# Stored data for newform 2736.3.o.a, downloaded from the LMFDB on 27 April 2024.
{"label": "2736.3.o.a", "space_label": "2736.3.o", "level": 2736, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 962123008688, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1173804847133630925, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-9, 1]], [7, [-5, 1]]], "qexp_display": "q+9q^{5}+5q^{7}+3q^{11}-15q^{17}+19q^{19}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "o", "char_is_real": true, "Nk2": 24624, "analytic_conductor": 74.55060032897723, "hecke_ring_index": 1, "level_radical": 114, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [2736, 2, [1711, 2053, 1217, 1009], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [721], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "2.811", "prec": 17}, {"__RealLiteral__": 0, "data": "0.149", "prec": 17}, {"__RealLiteral__": 0, "data": "9.267", "prec": 17}], "related_objects": [], "self_twist_discs": [-19], "cm_discs": [-19], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 0, 9, 5], "traces": [0, 1, 0, 0, 0, 9, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, -15, 0, 19, 0, 0, 0, -30, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 85, 0, 0, 0, 75, 0, -24, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 15, 0, 0, 0, 0, 0, 90, 0, -135, 0, 0, 0, 0, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -270, 0, 0, 0, -75, 0, -112, 0, 0, 0, 279, 0, 0, 0, 0, 0, -213, 0, 95, 0, 0, 0, -255, 0, 197, 0, 0, 0, 0, 0, 0, 0, 0, 0, 177, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -150, 0, -250, 0, 0, 0, 0, 0, 169, 0, 0, 0, 0, 0, 280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -45, 0, 0, 0, -93, 0, 0, 0, 0, 0, -90, 0, -227, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57, 0, 0, 0, 0, 0, 765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 465, 0, 675, 0, 0, 0, -453, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 27, 0, -90, 0, 0, 0, 0, 0, 0, 0, 0, 0, -405, 0, 0, 0, 0, 0, 0, 0, 142, 0, 0, 0, 168, 0, 535, 0, 0, 0, 0, 0, -395, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 425, 0, 0, 0, 927, 0, 0, 0, 0, 0, 603, 0, -590, 0, 0, 0, 0, 0, 0, 0, 0, 0, -285, 0, 0, 0, 0, 0, 375, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -365, 0, 0, 0, 675, 0, 527, 0, 0, 0, 510, 0, 0, 0, 0, 0, 243, 0, 361, 0, 0, 0, -225, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 135, 0, 0, 0, 153, 0, 450, 0, 0, 0, 0, 0, -745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 810, 0, 0, 0, 762, 0, 0, 0, 0, 0, -840, 0, 515, 0, 0, 0, 0, 0, 0, 0, 0, 0, -570, 0, 0, 0, 0, 0, -45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -625, 0, 0, 0, -447, 0, -755, 0, 0, 0, 915, 0, 0, 0, 0, 0, 255, 0, 1064, 0, 0, 0, -942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -918, 0, 0, 0, 0, 0, 0, 0, -523, 0, 0, 0, 930, 0, 918, 0, 0, 0, 0, 0, -125, 0, 0, 0, 0, 0, 225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 371, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, -457, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1095, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -458, 0, 0, 0, -1680, 0, -1145, 0, 0, 0, 450, 0, 0, 0, 0, 0, -1125, 0, 0, 0, 0, 0, 30, 0, -675, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 0, 0, 295, 0, 0, 0, 1065, 0, 662, 0, 0, 0, 0, 0, 1111, 0, 0, 0, 0, 0, 1037, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1115, 0, 0, 0, -1005, 0, 0, 0, 0, 0, -375, 0, -1917, 0, 0, 0, 0, 0, 0, 0, 0, 0, 855, 0, 0, 0, 0, 0, 309, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2295, 0, 0, 0, 0, 0, 157, 0, 0, 0, 1773, 0, 0, 0, 0, 0, -1098, 0, 0, 0, 0, 0, 510, 0, -1318, 0, 0, 0, 0, 0, 0, 0, 0, 0, 963, 0, 0, 0, 0, 0, 0, 0, 85, 0, 0, 0, -1275, 0, -1270, 0, 0, 0, 0, 0, -547, 0, 0, 0, 0, 0, 1593, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -785, 0, 0, 0, -1503, 0, 0, 0, 0, 0, 0, 0, 1063, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1125, 0, 0, 0, -75, 0, -1350, 0, 0, 0, 1593, 0, 0, 0, 0, 0, -2250, 0, 1615, 0, 0, 0, -1167, 0, 1565, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, 0, 0, 841, 0, 0, 0, 1521, 0, -560, 0, 0, 0, 0, 0, -1030, 0, 0, 0, 0, 0, 1493, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1395, 0, 0, 0, 0, 0, 537, 0, -835, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270, 0, 0, 0, -1065, 0, -1762, 0, 0, 0, 0, 0, 0, 0, 0, 0, -642, 0, -456, 0, 0, 0, -405, 0, 335, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1830, 0, 0, 0, 0, 0, 0, 0, -837, 0, 0, 0, -1275, 0, 961, 0, 0, 0, 0, 0, 1790, 0, 0, 0, 0, 0, 985, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -810, 0, 0, 0, -2550, 0, 0, 0, 0, 0, -2043, 0, 