# Stored data for newform 2800.2.g.d, downloaded from the LMFDB on 25 April 2024. {"label": "2800.2.g.d", "space_label": "2800.2.g", "level": 2800, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511211232529136, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 709340868142345238, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [4, 0, 1]], [11, [5, 1]], [13, [0, 1]]], "qexp_display": "q+2iq^{3}-iq^{7}-q^{9}-5q^{11}+8iq^{17}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "g", "char_is_real": true, "Nk2": 11200, "analytic_conductor": 22.358112565958507, "hecke_ring_index": 1, "level_radical": 70, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": [2800, 2, [351, 2101, 2577, 801], [2, 2, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [449], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.949", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.350", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "150.435", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, -32, 0, 0, 0, 0, 0, 0, 0, -8, 0, -12, 0, 0, 0, 0, 0, 0, 0, 28, 0, -10, 0, 0, 0, 0, 0, 0, 0, -26, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -36, 0, 0, 0, 0, 0, 0, 0, -10, 0, 4, 0, 0, 0, 0, 0, 0, 0, 16, 0, 28, 0, 0, 0, 0, 0, 0, 0, -12, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 24, 0, 0, 0, 0, 0, 0, 0, 34, 0, 38, 0, 0, 0, 0, 0, 0, 0, 40, 0, -14, 0, 0, 0, 0, 0, 0, 0, 26, 0, 4, 0, 0, 0, 0, 0, 0, 0, -48, 0, -44, 0, 0, 0, 0, 0, 0, 0, 8, 0, -24, 0, 0, 0, 0, 0, 0, 0, 52, 0, 52, 0, 0, 0, 0, 0, 0, 0, 20, 0, -40, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, -20, 0, 0, 0, 0, 0, 0, 0, 48, 0, -44, 0, 0, 0, 0, 0, 0, 0, -64, 0, 8, 0, 0, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 0, 0, 0, 0, 48, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 18, 0, 0, 0, 0, 0, 0, 0, -94, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, -30, 0, -48, 0, 0, 0, 0, 0, 0, 0, -12, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 40, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, -30, 0, 0, 0, 0, 0, 0, 0, 4, 0, -20, 0, 0, 0, 0, 0, 0, 0, 30, 0, 52, 0, 0, 0, 0, 0, 0, 0, -10, 0, 112, 0, 0, 0, 0, 0, 0, 0, -8, 0, 50, 0, 0, 0, 0, 0, 0, 0, -12, 0, 72, 0, 0, 0, 0, 0, 0, 0, 32, 0, -66, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, -32, 0, 2, 0, 0, 0, 0, 0, 0, 0, -62, 0, 20, 0, 0, 0, 0, 0, 0, 0, -64, 0, -80, 0, 0, 0, 0, 0, 0, 0, -26, 0, -40, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 22, 0, 0, 0, 0, 0, 0, 0, 8, 0, -32, 0, 0, 0, 0, 0, 0, 0, 48, 0, -12, 0, 0, 0, 0, 0, 0, 0, -88, 0, -36, 0, 0, 0, 0, 0, 0, 0, -52, 0, 8, 0, 0, 0, 0, 0, 0, 0, 10, 0, -26, 0, 0, 0, 0, 0, 0, 0, 12, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, -26, 0, -38, 0, 0, 0, 0, 0, 0, 0, 68, 0, 32, 0, 0, 0, 0, 0, 0, 0, 16, 0, 12, 0, 0, 0, 0, 0, 0, 0, -10, 0, 80, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 56, 0, 0, 0, 0, 0, 0, 0, 16, 0, -14, 0, 0, 0, 0, 0, 0, 0, 10, 0, -14, 0, 0, 0, 0, 0, 0, 0, 40, 0, -16, 0, 0, 0, 0, 0, 0, 0, 40, 0, 60, 0, 0, 0, 0, 0, 0, 0, 56, 0, 60, 0, 0, 0, 0, 0, 0, 0, -24, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, -116, 0, 60, 0, 0, 0, 0, 0, 0, 0, -60, 0, 26, 0, 0, 0, 0, 0, 0, 0, 12, 0, -4, 0, 0, 0, 0, 0, 0, 0, -26, 0, -48, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -24, 0, 0, 0, 0, 0, 0, 0, -140, 0, 96, 0, 0, 0, 0, 0, 0, 0, -68, 0, 48, 0, 0, 0, 0, 0, 0, 0, 8, 0, 50, 0, 0, 0, 0, 0, 0, 0, 20, 0, -2, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, -40, 0, -88, 0, 0, 0, 0, 0, 0, 0, 92, 0, -40, 0, 0, 0, 0, 0, 0, 0, -40, 0, -14, 0, 0, 0, 0, 0, 0, 0, -28, 0, -8, 0, 0, 0, 0, 0, 0, 0, 130, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 40, 