# Stored data for newform 324.3.d.g, downloaded from the LMFDB on 19 April 2024. {"label": "324.3.d.g", "space_label": "324.3.d", "level": 324, "weight": 3, "hecke_orbit": 7, "hecke_orbit_code": 27021803972985156, "dim": 8, "is_polredabs": true, "nf_label": "8.0.1919698923024.1", "trace_hash": 1344201019948120373, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-296, 255, -53, -3, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(\\beta _{1}+\\beta _{2}+\\beta _{5}-\\beta _{6})q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "d", "char_is_real": true, "Nk2": 2916, "analytic_conductor": 8.82836056527362, "hecke_ring_index": 16, "level_radical": 6, "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": "0.504", "prec": 17}, "analytic_rank_proved": true, "char_values": [324, 2, [163, 245], [1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [163], "field_disc": 1919698923024, "field_disc_factorization": [[2, 4], [3, 6], [12829, 2]], "field_poly": [256, -192, 32, 48, -36, 12, 2, -3, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "6.826", "prec": 17}, {"__RealLiteral__": 0, "data": "1.655", "prec": 17}, {"__RealLiteral__": 0, "data": "254.214", "prec": 24}, {"__RealLiteral__": 0, "data": "224.544", "prec": 24}, {"__RealLiteral__": 0, "data": "14163.533", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "2.2.3.c2", "trace_display": [-3, 0, 6, 0], "traces": [0, 8, -3, 0, 5, 6, 0, 0, 27, 0, 10, 0, 0, 46, -12, 0, 17, -6, 0, 0, 36, 0, -33, 0, 0, 30, -36, 0, 6, 42, 0, 0, 87, 0, -11, 0, 0, 28, -99, 0, -68, 84, 0, 0, 111, 0, -132, 0, 0, -58, -219, 0, -110, 36, 0, 0, 270, 0, 16, 0, 0, 34, -258, 0, -127, -30, 0, 0, 375, 0, -150, 0, 0, 58, -372, 0, 15, -330, 0, 0, 360, 0, 127, 0, 0, 140, -273, 0, -75, 192, 0, 0, 258, 0, -36, 0, 0, 148, -585, 0, 87, -330, 0, 0, 150, 0, 196, 0, 0, 196, -294, 0, 78, 330, 0, 0, 378, 0, 153, 0, 0, 80, -414, 0, 348, -822, 0, 0, 375, 0, 98, 0, 0, 132, -123, 0, -119, 780, 0, 0, 384, 0, 192, 0, 0, -226, -471, 0, 28, -174, 0, 0, 297, 0, -420, 0, 0, -158, -606, 0, -104, 726, 0, 0, 447, 0, -114, 0, 0, -810, -264, 0, 447, -966, 0, 0, 663, 0, -482, 0, 0, -536, -402, 0, -582, 468, 0, 0, 354, 0, 384, 0, 0, 4, -147, 0, -235, -132, 0, 0, 33, 0, -230, 0, 0, -322, -132, 0, 166, 882, 0, 0, -276, 0, 327, 0, 0, -78, 168, 0, 984, -792, 0, 0, -78, 0, -128, 0, 0, -914, 582, 0, 334, 606, 0, 0, 69, 0, 1014, 0, 0, 484, 414, 0, -788, -420, 0, 0, -216, 0, 206, 0, 0, 342, 882, 0, 449, 816, 0, 0, -204, 0, -138, 0, 0, -196, 558, 0, 561, -1284, 0, 0, -633, 0, -557, 0, 0, 382, -159, 0, 156, 546, 0, 0, -324, 0, -288, 0, 0, 18, 534, 0, -1157, -606, 0, 0, -852, 0, 1540, 0, 0, 810, 708, 0, -1185, 1986, 0, 0, -474, 0, -342, 0, 0, 460, 738, 0, 1044, -1110, 0, 0, -696, 0, 558, 0, 0, 36, -288, 0, 793, 1074, 0, 0, -1248, 0, -882, 0, 0, 520, 249, 0, 1208, -1074, 0, 0, -891, 0, 1552, 0, 0, -614, 1062, 0, -927, 1416, 0, 0, -1182, 0, 264, 0, 0, 458, 1326, 0, -36, -3132, 0, 0, -222, 0, -1720, 0, 0, 358, 147, 0, -966, -462, 0, 0, -1800, 0, -1440, 0, 0, -414, 1413, 0, -59, -1734, 0, 0, -1221, 0, -1520, 0, 0, -644, 954, 0, -2361, 