1975, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1185, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1662, 0, 850, 0, 0, 0, -1545, 0, 0, 0, 0, 0, 885, 0, 513, 0, 0, 0, -1623, 0, -202, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2103, 0, 0, 0, 0, 0, 0, 0, -2137, 0, 0, 0, 0, 0, 4760, 0, 0, 0, 0, 0, -2250, 0, 0, 0, 0, 0, -635, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 1275, 0, 0, 0, 0, 0, 993, 0, 306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1250, 0, 0, 0, -153, 0, 0, 0, 0, 0, 402, 0, 0, 0, 0, 0, 0, 0, 1957, 0, 0, 0, 1395, 0, 4185, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4200, 0, 0, 0, 0, 0, 0, 0, 845, 0, 0, 0, -1350, 0, 0, 0, 0, 0, 0, 0, -4077, 0, 0, 0, 0, 0, -1873, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -310, 0, 0, 0, 2430, 0, 0, 0, 0, 0, -765, 0, -1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 375, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243, 0, 0, 0, 618, 0, 0, 0, 0, 0, -810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -255, 0, 1717, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1647, 0, 0, 0, 0, 0, 0, 0, -2270, 0, 0, 0, -2298, 0, -2435, 0, 0, 0, 0, 0, -225, 0, 0, 0, 0, 0, -3645, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1970, 0, 0, 0, -699, 0, 0, 0, 0, 0, -465, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1369, 0, 0, 0, 2745, 0, 837, 0, 0, 0, -450, 0, 0, 0, 0, 0, 4815, 0, -475, 0, 0, 0, 0, 0, -1135, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3090, 0, 0, 0, 0, 0, 0, 0, -1350, 0, 0, 0, -3555, 0, 0, 0, 0, 0, 0, 0, -1915, 0, 0, 0, 0, 0, -2633, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -639, 0, 0, 0, -576, 0, 0, 0, 0, 0, 2427, 0, -305, 0, 0, 0, 0, 0, 0, 0, 0, 0, 285, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2525, 0, 0, 0, 2955, 0, -1297, 0, 0, 0, -2055, 0, 0, 0, 0, 0, 1098, 0, 0, 0, 0, 0, 3825, 0, -765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5768, 0, 0, 0, 591, 0, 1213, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3070, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5427, 0, 0, 0, -93, 0, 0, 0, 0, 0, -5310, 0, -835, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1710, 0, 0, 0, 0, 0, -2325, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2890, 0, 0, 0, -2727, 0, -85, 0, 0, 0, -510, 0, 0, 0, 0, 0, 2265, 0, -2565, 0, 0, 0, 3162, 0, -1033, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2325, 0, 0, 0, 0, 0, 0, 0, 531, 0, 0, 0, 0, 0, 3375, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1550, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -937, 0, 0, 0, -2265, 0, 0, 0, 0, 0, 750, 0, 1681, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1095, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3285, 0, -1530, 0, 0, 0, 3417, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, -255, 0, 6075, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4743, 0, 0, 0, 0, 0, 0, 0, -1985, 0, 0, 0, 135, 0, -3043, 0, 0, 0, 0, 0, 4590, 0, 0, 0, 0, 0, -450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3490, 0, 0, 0, -3285, 0, 0, 0, 0, 0, -750, 0, 2187, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3249, 0, 0, 0, 0, 0, 3603, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1400, 0, 0, 0, 0, 0, 62, 0, 0, 0, -450, 0, 0, 0, 0, 0, -2025, 0, 0, 0, 0, 0, -3165, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 507, 0, 0, 0, 0, 0, 0, 0, -2195, 0, 0, 0, -3117, 0, 2815, 0, 0, 0, 0, 0, 1733, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 710, 0, 0, 0, 3798, 0, 0, 0, 0, 0, 1515, 0, -2700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1938, 0, 0, 0, 0, 0, 840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2675, 0, 0, 0, 0, 0, 1377, 0, 0, 0, 3702, 0, 0, 0, 0, 0, 4050, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1545, 0, 0, 0, 0, 0, 0, 0, -1975, 0, 0, 0, -6705, 0, 2885, 0, 0, 0, 0, 0, 775, 0, 0, 0, 0, 0, 277, 0], "weight_parity": -1, "has_non_self_twist": 0, "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, -19]], "char_orbit_index": 15, "prim_orbit_index": 2, "minimal_twist": "19.3.b.a", "char_is_minimal": false, "conrey_index": 721, "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], [1], [0], [0], [0], [9], [0], [5], [0], [0], [0], [3], [0], [0], [0], [0], [0], [-15], [0], [19], [0], [0], [0], [-30], [0], [56], [0], [0], [0], [0], [0], [0], [0], [0], [0], [45], [0], [0], [0], [0], [0], [0], [0], [85], [0], [0], [0], [75], [0], [-24], [0], [0], [0], [0], [0], [27], [0], [0], [0], [0], [0], [103], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-25], [0], [0], [0], [15], [0], [0], [0], [0], [0], [90], [0], [-135], [0], [0], [0], [0], [0], [0], [0], [0], [0], [171], [0], [0], [0], [0], [0]]}