# Stored data for newform 147.4.e.n, downloaded from the LMFDB on 16 April 2024.
{"label": "147.4.e.n", "space_label": "147.4.e", "level": 147, "weight": 4, "hecke_orbit": 14, "hecke_orbit_code": 58547070100832403, "dim": 6, "is_polredabs": true, "nf_label": "6.0.9924270768.1", "trace_hash": 489644630105196366, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [36, 144, 582, -12, 25, 1, 1]], [5, [1527696, -237312, 50460, -360, 313, -11, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-3+3\\beta _{4})q^{3}+(-8+\\beta _{1}+\\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": 2352, "analytic_conductor": 8.67328077084387, "hecke_ring_index": 3, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [147, 3, [50, 52], [3, 2]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [67, 79], "field_disc": -9924270768, "field_disc_factorization": [[-1, 1], [2, 4], [3, 3], [4793, 2]], "field_poly": [36, -144, 582, 12, 25, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.722", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "135.758", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5702.416", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c3", "trace_display": [-1, -9, 11, 0], "traces": [0, 6, -1, -9, -25, 11, 6, 0, 78, -27, -55, -35, -75, -124, 0, -66, -241, 48, -9, -202, -878, 0, -14, -216, -117, -130, 274, 162, 0, 106, -165, -95, -683, -105, 48, 0, 450, -262, -398, 186, 21, -488, 0, 720, 905, 99, 1056, -210, 1446, 0, -2756, 144, 324, -393, -27, 2062, 0, 1212, 1249, 1143, 1317, -70, -2118, 0, -798, 472, 21, 628, 1944, 1296, 0, 636, -351, 988, -1002, -390, 4680, 0, -1644, -861, 175, -243, 124, -1038, 0, 3600, 3208, -159, 891, 1766, 990, 0, -1344, -285, -3294, 736, -2049, -38, 0, 630, -348, 2362, -72, -2646, -5280, 0, -6234, -2609, -675, -1888, 331, 1572, 0, 4168, -1194, 576, -1405, 558, -8058, 0, -126, 32, -5090, 732, -713, -2418, 0, 3278, -3099, -1080, -2096, -2521, -5430, 0, 296, 297, 1848, -3042, 3168, 472, 0, 1260, -5826, 1808, -2169, 3691, 8712, 0, 6608, -5202, 4134, 873, -5928, -864, 0, -4902, 972, -4528, 1945, -1179, -10538, 0, 162, 2344, -3448, -3093, 2925, 44, 0, -7194, 2904, -1818, 826, -2078, -7494, 0, 2558, 3429, 8642, 8696, 3951, 6956, 0, 420, 8688, 252, 3177, -4152, 30684, 0, 784, 2020, 1197, -5091, -3063, -2832, 0, -2804, 63, -812, 10416, 1884, 1732, 0, -11664, 4672, -2914, -1944, 9348, 2096, 0, -7988, 3639, -954, -1979, 4150, 2106, 0, 34416, 2964, 1793, 792, -3006, -3130, 0, 2340, -2180, 9021, -7020, 7038, 30048, 0, -16962, -4164, 2466, 7914, 999, 5166, 0, -21720, 525, -8565, -8, -729, -6540, 0, -744, 5502, 7569, 1557, -11829, -19726, 0, 15360, 3387, -5400, 375, 7858, -19248, 0, 9896, -477, 13685, 11758, 2673, -2046, 0, -10596, -13566, -6747, -1485, -5125, -9360, 0, 4236, -880, 2016, -9890, -15828, 1710, 0, -9316, -9882, -304, -11922, 2208, 5984, 0, 12294, 7635, -17135, 57, -4550, -3194, 0, -23262, -11844, -945, -1302, 168, 2088, 0, 14314, 7086, -22836, -13730, -216, -20428, 0, 15876, -14751, 4740, 7920, 3639, -15680, 0, 48622, -9741, 9351, 4805, -3673, 15654, 0, -9072, -2025, -5106, -28024, -5664, 3936, 0, -1986, -5730, -4125, -2358, 17894, -31564, 0, 18118, -5289, -6252, -12216, 837, 7164, 0, -51540, 1728, 20686, 6908, -4215, 25316, 0, -3348, 5531, 4196, 12087, -1002, -59564, 0, -10048, 11426, 189, 4335, 15238, -192, 0, 420, -15270, -11381, 5424, 2196, -10104, 0, 4278, -12030, -1176, 3627, -42114, 14936, 0, -23668, 