# Stored data for newform 392.3.k.j, downloaded from the LMFDB on 24 April 2024.
{"label": "392.3.k.j", "space_label": "392.3.k", "level": 392, "weight": 3, "hecke_orbit": 10, "hecke_orbit_code": 40533083891433864, "dim": 8, "is_polredabs": true, "nf_label": "8.0.796594176.2", "trace_hash": 1118467486805855624, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [4, -8, 14, -4, 1]], [5, [38416, 0, -16464, 0, 6860, 0, -84, 0, 1]]], "qexp_display": "q+(-\\beta _{2}-\\beta _{3}-\\beta _{4})q^{2}+(2+2\\beta _{1}+\\beta _{3}+\\cdots)q^{3}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 56, "char_orbit_label": "k", "char_is_real": false, "Nk2": 3528, "analytic_conductor": 10.681226362923638, "hecke_ring_index": 4, "level_radical": 14, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [392, 6, [295, 197, 297], [3, 3, 4]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [2, 7], "conrey_indexes": [67, 275], "field_disc": 796594176, "field_disc_factorization": [[2, 12], [3, 4], [7, 4]], "field_poly": [4, 24, 22, -104, 83, -40, 18, -4, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "7.346", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "397.370", "prec": 24}, {"__RealLiteral__": 0, "data": "156.490", "prec": 24}, {"__RealLiteral__": 0, "data": "36764.963", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 8, 0, 0], "traces": [0, 8, 0, 8, 12, 0, -8, 0, 0, 12, -28, -16, -24, 0, 0, 0, -8, 72, -16, 8, -112, 0, -48, 0, -40, 68, 28, 128, 0, 0, 0, 0, 0, -16, -32, 0, 72, 0, -76, 0, 56, 80, 0, -160, 48, 0, -224, 0, -32, 0, 224, -176, -56, 0, -16, 0, 0, -272, 168, 184, -56, 0, 224, 0, 288, -168, -32, 224, -216, 0, 0, 0, 160, 232, 280, 88, 48, 0, 0, 0, -336, 52, -48, -176, 0, 0, -8, 0, -240, 312, -616, 0, 112, 0, -112, 0, 176, 272, 0, -480, -204, 0, -104, 0, 112, 0, 672, 96, 192, 0, -448, 0, 0, -608, 144, 336, 0, 0, -88, 0, 0, 132, -84, 176, -336, 0, 0, 0, 0, -144, 112, -136, -96, 0, 128, 0, -160, -184, 504, 304, 0, 0, -448, 0, 24, -336, -64, 0, -448, 0, 156, 0, 760, 176, 0, 896, 56, 0, -448, 0, -224, 0, -480, 272, 120, 0, -52, 0, 0, 1016, 280, -632, -240, 0, 672, 0, 64, -456, -96, -704, -392, 0, 0, 0, 448, -112, 560, 96, 448, 0, -2240, 0, 288, 208, 368, -224, 0, 0, -136, 0, 1120, -320, -56, 0, -1056, 0, 560, 0, 336, -1888, 0, 0, -560, 0, -112, 0, -320, 0, 1008, -528, 560, 0, -784, 0, 0, 2200, -176, -216, -408, 0, 784, 0, 672, 1224, -308, -224, -552, 0, 0, 0, 336, -776, 192, -8, 560, 0, -272, 0, 224, -72, 1344, 528, 0, 0, -896, 0, 992, -216, 128, 0, -1008, 0, 380, 0, 320, 896, 0, 864, -672, 0, -224, 0, -288, 0, 64, 1616, 560, 0, -412, 0, 0, -2288, 448, -1048, -448, 0, -896, 0, 1408, -268, 336, -464, -696, 0, 0, 0, -560, -64, 224, -336, 528, 0, 896, 0, 16, -392, 240, -2160, 0, 0, 112, 0, 0, 984, 1512, 0, -448, 0, 1232, 0, 1120, -64, 0, -928, -156, 0, 488, 0, -960, 0, -672, -1072, -264, 0, -1904, 0, 0, 0, -112, -256, -784, 0, -520, 0, -160, 112, -532, 880, -336, 0, 0, 0, 1056, -1000, -272, 0, 1872, 0, -672, 0, -616, -1460, 1372, 1296, 0, 0, 448, 0, 336, -264, -672, 0, -1792, 0, -368, 0, 224, -672, 0, 1632, -1176, 0, 224, 0, 832, 0, 1184, -304, 408, 0, -56, 0, 0, 976, 1008, 1344, -720, 