# Stored data for newform 58.3.c.a, downloaded from the LMFDB on 23 October 2026.
{"Nk2": 522, "analytic_conductor": 1.580385533289722, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 29, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 4, "char_parity": -1, "char_values": [58, 4, [31], [3]], "cm_discs": [], "conrey_index": 17, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [1, 4, 8, -4, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 137489285178, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 29, 3, -1, 4, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "58.3.c.a", "level": 58, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [2, 29], "level_radical": 58, "minimal_twist": "58.3.c.a", "nf_label": "4.0.2304.2", "prim_orbit_index": 3, "qexp_display": "q+(1-\\beta _{2})q^{2}+(1-\\beta _{2}+\\beta _{3})q^{3}-2\\beta _{2}q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "58.3.c", "trace_display": [4, 4, 0, 8], "trace_hash": 1078987121201310131, "trace_moments": [0, {"__RealLiteral__": 0, "data": "3.884", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "55.866", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "1177.516", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.252", "prec": 10}, "traces": [0, 4, 4, 4, 0, 0, 0, 8, -8, 0, -4, -12, -8, 0, 8, 20, -16, -32, 16, 0, -8, -28, 0, 16, -16, 0, 12, 28, 0, -116, 40, 76, -16, 0, 0, 0, 32, -32, 0, 60, -8, -116, 0, 156, 24, 112, 16, -28, -16, 36, 0, 0, 24, -140, 56, 180, -16, 0, -116, -64, 40, -16, 0, 0, 0, -180, -60, 0, 64, -176, -152, 0, 32, 48, -64, 48, 0, -276, 120, -132, 0, 20, -232, 112, 56, 224, 0, -116, 48, 204, 112, 0, 0, 0, -56, -48, 0, 276, 36, -216, 0, 480, -32, 488, 24, -68, -140, 8, 56, 0, 360, -64, -32, 156, 24, 0, 0, 144, -64, -352, 0, 0, 0, -472, -152, 0, 176, -456, 32, 0, -180, -136, -120, 72, 224, -188, 128, -512, 0, -176, -304, 268, -40, 300, 0, 0, 96, -108, -64, 0, 0, 0, 0, -320, 0, 188, 120, -36, 0, 100, 16, 1184, 20, -380, -232, 132, 112, 0, 112, 256, 448, 48, -312, 0, 0, -288, 48, -160, 0, 0, 0, -124, -264, 0, -32, -32, -284, 0, -56, -268, -96, 200, 32, -220, 552, -204, 0, 320, -432, 488, 0, 128, 0, -232, -64, 364, 488, 0, 0, 0, -136, -500, 0, 20, 8, 252, 0, -244, 100, 816, 360, 288, -64, 40, -32, 0, 312, 568, 48, 324, -784, 0, 232, -60, 144, -676, 0, 0, 0, -592, -80, 0, -176, 176, 32, 0, -472, -96, -304, -272, 92, 84, 352, -1392, 0, -32, 64, 140, -516, -64, 0, 0, -272, -140, -120, 0, 0, 0, 448, -784, 0, 308, 128, -276, 0, 336, 352, 544, -176, 40, -304, -732, 268, 0, -80, -72, 600, 488, -64, 0, 116, 120, 96, -236, 0, 0, 0, 588, -44, 