# Stored data for newform 180.3.g.a, downloaded from the LMFDB on 25 April 2024. {"label": "180.3.g.a", "space_label": "180.3.g", "level": 180, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 412367192244, "dim": 4, "is_polredabs": true, "nf_label": "4.0.6400.1", "trace_hash": 1611043374696711743, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\beta _{2}q^{5}+(-4-\\beta _{3})q^{7}+(-\\beta _{1}-6\\beta _{2}+\\cdots)q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "g", "char_is_real": true, "Nk2": 1620, "analytic_conductor": 4.904644758485344, "hecke_ring_index": 18, "level_radical": 30, "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": [180, 2, [91, 101, 37], [2, 1, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [161], "field_disc": 6400, "field_disc_factorization": [[2, 8], [5, 2]], "field_poly": [9, 0, -4, 0, 1], "hecke_ring_index_factorization": [[2, 1], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "3.767", "prec": 17}, {"__RealLiteral__": 0, "data": "0.787", "prec": 17}, {"__RealLiteral__": 0, "data": "72.540", "prec": 20}, {"__RealLiteral__": 0, "data": "15.515", "prec": 20}, {"__RealLiteral__": 0, "data": "2007.204", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, -16], "traces": [0, 4, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 228, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 328, 0, 0, 0, 0, 0, -424, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 592, 0, 0, 0, 0, 0, 392, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, -784, 0, 0, 0, 0, 0, -300, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 440, 0, 0, 0, 0, 0, -376, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 688, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, 784, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, -536, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 1448, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, -1040, 0, 0, 0, 0, 0, 1376, 0, 0, 0, 0, 0, 1208, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, 824, 0, 0, 0, 0, 0, -3008, 0, 0, 0, 0, 0, -376, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 1088, 0, 0, 0, 0, 0, 1640, 0, 0, 0, 0, 0, 728, 0, 0, 0, 0, 0, 840, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 736, 0, 0, 0, 0, 0, -1192, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -808, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, -1912, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 3096, 0, 0, 0, 0, 0, -1960, 0, 0, 0, 0, 0, 896, 0, 0, 0, 0, 0, 1216, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, -1352, 0, 0, 0, 0, 0, 1712, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 1328, 0, 0, 0, 0, 0, -1080, 0, 0, 0, 0, 0, -2768, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, -2320, 0, 0, 0, 0, 0, 1108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1880, 0, 0, 0, 0, 0, -2464, 0, 0, 0, 0, 0, 1360, 0, 0, 0, 0, 0, -560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 464, 0, 0, 0, 0, 0, -376, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 1504, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -1264, 0, 0, 0, 0, 0, -2152, 0, 0, 0, 0, 0, 1688, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 1304, 0, 0, 0, 0, 0, -2424, 0, 0, 0, 0, 0, 1760, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 840, 0, 0, 0, 0, 0, -2344, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, 2792, 0, 0, 0, 0, 0, 2416, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, -3248, 0, 0, 0, 0, 0, -1720, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 5848, 0, 0, 0, 0, 0, 848, 0, 0, 0, 0, 0, -184, 0, 0, 0, 0, 0, 2096, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 0, 1208, 0, 0, 0, 0, 0, 3184, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, -3520, 0, 0, 0, 0, 0, -2240, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 1200, 0, 0, 0, 0, 0, 632, 0, 0, 0, 0, 0, -800, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 2024, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, -1964, 0, 0, 0, 0, 0, 5552, 0, 0, 0, 0, 0, 440, 0, 0, 0, 0, 0, 824, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, -608, 0, 0, 0, 0, 0, 4280, 0, 0, 0, 0, 0, -400, 0, 0, 0, 0, 0, 2920, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, -6184, 0, 0, 0, 0, 0, 680, 0, 0, 0, 0, 0, -3936, 0, 0, 0, 0, 0, 584, 0, 0, 0, 0, 0, 3312, 0, 0, 0, 0, 0, -1856, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -2388, 0, 0, 0, 0, 0, -544, 0, 0, 0, 0, 0, -5888, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 2040, 0, 0, 0, 0, 0, 2936, 0, 0, 0, 0, 0, 1208, 0, 0, 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, 3, 2, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 2, "minimal_twist": "180.3.g.a", "char_is_minimal": true, "conrey_index": 161, "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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [-4, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, -6, 0], [0, 0, 0, 0], [2, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [8, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, -6, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8, -6, 0], [0, 0, 0, 0], [2, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5, 4, 0], [0, 0, 0, 0], [-34, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 3, 24, 0], [0, 0, 0, 0], [20, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 14, -12, 0], [0, 0, 0, 0], [57, 0, 0, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -10, 24, 0], [0, 0, 0, 0], [-30, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -17, 18, 0], [0, 0, 0, 0], [-10, 0, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5, -2, 0], [0, 0, 0, 0], [-76, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, -12, 0], [0, 0, 0, 0], [38, 0, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 34, 42, 0], [0, 0, 0, 0], [50, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, -24, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -21, 12, 0], [0, 0, 0, 0], [82, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 10, -8, 0], [0, 0, 0, 0], [-106, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}