, 0, -46854652, -50569470, 0, -16856548, 27987288, 0, -29441616, -47636316, 0, -8587152, -7024608, 0, 30738036, 97581972, 0, -104817210, 54053892, 0, -20895344, -102606747, 0, 80248908, 36586692, 0, -49074546, -77037474, 0, -107645216, 26595000, 0, 40738976, 38387028, 0, 392019, 18927132, 0, 48470026, 5065833, 0, -70321416, -45940728, 0, 50576560, 24968868, 0, 61542996, -79954536, 0, 47095596, -55262916, 0, 94479802, 80511516, 0, 61607618, -23459178, 0, 47612736, -32328768, 0, -108977756, -72687690, 0, -14630907, 62397180, 0, -22751588, -106924596, 0, -21089904, -4486032, 0, -2239516, -17898252, 0, 74270084, 38766048, 0, -113893534, -1893234, 0, -113360832, 26607558, 0, -15424308, 60055863, 0, -71887849, 18427920, 0, 30903916, -120853536, 0, 17361225, -13382256, 0, 29444744, 122352060, 0, 47653447, 19983900, 0, 49587584, -2004468, 0, -10957824, -65876826, 0, 46902948, 2822256, 0, -214250928, -72772644, 0, 75602638, 61950273, 0, 127932676, 50568672, 0, -47941386, -13106967, 0, -39135144, 8945220, 0, 34280746, 9789984, 0, 93628882, -86279736, 0, 162121940, -35978898, 0, 31348537, 74066064, 0, -74103144, -36743760, 0, -15836448, -2120916, 0, -200860600, 77509512, 0, 3647802, 11326740, 0, -59852352, -110072406, 0, -96779972, 12922332, 0, -47108402, 82905990, 0, -141625200, -196984488, 0, 76517488, 95956728, 0, -53377604, -21032556, 0, 38000768, 45627630, 0, 115148181, -15948288, 0, -5919852, 49994046, 0, 9070887, -59578278, 0, 43364330, 94159338, 0, 42398938, -23795544, 0, 172751392, 79766139, 0, -94348247, 70570896, 0, -10438772, 173698032, 0, 491037312, -5072568, 0, -33780254, 25151313, 0, 25256700, 121401888, 0, 67333710, 75301308, 0, -61130154], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "21.6.e.c", "char_is_minimal": true, "conrey_index": 37, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 18, 1, 0, 0, 1, 0], [0, -2, 1, 1, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [53, -2, 45, 0, 1, 1, 6, 1], [-37, 0, 0, 0, -1, -2, 27, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -23, 76, -1, 0, 0, 23, 0], [0, 8, -107, -9, 0, 0, -8, 3], [0, 0, 0, 0, 0, 0, 0, 0], [97, 0, 0, 0, -1, -9, 76, 9], [-299, -114, -113, -1, -9, 0, 83, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-839, 85, -840, -1, -1, -6, 0, 0], [0, 108, -92, 8, 0, 0, -108, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-73, -220, -72, 1, 1, -15, 0, 0], [-1177, 0, 0, 0, 9, -30, -29, 30], [0, 0, 0, 0, 0, 0, 0, 0], [449, 0, 0, 0, -1, 12, -419, -12], [1796, -300, 1804, 8, 8, -20, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 80, 636, -95, 0, 0, -80, 45], [-3762, 116, -3865, -103, -103, -20, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2855, 485, 896, -1, -95, 40, 50, -26], [-250, 0, 0, 0, 103, 5, 254, -5], [0, 0, 0, 0, 0, 0, 0, 0], [0, -130, -1523, 94, 0, 0, 130, -24], [0, 131, -3948, -71, 0, 0, -131, 50], [0, 0, 0, 0, 0, 0, 0, 0], [5160, 0, 0, 0, 96, -24, 312, 24], [3240, 24, -1706, 104, -71, 29, 208, -37], [0, 0, 0, 0, 0, 0, 0, 0], [-3603, -1028, -3508, 95, 95, -9, 0, 0], [0, 316, 10321, 175, 0, 0, -316, -28], [0, 0, 0, 0, 0, 0, 0, 0], [2025, 633, 1932, -93, -93, -42, 0, 0], [-1190, 0, 0, 0, 62, 142, 328, -142], [0, 0, 0, 0, 0, 0, 0, 0], [7049, 0, 0, 0, 93, 33, 816, -33], [17697, -379, 17864, 167, 167, 118, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1752, 16008, 240, 0, 0, 1752, -24], [-3874, 324, -3818, 56, 56, 28, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5892, -152, 5315, 94, 239, -61, 1576, 11], [2454, 0, 0, 0, -55, 100, -2404, -100], [0, 0, 0, 0, 0, 0, 0, 0], [0, 6036, -13450, -144, 0, 0, -6036, 42], [0, -1338, -3095, -13, 0, 0, 1338, -239], [0, 0, 0, 0, 0, 0, 0, 0], [18322, 0, 0, 0, -335, 315, 506, -315], [-9514, 3429, -22170, -159, -4, -8, 129, 26], [0, 0, 0, 0, 0, 0, 0, 0], [-11915, -4171, -12154, -239, -239, 216, 0, 0], [0, 888, -9011, -163, 0, 0, -888, -71], [0, 0, 0, 0, 0, 0, 0, 0], [1514, -796, 1566, 52, 52, 240, 0, 0], [-4447, 0, 0, 0, -58, -140, 1875, 140], [0, 0, 0, 0, 0, 0, 0, 0], [-17549, 0, 0, 0, -51, -150, -3189, 150], [16466, 1660, 16136, -330, -330, -246, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2764, -2286, -193, 0, 0, -2764, -465], [-13184, -5280, -13312, -128, -128, 272, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4783, -809, -7658, -145, -97, -276, 2406, 192], [-21414, 0, 0, 0, 24, -180, -3660, 180], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3056, 14074, -143, 0, 0, -3056, 93], [0, -216, 46915, 1001, 0, 0, 216, 172], [0, 0, 0, 0, 0, 0, 0, 0], [2630, 0, 0, 0, 432, -774, 9924, 774], [1232, -3730, -16115, 183, 1063, -367, 228, 196], [0, 0, 0, 0, 0, 0, 0, 0], [11539, -2286, 11635, 96, 96, -786, 0, 0], [0, 3607, 6920, -1047, 0, 0, -3607, 690], [0, 0, 0, 0, 0, 0, 0, 0], [-13420, -4112, -13322, 98, 98, 408, 0, 0], [51006, 0, 0, 0, -1005, -129, 6432, 129], [0, 0, 0, 0, 0, 0, 0, 0], [9924, 0, 0, 0, -192, -372, -2988, 372], [-30988, -11582, -31705, -717, -717, 252, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -13545, 25668, 765, 0, 0, 13545, 186], [-22548, 9508, -20966, 1582, 1582, -622, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-25799, 9748, -73960, -47, 431, 203, 1948, 230], [-42800, 0, 0, 0, -1424, -1072, 15792, 1072], [0, 0, 0, 0, 0, 0, 0, 0], [0, 990, -18798, -240, 0, 0, -990, 168], [0, -3820, 55528, -1542, 0, 0, 3820, 294], [0, 0, 0, 0, 0, 0, 0, 0], [-46842, 0, 0, 0, -863, 669, 464, -669], [-86434, -2987, -76298, -1607, -1609, 268, 8219, 88], [0, 0, 0, 0, 0, 0, 0, 0], [143318, 516, 142982, -336, -336, 1530, 0, 0]]}