0, 1568, 0, -272, -800, -96, 448, 168, 0, 0, 0, 1040, 1192, 392, 432, 672, 0, -896, 0, -112, 1128, -352, -5328, 0, 0, -464, 0, 672, -328, -2688, 0, 576, 0, 672, 0, -128, 1840, 0, 0, 672, 0, -296, 0, -1792, 0, 560, -224, -1008, 0, 0, 0, 0, -784, 608, 416, -912, 0, -904, 0, 2880, 496, -588, 1280, -1008, 0, 0, 0, 0, 672, 320, -2232, -784, 0, 0, 0, -440, 416, 672, 8784, 0, 0, -672, 0, 0, 112, 1504, 0, 792, 0, -388, 0, 168, 3040, 0, -1792, -528, 0, -1120, 0, -4032, 0, -32, 224, -1120, 0, 540, 0, 0, -560, -560, 1240, -56, 0, -448, 0, 0, -480, -1056, -1792, 432, 0, 0, 0, -1120, 2088, -504, 2776, -816, 0, 896, 0, -32, 1580, -112, 400, 0, 0, -120, 0, 640, 736, -1400, 0, -1344, 0, -2912, 0, 704, -4704, 0, -4192, 552, 0, -856, 0, 2016, 0, 2016, -448, 456, 0, -1008, 0, 0, -1088, 384, 1240, 672, 0, 472, 0, -1792, 896, -1064, 208, -560, 0, 0, 0, 432, 408, -576, 768, -2016, 0, 1200, 0, -320, 1400, -1092, 1200, 0, 0, 672, 0, -1344, -696, -640, 0, 4704, 0, 392, 0, -1560, 2064, 0, 2368, 1848, 0, -224, 0, 6688, 0, -224, 224, 264, 0, -132, 0, 0, -2112, -784, -888, 1344, 0, 448, 0, 672, -3228, 464, -1184, -1176, 0, 0, 0, 896, 928, -896, 1680, -3584, 0, -1344, 0, -1568, -1344, 128, -6192, 0, 0, 1336, 0, -2400, 208, 4088, 0, 1632, 0, 336, 0, -80, 880, 0, -4192, -224, 0, 152, 0, -1040, 0, -112, -2688, 448, 0, 2464, 0, 0, 400, -464, 192, 1524, 0, -96, 0, 1120, -472, 1568, 2464, 1896, 0, 0, 0, 160, 448, 448, -2824, 2352, 0, 624, 0, 672, 1104, -2716, 6176, 0, 0, 224, 0, -576, 448, -1856, 0, -2736, 0, -448, 0, 960, -4928, 0, 4032, 2112, 0, 0, 0, -4704, 0, -608, 3056, 1512, 0, -516, 0, 0, -648, 1176, -1376, 728, 0, -2240, 0, -1792, 1664, -16, 1104, 336, 0, 0, 0, -1120, -5152, 2912, -680, 576, 0, 3136, 0, 1344, -552, -336, -9184, 0, 0, -232, 0, -2240, -776, -3696, 0, 2688, 0, -784, 0, -1984, 1872, 0, -5088, -624, 0, 344, 0, 7360, 0, 112, -1744, -336, 0, 4256, 0, 0, 1680, -624, 2760, -112, 0, 2240, 0, -2720, 392, 4564, 1120, 3024, 0, 0, 0, -4928, -1704, -336, 544, -1920, 0, 224, 0, -56, -3376, -2996, 6320, 0, 0, -224, 0, -352, -464, 864, 0, 224, 0, 248, 0, -1120, 3040, 0, 7296, -1624, 0, 1344, 0, 2240, 0, -1952, 4704, -2832, 0, 116, 0, 0, 2696, -2576, -3056, 0, 0, 1120, 0, -6720, 2568, 1744, -4928, 1792, 0, 0, 0, 1120, 2024, -336, -1896, 2464, 0, -2240, 0, -704, -1288, 1040, -3376, 0, 0, -336, 0, 1008, 3352, 1232, 0, -3168, 0, -1792, 0, -3360, 4752, 0, 8640, 784, 0, 1536, 0, -3136, 0, -7056, -2672, 112, 0, 1904, 0, 0, 224, -1024, -1344, 3300, 0, -96, 0, -3520, 280, -952, 416, 648, 0, 0, 0, 272, 976, 1104, 560, -3248, 0, -1088, 0, 3920, -1896, -3612, 0, 0, 0, 2240, 0, -672, -2008, -448, 0, 7344, 0, 596, 0, 616, -5968, 0, 5792, 672, 0, 2688, 0, -736, 0, 1024, 3632, 448, 0, 1516, 0, 0, 7504, -1232, -3136, 2520, 0, 672, 0, 2240, 1084, -336, -1184, 2328, 0, 0, 0, -1920, -3600, -6104, 120, -48, 0, 3136, 0, 1680, -632, -1248, -4800, 0, 0, -464, 0, -1360, -2240, 6048, 0, -2352, 0, 3584, 0, 448, -3680, 0, -15232, 216, 0, 80, 0, 5376], "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], [1, 1, 8, 4, -1, 2, 0], [1, 1, 56, 11, -1, 6, 0]], "char_orbit_index": 11, "prim_orbit_index": 