# Stored data for newform 1216.3.e.g, downloaded from the LMFDB on 25 April 2024.
{"label": "1216.3.e.g", "space_label": "1216.3.e", "level": 1216, "weight": 3, "hecke_orbit": 7, "hecke_orbit_code": 27021872692462784, "dim": 2, "is_polredabs": true, "nf_label": "2.0.52.1", "trace_hash": 1305742405856891333, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [13, 0, 1]], [5, [4, 1]], [7, [5, 1]]], "qexp_display": "q+\\beta q^{3}-4q^{5}-5q^{7}-4q^{9}+10q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": true, "Nk2": 10944, "analytic_conductor": 33.1336001462121, "hecke_ring_index": 1, "level_radical": 38, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [1216, 2, [191, 837, 705], [2, 2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [1025], "field_disc": -52, "field_disc_factorization": [[-1, 1], [2, 2], [13, 1]], "field_poly": [13, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.929", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.437", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "153.585", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, -8, -10], "traces": [0, 2, 0, 0, 0, -8, 0, -10, 0, -8, 0, 20, 0, 0, 0, 0, 0, 30, 0, 12, 0, 0, 0, 70, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 26, 0, 0, 0, 40, 0, 32, 0, 20, 0, -48, 0, 0, 0, 0, 0, -80, 0, 130, 0, 0, 0, 80, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 210, 0, 0, 0, -100, 0, 0, 0, -202, 0, 80, 0, -120, 0, 130, 0, 0, 0, 0, 0, 260, 0, -48, 0, 0, 0, -80, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, -280, 0, 0, 0, -150, 0, -42, 0, -260, 0, 272, 0, 0, 0, 0, 0, -224, 0, -60, 0, 0, 0, 250, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, -120, 0, 0, 0, -20, 0, -546, 0, -350, 0, 540, 0, 0, 0, 0, 0, 312, 0, -48, 0, 0, 0, 90, 0, 130, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 0, 0, 0, 386, 0, 0, 0, -104, 0, -180, 0, 246, 0, 286, 0, 0, 0, 0, 0, -280, 0, 120, 0, 0, 0, -780, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 320, 0, 0, 0, -540, 0, -80, 0, 260, 0, 394, 0, 0, 0, 0, 0, 192, 0, -130, 0, 0, 0, 804, 0, 700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 620, 0, 0, 0, 0, 0, 0, 0, 210, 0, -130, 0, -180, 0, 100, 0, 0, 0, 0, 0, 640, 0, -520, 0, 0, 0, -128, 0, -884, 0, 0, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 0, -320, 0, 0, 0, -416, 0, 790, 0, 250, 0, -160, 0, 0, 0, 0, 0, 546, 0, 180, 0, 0, 0, -1430, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 884, 0, 0, 0, 730, 0, 0, 0, 80, 0, -196, 0, 130, 0, -370, 0, 0, 0, 0, 0, -450, 0, -578, 0, 0, 0, -840, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0, 936, 0, 0, 0, 400, 0, -160, 0, 956, 0, 1050, 0, 0, 0, 0, 0, -1500, 0, -650, 0, 0, 0, -260, 0, 808, 0, 0, 0, 0, 0, 0, 0, 0, 0, -320, 0, 0, 0, -224, 0, 0, 0, -80, 0, -270, 0, -400, 0, 260, 0, 0, 0, 0, 0, -520, 0, 420, 0, 0, 0, 192, 0, -1340, 0, 0, 0, 0, 0, 0, 0, 0, 0, -260, 0, 0, 0, -1510, 0, 0, 0, -1544, 0, -700, 0, -1040, 0, -140, 0, 0, 0, 0, 0, 400, 0, -108, 0, 0, 0, -740, 0, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1264, 0, 0, 0, 320, 0, 0, 0, -760, 0, -884, 0, -90, 0, -400, 0, 0, 0, 0, 0, -1050, 0, 650, 0, 0, 0, 200, 0, -884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1392, 0, 0, 0, 260, 0, 0, 0, 260, 0, -480, 0, 1200, 0, 780, 0, 0, 0, 0, 0, -320, 0, -650, 0, 0, 0, 624, 0, -760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1010, 0, 0, 0, 1580, 0, 0, 0, -630, 0, 1350, 0, -1924, 0, -400, 0, 0, 0, 0, 0, 560, 0, -1300, 0, 0, 0, 1500, 0, 600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, -650, 0, 0, 0, 2400, 0, 1040, 0, -700, 0, -1120, 0, 0, 