# Stored data for newform 243.3.d.c, downloaded from the LMFDB on 24 June 2026. {"Nk2": 2187, "analytic_conductor": 6.621270423955215, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 6, "char_parity": -1, "char_values": [243, 6, [2], [1]], "cm_discs": [-3], "conrey_index": 80, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[2, [0, 1]], [5, [0, 1]], [7, [121, 11, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007405463503091, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 9, 3, 1, 3, 0], [1, 1, 9, 4, -1, 6, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "243.3.d.c", "level": 243, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "243.3.b.b", "nf_label": "2.0.3.1", "prim_orbit_index": 4, "qexp_display": "q-4\\zeta_{6}q^{4}+(-11+11\\zeta_{6})q^{7}+22\\zeta_{6}q^{13}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "2.2.1.d6", "self_twist_discs": [-3], "self_twist_type": 1, "space_label": "243.3.d", "trace_display": [0, 0, 0, -11], "trace_hash": 2249037115825990932, "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "2.053", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "18.870", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "232.049", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 2, 0, 0, -4, 0, 0, -11, 0, 0, 0, 0, 0, 22, 0, 0, -16, 0, 0, 52, 0, 0, 0, 0, 0, -25, 0, 0, 88, 0, 0, 13, 0, 0, 0, 0, 0, -146, 0, 0, 0, 0, 0, -83, 0, 0, 0, 0, 0, -72, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 121, 0, 0, 128, 0, 0, 109, 0, 0, 0, 0, 0, -194, 0, 0, -104, 0, 0, 142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -484, 0, 0, 0, 0, 0, -2, 0, 0, 200, 0, 0, 37, 0, 0, 0, 0, 0, 142, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, -121, 0, 0, 52, 0, 0, 214, 0, 0, 0, 0, 0, -286, 0, 0, 0, 0, 0, 229, 0, 0, 0, 0, 0, 0, 0, 0, 292, 0, 0, -59, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, -74, 0, 0, 0, 0, 0, -315, 0, 0, 664, 0, 0, -275, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -143, 0, 0, -288, 0, 0, 772, 0, 0, 0, 0, 0, 0, 0, 0, -704, 0, 0, 166, 0, 0, 0, 0, 0, -286, 0, 0, 0, 0, 0, 421, 0, 0, 0, 0, 0, -383, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -479, 0, 0, -968, 0, 0, 572, 0, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 803, 0, 0, 0, 0, 0, 0, 0, 0, 436, 0, 0, 598, 0, 0, 0, 0, 0, 529, 0, 0, 0, 0, 0, -59, 0, 0, 0, 0, 0, 578, 0, 0, 388, 0, 0, 0, 0, 0, 0, 0, 0, -913, 0, 0, -416, 0, 0, -716, 0, 0, 0, 0, 0, 457, 0, 0, -1136, 0, 0, 0, 0, 0, 0, 0, 0, -1100, 0, 0, 0, 0, 0, -362, 0, 0, 0, 0, 0, -167, 0, 0, 0, 0, 0, 506, 0, 0, 0, 0, 0, 169, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 630, 0, 0, 968, 0, 0, -491, 0, 0, 0, 0, 0, -698, 0, 0, 0, 0, 0, 1222, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 862, 0, 0, -400, 0, 0, -286, 0, 0, 0, 0, 0, 769, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, -839, 0, 0, 0, 0, 0, 1331, 0, 0, 0, 0, 0, 1006, 0, 0, -284, 0, 0, 94, 0, 0, 0, 0, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, 526, 0, 0, 0, 0, 0, -2398, 0, 0, 0, 0, 0, -650, 0, 0, 0, 0, 0, -1606, 0, 0, -484, 0, 0, 1924, 0, 0, 0, 0, 0, 0, 0, 0, -416, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, -428, 0, 0, 1067, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1606, 0, 0, 0, 0, 0, -529, 0, 0, 2288, 0, 0, 0, 0, 0, 0, 0, 0, -1586, 0, 0, 0, 0, 0, 1093, 0, 0, 0, 0, 0, 1562, 0, 0, 916, 0, 0, -3652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1067, 0, 0, 0, 0, 0, -2066, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 338, 0, 0, 1168, 0, 0, 0, 0, 0, 0, 0, 0, -1199, 0, 0, 472, 0, 0, 373, 0, 0, 0, 0, 0, 1966, 0, 0, 0, 0, 0, 949, 0, 0, 0, 0, 0, -625, 0, 0, 772, 0, 0, -2522, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, -314, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, -1079, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1154, 0, 0, 2520, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, -1328, 0, 0, -299, 0, 0, 0, 0, 0, 0, 0, 0, -1100, 0, 0, -3796, 0, 0, 0, 0, 0, 934, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -814, 0, 0, 4, 0, 0, -482, 0, 0, 0, 0, 0, 1417, 0, 0, 0, 0, 0, 2662, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1381, 0, 0, 0, 0, 0, -1346, 0, 0, 0, 0, 0, -781, 0, 0, 0, 0, 0, 1534, 0, 0, -572, 0, 0, -650, 0, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 613, 0, 0, 0, 0, 0, 5324, 0, 0, -1544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -506, 0, 0, 0, 0, 0, -2158, 0, 0, 0, 0, 0, -1058, 0, 0, 0, 0, 0, 916, 0, 0, 1408, 0, 0, 0, 0, 0, 0, 0, 0, -841, 0, 0, 664, 0, 0, 2662, 0, 0, 0, 0, 0, 481, 0, 0, 0, 0, 0, -131, 0, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, -2398, 0, 0, 0, 0, 0, 1129, 0, 0, 0, 0, 0, -3404, 0, 0, 0, 0, 0, -1177, 0, 0, -3368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 214, 0, 0, 0, 0, 0, 0, 0, 0, -1532, 0, 0, 1732, 0, 0, 0, 0, 0, 1825, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, -1298, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2134, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 792, 0, 0, 3832, 0, 0, 253, 0, 0, 0, 0, 0, -5038, 0, 0, 1936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2288, 0, 0, 3478, 0, 0, 0, 0, 0, 1894, 0, 0, 0], "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], [1, 0], [0, 0], [0, 0], [0, -4], [0, 0], [0, 0], [-11, 11], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 22], [0, 0], [0, 0], [-16, 16], [0, 0], [0, 0], [26, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-25, 25], [0, 0], [0, 0], [44, 0], [0, 0], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-73, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-83, 83], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -72], [0, 0], [0, 0], [88, -88], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [121, -121], [0, 0], [0, 0], [64, 0], [0, 0], [0, 0], [0, 109], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-97, 0], [0, 0], [0, 0], [0, -104], [0, 0], [0, 0], [142, -142], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-242, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-2, 2], [0, 0], [0, 0], [100, 0]]}