11, "minimal_twist": "56.3.g.a", "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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, 0, 0, 0], [2, 2, 0, 1, 0, 0, -1, 0], [3, 3, 0, 0, 0, 1, 0, -1], [0, 0, 2, 2, 2, -2, -1, 0], [-1, 0, -2, -2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, -6, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, -4, 0], [-7, -7, 0, 8, 2, -1, -8, 1], [-4, -4, 0, 6, 0, 0, -6, 0], [0, 6, 2, 2, 2, 2, -4, 0], [0, 0, 2, 1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2], [0, 2, 0, 0, 0, 6, 0, 0], [18, 18, 0, 4, 0, 0, -4, 0], [-4, -4, 0, 0, -3, 4, 0, -4], [0, -2, 0, 0, 0, 0, -19, 0], [-14, 0, 6, 10, 0, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 4, 4, 0, 0, 0, -6], [0, 0, 16, 16, 16, 2, -8, 0], [-10, -10, 0, -8, 4, 2, 8, -2], [17, 17, 0, -28, 0, 0, 28, 0], [0, -7, 2, 2, 2, -1, -8, 0], [16, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 12, 6, 0, 0, 0, 0], [0, 0, 2, 2, 2, 0, -8, 0], [0, 0, 0, -4, -8, -12, 4, 12], [0, 0, 0, -24, -4, 0, 24, 0], [0, 4, 0, 0, 0, 0, -8, 0], [-4, 0, -18, -18, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 8, -8, 0, 0, 0, -3], [0, 0, -20, -20, -20, -8, 10, 0], [-19, -19, 0, 0, -2, 19, 0, -19], [0, 0, 0, 0, 0, 2, 0, -2], [0, -14, 20, 20, 20, -10, -24, 0], [10, 0, 0, 12, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-20, 0, 0, 2, 0, 0, 0, 0], [0, -12, 12, 12, 12, -4, -24, 0], [0, 0, 0, 11, 22, -14, -11, 14], [-56, -56, 0, -8, -2, -8, 8, 8], [0, 0, 8, 8, 8, 8, -4, 0], [-4, 0, 12, 4, 0, 0, 0, 12], [0, 0, 0, 0, 0, 0, 0, 0], [28, 0, -17, -17, 0, 0, 0, 28], [0, 44, 0, 0, 0, 0, -26, 0], [-14, -14, 0, 4, -6, 6, -4, -6], [0, 0, 0, -12, -24, -20, 12, 20], [0, 4, -16, -16, -16, -4, 0, 0], [0, 0, -32, -16, 0, 0, 0, 20], [0, 0, 0, 0, 0, 0, 0, 0], [-34, 0, 0, -36, 0, 0, 0, 0], [0, -42, 0, 0, 0, -6, 0, 0], [46, 46, 0, 11, 0, 0, -11, 0], [-14, -14, 0, 0, 0, 6, 0, -6], [0, 0, 6, 6, 6, 10, -3, 0], [28, 0, -12, 36, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [36, 0, 0, 0, 0, 0, 0, 20], [0, 42, 0, 0, 0, 0, 28, 0], [-8, -8, 0, 0, 4, 8, 0, -8], [56, 56, 0, -16, 0, 0, 16, 0], [0, 54, 8, 8, 8, 18, -16, 0], [0, 0, 36, 18, 0, 0, 0, 20], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -32, -16, 0, 0, 0, -16], [0, -40, -6, -6, -6, 8, -12, 0], [58, 58, 0, 8, 0, 0, -8, 0], [70, 70, 0, 32, 8, 10, -32, -10], [0, -22, 0, 0, 0, 0, 39, 0], [6, 0, 38, -38, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -6, 0, 0, 0, 0], [0, 0, 32, 32, 32, -8, -16, 0], [-84, -84, 0, 40, -4, 4, -40, -4], [13, 13, 0, 60, 0, 0, -60, 0], [0, 12, -10, -10, -10, -12, 0, 0], [-22, 0, 0, 13, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 20, 10, 0, 0, 0, -28], [0, 2, 20, 20, 20, -2, 0, 0], [0, 0, 0, -12, -24, -12, 12, 12], [-60, -60, 0, 16, -8, 12, -16, -12], [0, -78, 0, 0, 0, 0, -24, 0], [-77, 0, -14, 42, 0, 0, 0, 11], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, 48, 80, 0, 0, 0, 6], [0, 0, -40, -40, -40, -32, 20, 0], [-28, -28, 0, -32, -8, -4, 32, 4], [0, 0, 0, 40, 80, -42, -40, 42], [0, -44, -8, -8, -8, -4, 48, 0], [34, 0, 0, -92, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-60, 0, 0, 34, 0, 0, 0, 0], [0, 51, -56, -56, -56, 17, 112, 0]]}