3948, 0, 0, -1092, 0, 1218, 0, 0, -524, 1158, 0, -1254, -2190, 0, 0, -198, 0, -813, 0, 0, -902, 2226, 0, 652, 1218, 0, 0, -1179, 0, 66, 0, 0, 574, 654, 0, 1384, -1476, 0, 0, -1620, 0, 86, 0, 0, 44, 1356, 0, 2478, 2898, 0, 0, -1314, 0, 447, 0, 0, 1084, -108, 0, -1896, -2238, 0, 0, -810, 0, 1291, 0, 0, -162, 1758, 0, 543, -636, 0, 0, -246, 0, -1872, 0, 0, 140, 2421, 0, -1510, -1854, 0, 0, -1668, 0, -1328, 0, 0, 1952, -1386, 0, 108, 3240, 0, 0, -492, 0, -2907, 0, 0, -154, 996, 0, -1386, -1266, 0, 0, -729, 0, 1945, 0, 0, 1194, -96, 0, -532, 2466, 0, 0, 1212, 0, 120, 0, 0, 1142, 1008, 0, 2418, -306, 0, 0, -189, 0, 2152, 0, 0, 1588, -180, 0, 2017, 2628, 0, 0, -477, 0, 363, 0, 0, 462, -156, 0, 2145, -1680, 0, 0, 192, 0, 2836, 0, 0, -154, 462, 0, -2484, -732, 0, 0, 114, 0, 1284, 0, 0, 1018, -258, 0, 1052, -1014, 0, 0, 885, 0, -2060, 0, 0, -1176, -822, 0, -1460, 2208, 0, 0, -522, 0, -870, 0, 0, -1880, 1308, 0, -126, -3444, 0, 0, 153, 0, -4102, 0, 0, 1444, -585, 0, -2118, 1176, 0, 0, 264, 0, 2424, 0, 0, -788, -783, 0, -2024, 1488, 0, 0, -216, 0, 160, 0, 0, 64, 660, 0, 3784, 4740, 0, 0, 2112, 0, 2643, 0, 0, -2760, -690, 0, 48, -1878, 0, 0, -237, 0, -786, 0, 0, -1214, 1518, 0, 3444, -1152, 0, 0, 420, 0, 2490, 0, 0, -2042, -2037, 0, -2517, 1758, 0, 0, -432, 0, 2610, 0, 0, -3442, -114, 0, 159, 804, 0, 0, -90, 0, -2745, 0, 0, 1670, -1794, 0, -2334, -3336, 0, 0, 3159, 0, -4451, 0, 0, 322, -1836, 0, -122, -2454, 0, 0, 1296, 0, -2310, 0, 0, -1374, 456, 0, -3278, 1956, 0, 0, 2160, 0, 3488, 0, 0, -698, -1974, 0, -114, 1140, 0, 0, 1104, 0, -936, 0, 0, 14, -2208, 0, 1737, -4068, 0, 0, 42, 0, -286, 0, 0, -104, -2295, 0, 3672, -1830, 0, 0, 2982, 0, 1482, 0, 0, -2, -1794, 0, 4573, -1968, 0, 0, 1299, 0, 3760, 0, 0, -624, 114, 0, -3931, 3786, 0, 0, 2004, 0, 3174, 0, 0, 1814, -4836, 0, 522, -1146, 0, 0, 2193, 0, -3005, 0, 0, -1074, -2622, 0, -1868, -942, 0, 0, -516, 0, -1860, 0, 0, -1470, -2691, 0, 1052, 1482, 0, 0, 3186, 0, -3696, 0, 0, 2920, -2706, 0, -1610, 1278, 0, 0, 3609, 0, 2742, 0, 0, -3882, -1530, 0, -2304, -816, 0, 0, 1596, 0, -1629, 0, 0, -2114, -4038, 0, 4995, -3342, 0, 0, -768, 0, 1014, 0, 0, -970, -273, 0, 4020, 1938, 0, 0, -96, 0, -222, 0, 0, 3442, -498, 0, 3720, 3024, 0, 0, 3354, 0, 6381, 0, 0, 2376, -840, 0, -4434, -1332, 0, 0, 3282, 0, 2041, 0, 0, -2656, 1101, 0, 1306, -1644, 0, 0, -1689, 0, -1806, 0, 0, 2334, -4167, 0, -170, 6486, 0, 0, 1836, 0, -2972, 0, 0, 3144, -1122, 0, 2890, 1050, 0, 0, -579, 0, -3303, 0, 0, 352, -3072, 0, -4464, -7266, 0, 0, 2613, 0, 3657, 0, 0, 2720, 243, 0, -2634, -2238, 0, 0, 3246, 0, -1668, 0, 0, 1742, -264, 0, 3505, 3138, 0, 0, 2910, 0, 2858, 0, 0, -378, -1710, 0, 2224, 3684, 0, 0, 168, 0, -3333, 0, 0, -1276, 6, 0, 1290, -4422, 0, 0, -3756, 0, 5388, 0, 0, -206, -969, 0, -3268], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "36.3.f.c", "char_is_minimal": true, "conrey_index": 163, "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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, -1, 0], [1, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, -1], [4, -2, -1, -1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -1, -1, 