0, 0, 0, -638, 0, 1300, 0, 0, 0, -2100, 0, -1690, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2060, 0, 0, 0, 1110, 0, 0, 0, -1300, 0, -100, 0, 896, 0, -840, 0, 0, 0, 0, 0, 390, 0, 240, 0, 0, 0, 1456, 0, 800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1846, 0, 0, 0, -1000, 0, 0, 0, 546, 0, 1640, 0, 400, 0, 400, 0, 0, 0, 0, 0, 1080, 0, 780, 0, 0, 0, -500, 0, -536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 210, 0, 0, 0, -2860, 0, 0, 0, 1390, 0, -362, 0, 600, 0, -320, 0, 0, 0, 0, 0, -2056, 0, 156, 0, 0, 0, 560, 0, -320, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, -1310, 0, 0, 0, 480, 0, -130, 0, -370, 0, 3016, 0, 0, 0, 0, 0, 780, 0, 1300, 0, 0, 0, 650, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2184, 0, 0, 0, 300, 0, 0, 0, 2100, 0, 1400, 0, 780, 0, -14, 0, 0, 0, 0, 0, -2160, 0, 240, 0, 0, 0, -1684, 0, 1550, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 1300, 0, 0, 0, 1032, 0, 2080, 0, -1248, 0, 210, 0, 0, 0, 0, 0, -800, 0, 192, 0, 0, 0, -2864, 0, 1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, -286, 0, 0, 0, -1360, 0, 0, 0, -1586, 0, 1500, 0, -240, 0, -520, 0, 0, 0, 0, 0, -2020, 0, 120, 0, 0, 0, 910, 0, -1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, -400, 0, 0, 0, 800, 0, 0, 0, 1120, 0, -1026, 0, 1716, 0, 780, 0, 0, 0, 0, 0, -2434, 0, -288, 0, 0, 0, -1200, 0, -2190, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1280, 0, 0, 0, 26, 0, 0, 0, -1544, 0, 1300, 0, -1250, 0, -678, 0, 0, 0, 0, 0, -2020, 0, 1950, 0, 0, 0, 500, 0, -234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 0, 0, 0, 1400, 0, 0, 0, -1430, 0, -984, 0, 340, 0, -780, 0, 0, 0, 0, 0, -1144, 0, 2730, 0, 0, 0, -416, 0, -620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2600, 0, 0, 0, -260, 0, 0, 0, -2180, 0, -1030, 0, 1120, 0, 1200, 0, 0, 0, 0, 0, 700, 0, -480, 0, 0, 0, 100, 0, -404, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3660, 0, 0, 0, 3120, 0, 0, 0, 2740, 0, 600, 0, 780, 0, -360, 0, 0, 0, 0, 0, 700, 0, 1560, 0, 0, 0, -2630, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, -310, 0, 0, 0, -1300, 0, -1264, 0, 1000, 0, 2730, 0, 0, 0, 0, 0, -3146, 0, -650, 0, 0, 0, -1088, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3510, 0, 0, 0, -2700, 0, 0, 0, -1280, 0, 1560, 0, -1456, 0, -54, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, -2660, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 896, 0, 0, 0, -1560, 0, -1040, 0, 1140, 0, 1300, 0, 0, 0, 0, 0, -1576, 0, 240, 0, 0, 0, -1354, 0, 2080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2180, 0, 0, 0, 3070, 0, 0, 0, -1560, 0, 4190, 0, 432, 0, 260, 0, 0, 0, 0, 0, -1000, 0, 520, 0, 0, 0, -650, 0, 3150, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400, 0, 0, 0, -3216, 0, 0, 0, -2120, 0, 884, 0, 4550, 0, -2800, 0, 0, 0, 0, 0, 2600, 0, -1430, 0, 0, 0, -1940, 0, 570, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2894, 0, 0, 0, 3120, 0, 0, 0, 1830, 0, 5304, 0, 2840, 0, 580, 0, 0, 0, 0, 0, -1500, 0, 4550, 0, 0, 0, -2480, 0, -5720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3290, 0, 0, 0, -2840, 0, 0, 0, 0, 0, -1930, 0, 416, 0, 560, 0, 0, 0, 0, 0, 260, 0, 3900, 0, 0, 0, -2600, 0, -840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 520, 0, 0, 0, 1802, 0, 0, 0, -4520, 0, 2720, 0, -3030, 0, 900, 0, 0, 0, 0, 0, -400, 0, 1260, 0, 0, 0, -546, 0, -1230, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2800, 0, 0, 0, -1430, 0, 0, 0, 1200, 0, 80, 0, -2560, 0, 1430, 0, 0, 0, 0, 0, -1110, 0, -1170, 0, 0, 0, 1184, 0, -2730, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2240, 0, 0, 