26900, -4917, 31492, -4254, 18594, 0, 322, -3240, 17023, -7902, -6288, 3840, 0, 15126, 16054, 24757, 8145, 14602, 24552, 0, -31752, 1176, -444, -4502, 45158, -1782, 0, 3048, 5544, -423, -1520, -9126, 82784, 0, -19008, 12051, 16556, -708, 5096, -33048, 0, 32280, 45326, -1890, 27789, 4824, 34956, 0, 46034, 5424, -42710, 120, -6507, 55112, 0, -22146, -10390, -5304, -13068, -35477, -4758, 0, 23328, -13059, -9912, -5434, 24007, 31212, 0, -8352, 12402, 19376, -9880, 2619, -41070, 0, 35568, 6079, 2, 1296, 39984, 12580, 0, 9676, 17579, 7353, -14388, 3960, -5832, 0, -42492, -13584, 35517, -9022, 5835, -1020, 0, 7074, 14292, -3506, 15807, 9782, 4670, 0, -113172, -23073, -243, 15841, -37590, -14064, 0, 20918, -10344, 9768, 25370, -9279, -24158, 0, -17550, 1564, -18159, -66, -23491, 6000, 0, 74884, -15504, 10791, -12109, -9251, -17424, 0, -17818, -5454, -11234, 24980, 2478, -63756, 0, 12468, -20772, 2502, 11241, -6070, -29126, 0, 7756, 5568, -3837, -11499, -39267, -20574, 0, 21560, 25926, 8623, -13494, 26088, -27294, 0, -23706, -25548, -18911, -10434, 27192, 63156, 0, -23984, -63258, -630, -17488, 3068, -52128, 0, -114244, 756, -70814, -47387, 9531, 17404, 0, 24912, -13858, 23063, -46026, -2816, -36224, 0, 118332, 6592, -1176, 1080, -26396, -12120, 0, 81456, 3591, 24101, 7217, -15273, -56758, 0, 18378, -18831, -37422, 4248, 37783, 15326, 0, -452, -31347, 4206, -38632, -37812, -378, 0, 97044, -2436, -5040, 14706, 31248, 3166, 0, -11304, 47449, -56474, -2598, 9399, 118328, 0, -126740, 10092, 17496, -14612, 18418, -28032, 0, -3156, -8742, -17932, 28935, -5832, -37176, 0, -56088, 15587, 26861, -3144, -95700, -10032, 0, -7998, -10473, 11982, -3975, 12327, -21834, 0, 28226, -2862, 54333, 31422, -5937, 7152, 0, -24900, 14256, -710, -3159, 46209, 14876, 0, 22464, -17667, -51624, 2723, 14888, -17784, 0, 50640, 5379, 31748, 67978, 2376, -40626, 0, 18036, -25296, 83374, 4695, -2998, 45020, 0, -58922, -1009, -3510, 33093, -38997, 13080, 0, -14832, 27063, -12945, 35475, -21060, -93708, 0, -42228, 34810, -4452, -45072, -18474, 128300, 0, -3832, 38214, 25443, 18192, 16426, 24984, 0, -71238, 7398, -24250, 32809, 23742, 214424, 0, -5994, -6490, 53538, -7749, 102450, 57936, 0, -55288, 40276, 32580, -34186, 43098, -3150, 0, 97350, -25695, -54168, -41260, -24, -6306, 0, 4374, 61554, 3768, 9810, -11744, -84450, 0, 3360, 63010, 1116, -4108, 28896, -33012, 0, 92460, 22707, 25110, -5426, 4671, -6768, 0, 70974, 32365, -88494, 29589, -4276, 116542, 0, 27156, -52962, -23040, 25236, -31548, -20322, 0, -131488, -16200, 78894, -54036, 1125, 21738, 0, -47148, -67205, -79430, 28872, -36758, 14886, 0, 194244, 11204, -14844, 12666, -55872, 2862, 0, -186536, 41055, -20734, 4370, 35274, 119410, 0, -16038, 35700, 76470, 3069, 4180, -104134, 0, -89664, 4076, 15894, 22896, 40506, 81396, 0, 7428, -20241, 42954, 24108, -4455, -21348, 0, 30750, 12708, -35440, 14040, -446, -161158, 0, 37328, -2725, -6354, -31336, -69996, 5280, 0, 63774, 6048, -31194, -31959, -29670, -57496, 0, 94968, -47674, 60988, -2565, 3588, -13840, 0, -58828, -83852, 13974, 10722, -29283, 59292, 0, -67614, -912, -69264, 3912, -35766, -78744, 0, -13248, -44067, -52402, -8976, 51834, -175588, 0, -31200, 22326, -18441, 97210, 6172, -45810, 0, -91654, -51405, -29634, -151830, 171, -141984, 0, 27300, -25460, 74865, 4791, -60295, -25236, 0, 67836, -39120, 34893, -63345, 105940, 71064, 0, 98396, -2835, 47853, -47076, -3906, -9112, 