1, 0, -2], [1, -2, -1, -1, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -1, 0, 0, -1, 2, 0], [-2, 0, -1, 2, 0, 1, -3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 1, 1, 1, 1, 2, 2], [-2, 2, 3, 0, 0, 2, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 2, 2, -1, -1, 0, 1], [5, -1, 0, 3, -1, 0, -3, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 2, 0, 5, -1, 3, -1, -2], [3, -6, -1, -1, -2, -3, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 6, 2, 0, -3, -1, -4, -3], [-2, -5, 1, 1, 1, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -6, 3, 3, 3, 1, 0], [4, 0, 3, 0, -2, 3, -6, -2], [0, 0, 0, 0, 0, 0, 0, 0], [5, -10, 1, -3, 0, -5, 0, 0], [11, -2, 7, -5, -1, 1, -6, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, -5, -3, -3, 4, 2, 0], [3, -6, -4, 5, 1, -3, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 12, 1, 0, 3, -5, -2, 3], [-13, 2, 5, -7, 1, 1, -6, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-7, -4, 0, -8, 4, 3, 2, 2], [10, -4, 3, 0, -3, 5, -6, -3], [0, 0, 0, 0, 0, 0, 0, 0], [6, -12, 0, -5, -2, -6, 0, 2], [15, 1, -5, -2, 6, -2, -3, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-19, 6, 7, -4, 2, 4, 1, 4], [2, -4, -6, 3, -3, -2, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 18, 1, 0, 0, -8, -2, 0], [-23, -6, -11, 1, 1, -5, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-19, 9, 6, -1, -1, 6, -9, -2], [7, -8, -3, 0, -1, 1, 6, -1], [0, 0, 0, 0, 0, 0, 0, 0], [9, -18, -9, -7, 2, -9, 0, -2], [35, -4, -6, 6, 6, 1, 6, -6], [0, 0, 0, 0, 0, 0, 0, 0], [4, -7, -5, -1, -1, 4, 0, 4], [-2, 4, -6, 3, 6, 2, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [6, 12, -7, 0, 12, -13, 14, 12], [-39, 10, 11, 2, -4, 10, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, -10, 1, 1, -11, 7, -6, 2], [-1, -2, -3, 0, 6, -2, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0], [3, -6, -9, 11, -1, -3, 0, 1], [49, 0, -1, 5, 5, -3, 12, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-22, 6, 1, 2, 8, 7, -5, -2], [-1, 2, 5, -22, -5, 1, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [4, 6, -5, 0, -12, -8, 10, -12], [-43, -8, -10, -4, -4, -7, 12, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 10, -1, -1, -13, 5, 6, -2], [-45, 16, 0, 0, 1, -8, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [11, -22, -5, 11, -4, -11, 0, 4], [38, 8, 8, 8, -12, 6, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [19, -11, -2, 0, 0, 7, -4, 6], [-5, 10, 26, -1, 1, 5, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [13, 12, 9, 0, 3, 3, -18, 3], [-41, 12, 14, -1, -3, 10, -3, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-8, -14, -7, 9, -3, 8, 12, -12], [25, 8, -9, 0, 3, -13, 18, 3], [0, 0, 0, 0, 0, 0, 0, 0], [4, -8, 11, 1, 4, -4, 0, -4], [28, 9, 6, -9, -13, -5, -3, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 4, 1, -6, 12, 1, 11, 6], [-14, 28, 22, 4, 2, 14, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 1, 0, -9, 1, -2, -9], [-70, 2, -19, -1, -1, -16, 18, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 34, 7, -1, 11, 1, 14, -2]]}