0, -96, -300, -504, 0, 0, -464, -640, -148, 552, 812, 376, 344, 0, -332, -72, 944, 264, 32, 0, 348, 32, 212, 1184, 0, 0, 0, -760, 220, 0, -1028, 132, 732, 0, 128, 952, 608, 112, 80, 256, 600, 448, 0, 96, 544, -624, -496, -384, 0, 232, -308, -288, -516, 0, 0, 0, -280, -408, 0, -56, 236, -224, 0, -124, 328, -528, -1392, 272, 1112, -64, -16, 0, -1720, -568, -484, -864, 644, 0, 0, -536, -600, -96, 0, 0, 0, 64, 1044, 0, 216, 552, 128, 0, -1664, -72, -1232, 320, 60, -432, -1412, 488, 0, 0, 772, 256, 756, -960, 0, -232, 192, -64, -652, 0, 0, 0, 448, 832, 0, -48, 112, 168, 0, -136, 144, -1000, 760, 280, 384, 40, 688, 0, 564, 504, -1536, -112, 944, 0, -580, 200, 384, 816, 0, 0, 0, 576, 1192, 0, -684, 40, 964, 0, 1548, -192, -984, 312, -276, 568, -216, 48, 0, 648, 416, -1568, -476, 168, 0, 464, 1156, -60, 372, 0, 0, 0, -696, 128, 0, 300, -96, 704, 0, -592, -1140, -160, 96, -388, 656, -352, 1140, 0, -664, 64, -1228, -612, 708, 0, 928, -192, -1176, -304, 0, 0, 0, 184, 700, 0, -492, 352, -288, 0, -32, 912, -980, -32, -2064, 64, -216, 140, 0, -1032, 2436, -128, -1344, 360, 0, -464, -1712, -272, -192, 0, 0, 0, 4092, 1100, 0, -144, 1308, -168, 0, 448, -1004, -1568, -1116, 376, -720, 616, 1340, 0, -380, -552, -2264, 1024, 416, 0, 0, 704, -156, 544, 0, 0, 0, 80, 1284, 0, 96, -732, 2596, 0, -420, -1200, -2408, -80, -708, -72, -2992, 600, 0, 976, -1536, -128, 192, -124, 0, 232, 2528, 120, 2100, 0, 0, 0, -480, 216, 0, -320, -880, 128, 0, 588, 1888, -88, 428, -1488, -44, -192, -196, 0, -1280, -1008, -2192, -1056, -932, 0, 812, -928, -1212, -640, 0, 0, 0, 1104, 2624, 0, 452, 376, -1616, 0, 1128, -240, -2116, -332, 96, -72, 512, 944, 0, 528, -1684, 64, 840, -200, 0, 0, 400, 32, 1424, 0, 0, 0, 2172, 192, 0, -40, -480, 384, 0, -760, -300, 440, 1784, 464, 1248, -2056, 2340, 0, 2624, 1464, 96, -224, -168, 0, -464, 1904, -500, 608, 0, 0, 0, 160, 432, 0, -772, 600, 1848, 0, 172, -468, 1408, 96, 704, 544, -72, -624, 0, -992, 80, -768, -1872, 968, 0, 464, -64, -308, -60, 0, 0, 0, 0, -96, 0, -608, 672, 320, 0, -280, -456, -816, -1808, -64, 372, -112, -1552, 0, -1464, -448, -968, 1396, -1252, 0, 0, 656, 888, -528, 0, 0, 0, 544, 0, 0, -252, -64, -1344, 0, -2708, 64, -264, -1720, -512, -568, -4076, -484, 0, -1728, -1208, 1288, 648, 112, 0, -348, -1416, -536, 2032, 0, 0, 0, 256, 720, 0, -400, -1856, 168, 0, 64, 1344, 2088, 1700, 440, -3060, 432, 528, 0, 448, 256, 480, 408, 540, 0, -812, -144, 1212, -1232, 0, 0, 0, 120, -552, 0, -1008, -1412, 20, 0, 912, -96, 3040, 0, 1296, 772, 4752, 256, 0, 1512, -1616, -1920, -3456, 1612, 0, 0, -1340, 192, 556, 0, 0, 0, 1008, -728, 0, 928, 2312, -976, 0, 