0, -1008, -122472, -34005, -3132, -8376, -8800, 0, 62976, 70732, -21471, -83982, 106041, -42516, 0, 81612, -68508, 36909, -38779, -41190, 35336, 0, 1296, -46086, -79056, 30642, -144086, -63240, 0, -29932, -60994, -23814, 137, -54242, 88506, 0, 101088, 14220, -23040, -22344, 23760, 134062, 0, -21834, 26370, -21149, 23520, 38640, -297918, 0, 85844, 79796, -72933, -5090, 91658, 58446, 0, -59692, 28053, 5320, 35160, 14415, 130396, 0, 22038, 60346, 39594, -23481, -62689, -93038, 0, -50726, 56586, 13608, 54045, 41541, 12150, 0, -152710, -15318, -92970, 30426, -84072, 16972, 0, 33984, 14735, 83388, -5904, 33346, 122448, 0, -126736, -107784, 2979, 38091, -1131, 34380, 0, 63960, -12375, 7604, -13756, -7074, 220746], "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": "21.4.e.b", "char_is_minimal": false, "conrey_index": 67, "id": 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], [1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [-3, 0, 0, 0, 3, 0], [-8, 1, 1, 0, 8, 1], [0, -1, 0, -1, 4, 1], [0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0], [10, 0, -9, -1, 0, 0], [0, 0, 0, 0, -9, 0], [-22, -11, -11, 0, 22, 1], [-12, -1, -1, 0, 12, -3], [0, -3, 0, 3, -24, -3], [-19, 0, 5, -1, 0, 0], [0, 0, 0, 0, 0, 0], [-12, 0, -3, 3, 0, 0], [0, -19, 0, 1, -74, -1], [16, 0, 0, 0, -16, -4], [0, 9, 9, 0, 0, 0], [0, -7, 0, 1, -65, -1], [-150, 0, -11, 3, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 13, 1, 0, 0], [0, 24, 0, -4, -80, 4], [-30, 27, 27, 0, 30, 3], [-53, -29, -29, 0, 53, 1], [0, 16, 0, -5, 86, 5], [27, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [26, 0, 25, -5, 0, 0], [0, 33, 0, 3, -66, -3], [-39, -22, -22, 0, 39, 2], [-218, 29, 29, 0, 218, 11], [0, 3, 0, -9, -36, 9], [24, 0, 48, 0, 0, 0], [0, 0, 0, 0, 0, 0], [72, 0, -9, -9, 0, 0], [0, -19, 0, 1, -81, -1], [-106, 80, 80, 0, 106, 7], [57, -15, -15, 0, -57, 3], [0, 75, 0, 3, -18, -3], [-82, 0, -2, -14, 0, 0], [0, 0, 0, 0, 0, 0], [143, 0, 69, 3, 0, 0], [0, 11, 0, 11, 298, -11], [36, 9, 9, 0, -36, -9], [360, 24, 24, 0, -360, -24], [0, -72, 0, 28, -46, -28], [222, 0, -57, -3, 0, 0], [0, 0, 0, 0, 0, 0], [-470, 0, -32, 29, 0, 0], [0, 0, 0, -12, 48, 12], [74, -102, -102, 0, -74, -24], [-154, -69, -69, 0, 154, -11], [0, -27, 0, 0, 0, 0], [350, 0, 19, 25, 0, 0], [0, 0, 0, 0, 0, 0], [195, 0, -21, -3, 0, 0], [0, -41, 0, -25, 430, 25], [358, -69, -69, 0, -358, 29], [450, 33, 33, 0, -450, -9], [0, -100, 0, -20, 10, 20], [-364, 0, -33, 22, 0, 0], [0, 0, 0, 0, 0, 0], [-194, 0, -183, -21, 0, 0], [0, -50, 0, 18, 174, -18], [-6, -39, -39, 0, 6, -3], [215, 17, 17, 0, -215, 47], [0, 24, 0, -16, 640, 16], [240, 0, 72, 12, 0, 0], [0, 0, 0, 0, 0, 0], [66, 0, -120, -12, 0, 0], [0, -81, 0, 9, -90, -9], [363, 101, 101, 0, -363, 23], [-298, 108, 108, 0, 298, 19], [0, 87, 0, 3, -159, -3], [718, 0, -186, -72, 0, 0], [0, 0, 0, 0, 0, 0], [-258, 0, 48, 15, 0, 0], [0, 36, 0, 48, -299, -48], [18, -121, -121, 0, -18, -51], [-81, 0, 0, 0, 81, 0], [0, -32, 0, 2, 52, -2], [-156, 0, 51, -27, 0, 0], [0, 0, 0, 0, 0, 0], [624, 0, 72, 0, 0, 0], [0, -50, 0, -69, 1086, 69], [-78, -75, -75, 0, 78, 15], [258, -117, -117, 0, -258, -3], [0, 170, 0, -22, 532, 22], [198, 0, 99, -9, 0, 0], [0, 0, 0, 0, 0, 0], [-112, 0, 336, -56, 0, 0], [0, 66, 0, 6, -117, -6], [-984, 342, 342, 0, 984, 72], [246, 2, 2, 0, -246, -54], [0, -87, 0, 33, -654, -33], [-24, 0, -53, 49, 0, 0], [0, 0, 0, 0, 0, 0], [108, 0, 9, 27, 0, 0], [0, 438, 0, 24, -262, -24]]}