0, 512, 0, 0, 0, 1400, 0, 2504, 0, -5240, 0, 3536, 0, 0, 0, 0, 0, 3744, 0, -600, 0, 0, 0, -2160, 0, -884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1950, 0, 0, 0, 3620, 0, 0, 0, -5270, 0, 3620, 0, 3900, 0, -1120, 0, 0, 0, 0, 0, -4640, 0, -1300, 0, 0, 0, 800, 0, 2500, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1560, 0, 0, 0, -1248, 0, 0, 0, -720, 0, 5980, 0, -1000, 0, -824, 0, 0, 0, 0, 0, 2730, 0, -1212, 0, 0, 0, -1850, 0, 1664, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3160, 0, 0, 0, -1564, 0, 0, 0, -4420, 0, -1000, 0, 1020, 0, 3354, 0, 0, 0, 0, 0, -360, 0, 480, 0, 0, 0, 3900, 0, -5430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 650, 0, 0, 0, -1880, 0, 0, 0, -2346, 0, -1600, 0, -2184, 0, -370, 0, 0, 0, 0, 0, 2320, 0, -720, 0, 0, 0, -1176, 0, -716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2700, 0, 0, 0, 5720, 0, 0, 0, -1400, 0, -4316, 0, 5460, 0, 400, 0, 0, 0, 0, 0, -936, 0, 780, 0, 0, 0, -5180, 0, -1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 860, 0, 0, 0, -1970, 0, 0, 0, 520, 0, 7350, 0, 762, 0, -1200, 0, 0, 0, 0, 0, 884, 0, 0, 0, 0, 0, -3536, 0, 3100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -260, 0, 0, 0, -650, 0, 0, 0, -2920, 0, 1500, 0, -1544, 0, -2830, 0, 0, 0, 0, 0, -200, 0, 650, 0, 0, 0, 4040, 0, -320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 784, 0, 0, 0, -5460, 0, 0, 0, 4610, 0, -520, 0, -4020, 0, -4990, 0, 0, 0, 0, 0, 1480, 0, 1560, 0, 0, 0, -3500, 0, 720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1390, 0, 0, 0, -580, 0, 0, 0, -984, 0, 5400, 0, 1800, 0, -3640, 0, 0, 0, 0, 0, -4420, 0, 2312, 0, 0, 0, 1430, 0, -4060, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7124, 0, 0, 0, -1890, 0, 0, 0, -1300, 0, -410, 0, 260, 0, -400, 0, 0, 0, 0, 0, -3100, 0, 4420, 0, 0, 0, 950, 0, -2898, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3120, 0, 0, 0, -7070, 0, 0, 0, -5300, 0, 0, 0, -1580, 0, 5630, 0, 0, 0, 0, 0, -3466, 0, -480, 0, 0, 0, 520, 0, -2340, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1050, 0, 0, 0, -2804, 0, 0, 0, -3744, 0, 6720, 0, 2800, 0, -624, 0, 0, 0, 0, 0, -3900, 0, 600, 0, 0, 0, -8840, 0, 900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 640, 0, 0, 0, -500, 0, 0, 0, -1430, 0, -3824, 0, 1300, 0, -5180, 0, 0, 0, 0, 0, -4200, 0, 2080, 0, 0, 0, -3276, 0, 260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1660, 0, 0, 0, 1430, 0, 0, 0, -3200, 0, 1430, 0, 6000, 0, 6940, 0, 0, 0, 0, 0, 2980, 0, 2600, 0, 0, 0, 1890, 0], "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, 19, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "19.3.b.b", "char_is_minimal": false, "conrey_index": 1025, "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], [1, 0], [0, 0], [0, 1], [0, 0], [-4, 0], [0, 0], [-5, 0], [0, 0], [-4, 0], [0, 0], [10, 0], [0, 0], [0, -1], [0, 0], [0, -4], [0, 0], [15, 0], [0, 0], [6, -5], [0, 0], [0, -5], [0, 0], [35, 0], [0, 0], [-9, 0], [0, 0], [0, 5], [0, 0], [0, -5], [0, 0], [0, -10], [0, 0], [0, 10], [0, 0], [20, 0], [0, 0], [0, 6], [0, 0], [13, 0], [0, 0], [0, 10], [0, 0], [20, 0], [0, 0], [16, 0], [0, 0], [10, 0], [0, 0], [-24, 0], [0, 0], [0, 15], [0, 0], [0, 21], [0, 0], [-40, 0], [0, 0], [65, 6], [0, 0], [0, -5], [0, 0], [40, 0], [0, 0], [20, 0], [0, 0], [0, 4], [0, 0], [0, -11], [0, 0], [0, 35], [0, 0], [0, 30], [0, 0], [105, 0], [0, 0], [0, -9], [0, 0], [-50, 0], [0, 0], [0, -10], [0, 0], [-101, 0], [0, 0], [40, 0], [0, 0], [-60, 0], [0, 0], [65, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [130, 0], [0, 0], [-24, 20], [0, 0], [0, 34], [0, 0], [-40, 0], [0, 0]]}