448, 132, 1664, -720, -1648, 1456, -96, -1440, 0, 1960, 336, 2252, 1048, -2964, 0, 3364, 288, -732, -1000, 0, 0, 0, 560, -528, 0, -128, 40, -1860, 0, 240, -16, -2892, 564, 1644, 504, 2584, -1536, 0, -224, 3456, 1888, 1412, 488, 0, -1160, 96, 200, -1968, 0, 0, 0, -2988, -2192, 0, -720, 2388, 720, 0, 576, -608, 2384, 284, 128, -1488, -1368, 2796, 0, -648, 1928, 3736, 64, -1872, 0, -2204, -384, 3040, -984, 0, 0, 0, -552, -2184, 0, 1728, -216, -676, 0, -3024, -2432, -880, 648, 2608, 416, -392, -1568, 0, -952, -360, 336, 0, 80, 0, 464, -1568, 1156, 288, 0, 0, 0, -4704, -288, 0, 1024, -548, 1352, 0, -696, 3376, 256, 308, -492, -372, 600, -3024, 0, -992, 1408, 196, -1520, -968, 0, 0, -2280, -1312, -160, 0, 0, 0, -776, -3044, 0, 1508, -352, 0, 0, 1016, -352, -2080, -664, 528, 64, 3636, -1228, 0, -1224, 80, 1416, 1100, 944, 0, 0, -904, -192, -2640, 0, 0, 0, 492, -440, 0, 544, -784, -960, 0, 184], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [1, 0, -1, 0], [1, 0, -1, 1], [0, 0, -2, 0], [0, -2, -1, -2], [0, 1, -2, 1], [2, 3, 0, -3], [-2, 0, -2, 0], [0, 2, 4, 2], [-1, -4, -1, 0], [-3, 0, 3, 7], [-2, 2, -2, 0], [0, -4, 3, -4], [2, 0, -2, -6], [5, -3, 5, 0], [-4, 0, 0, 0], [-8, 0, 8, 8], [4, 4, 4, 0], [0, 0, 0, -2], [-2, -4, 0, 4], [-7, 0, 7, -4], [0, 7, 6, 7], [4, 16, 0, -16], [-4, 2, 0, -2], [0, -4, 0, 4], [3, -8, 3, 0], [7, -9, 7, 0], [0, -6, -4, -6], [-29, 0, 0, 0], [10, -3, 0, 3], [19, 0, -19, 11], [-4, 0, 4, 0], [0, 4, -15, 4], [0, 8, 16, 8], [0, -7, -38, -7], [8, 4, 0, -4], [-8, 0, -8, 0], [0, -2, 0, -2], [15, -11, 15, 0], [-2, 0, 2, 8], [-29, 20, -29, 0], [0, -4, 14, -4], [39, 0, -39, 17], [6, 14, 6, 0], [28, 10, 0, -10], [4, 0, -4, -32], [-7, -27, -7, 0], [-4, 0, 4, -4], [9, 12, 0, -12], [0, 0, 0, 8], [0, 0, -8, 0], [6, -8, 0, 8], [-35, -20, 0, 20], [14, -9, 0, 9], [45, 19, 45, 0], [-4, -12, -4, 0], [0, -2, 6, -2], [-29, 0, 29, 0], [-16, 8, 0, -8], [10, 0, -10, 6], [-4, 0, 4, -20], [0, 11, -38, 11], [0, 16, 44, 16], [0, 0, 8, 0], [-45, 2, 0, -2], [-15, 8, -15, 0], [0, 8, 56, 8], [16, 16, 16, 0], [-44, 0, 44, -28], [-38, -14, -38, 0], [0, -5, -10, -5], [8, 0, -8, -8], [12, -60, 12, 0], [-16, 0, 0, 0], [12, 0, -12, 8], [0, -4, 0, 0], [-69, 0, 69, 32], [30, -11, 0, 11], [-33, 0, 33, -3], [0, 8, 4, 8], [5, -34, 0, 34], [-58, 20, 0, -20], [28, 32, 0, -32], [14, -8, 14, 0], [56, 40, 56, 0], [0, 17, -78, 17], [-29, 0, 29, -29], [12, 14, 0, -14], [51, 0, -51, -20], [28, 0, -28, -20], [0, 1, -66, 1], [0, -32, -8, -32], [0, 30, -71, 30], [-14, -27, 0, 27], [-12, -2, -12, 0], [0, -4, 8, -4], [69, 36, 69, 0], [9, 0, -9, -24], [-54, -40, -54, 0], [0, 8, 0, 8]]}