0, 0, 0, 0, 0, 0, 0, -26, 0, 110, 0, 0, 0, 0, 0, 0, 0, -24, 0, 160, 0, 0, 0, 0, 0, 0, 0, 36, 0, -54, 0, 0, 0, 0, 0, 0, 0, 30, 0, -48, 0, 0, 0, 0, 0, 0, 0, 44, 0, 4, 0, 0, 0, 0, 0, 0, 0, 56, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -36, 0, -30, 0, 0, 0, 0, 0, 0, 0, 64, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 42, 0, 26, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -56, 0, 0, 0, 0, 0, 0, 0, 30, 0, -76, 0, 0, 0, 0, 0, 0, 0, -4, 0, -70, 0, 0, 0, 0, 0, 0, 0, 36, 0, -116, 0, 0, 0, 0, 0, 0, 0, -24, 0, 90, 0, 0, 0, 0, 0, 0, 0, -80, 0, -36, 0, 0, 0, 0, 0, 0, 0, 48, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, -28, 0, -64, 0, 0, 0, 0, 0, 0, 0, 20, 0, -88, 0, 0, 0, 0, 0, 0, 0, -92, 0, 180, 0, 0, 0, 0, 0, 0, 0, 4, 0, 16, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 0, -8, 0, 0, 0, 0, 0, 0, 0, -48, 0, -84, 0, 0, 0, 0, 0, 0, 0, 24, 0, -24, 0, 0, 0, 0, 0, 0, 0, 16, 0, -66, 0, 0, 0, 0, 0, 0, 0, 8, 0, -20, 0, 0, 0, 0, 0, 0, 0, -12, 0, 72, 0, 0, 0, 0, 0, 0, 0, 50, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, -140, 0, -20, 0, 0, 0, 0, 0, 0, 0, 12, 0, -100, 0, 0, 0, 0, 0, 0, 0, -16, 0, 96, 0, 0, 0, 0, 0, 0, 0, -116, 0, 4, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 16, 0, 0, 0, 0, 0, 0, 0, -84, 0, -24, 0, 0, 0, 0, 0, 0, 0, 18, 0, 76, 0, 0, 0, 0, 0, 0, 0, 96, 0, 24, 0, 0, 0, 0, 0, 0, 0, -80, 0, -56, 0, 0, 0, 0, 0, 0, 0, 20, 0, -128, 0, 0, 0, 0, 0, 0, 0, 16, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 20, 0, -34, 0, 0, 0, 0, 0, 0, 0, -38, 0, -44, 0, 0, 0, 0, 0, 0, 0, 72, 0, -148, 0, 0, 0, 0, 0, 0, 0, -6, 0, 10, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, -56, 0, 0, 0, 0, 0, 0, 0, 42, 0, -256, 0, 0, 0, 0, 0, 0, 0, 60, 0, -6, 0, 0, 0, 0, 0, 0, 0, -140, 0, 80, 0, 0, 0, 0, 0, 0, 0, 118, 0, 40, 0, 0, 0, 0, 0, 0, 0, 14, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -96, 0, -74, 0, 0, 0, 0, 0, 0, 0, 36, 0, -20, 0, 0, 0, 0, 0, 0, 0, 106, 0, 52, 0, 0, 0, 0, 0, 0, 0, -152, 0, 96, 0, 0, 0, 0, 0, 0, 0, 8, 0, -26, 0, 0, 0, 0, 0, 0, 0, 20, 0, 16, 0, 0, 0, 0, 0, 0, 0, 44, 0, -182, 0, 0, 0, 0, 0, 0, 0, 58, 0, -120, 0, 0, 0, 0, 0, 0, 0, 96, 0, -28, 0, 0, 0, 0, 0, 0, 0, 16, 0, -84, 0, 0, 0, 0, 0, 0, 0, 64, 0, 128, 0, 0, 0, 0, 0, 0, 0, -28, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -72, 0, 48, 0, 0, 0, 0, 0, 0, 0, 24, 0, -86, 0, 0, 0, 0, 0, 0, 0, 44, 0, 58, 0, 0, 0, 0, 0, 0, 0, -170, 0, 68, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, -190, 0, 0, 0, 0, 0, 0, 0, 112, 0, -36, 0, 0, 0, 0, 0, 0, 0, -84, 0, -74, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, -20, 0, 0, 0, 0, 0, 0, 0, 90, 0, -24, 0, 0, 0, 0, 0, 0, 0, 24, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 40, 0, 0, 0, 0, 0, 0, 0, -200, 0, 32, 0, 0, 0, 0, 0, 0, 0, -42, 0, -120, 0, 0, 0, 0, 0, 0, 0, -36, 0, 70, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, -52, 0, 0, 0, 0, 0, 0, 0, -24, 0, 62, 0, 0, 0, 0, 0, 0, 0, 104, 0, -16, 0, 0, 0, 0, 0, 0, 0, -192, 0, 192, 0, 0, 0, 0, 0, 0, 0, 32, 0, -16, 0, 0, 0, 0, 0, 0, 0, 140, 0, -10, 0, 0, 0, 0, 0, 0, 0, 68, 0, 36, 0, 0, 0, 0, 0, 0, 0, -130, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 56, 0, -20, 0, 0, 0, 0, 0, 0, 0, -20, 0, 48, 0, 0, 0, 0, 0, 0, 0, 40, 0, 70, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 16, 0, 0, 0, 0, 0, 0, 0, -64, 0, -156, 0, 0, 0, 0, 0, 0, 0, 44, 0, -104, 0, 0, 0, 0, 0, 0, 0, -144, 0, 44, 0, 0, 0, 0, 0, 0, 0, 72, 0, -20, 0, 0, 0, 0, 0, 0, 0, 240, 0, 48, 0, 0, 0, 0, 0, 0, 0, -68, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 220, 0, 0, 0, 0, 0, 0, 0, 110, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 2, "minimal_twist": "1400.2.a.b", "char_is_minimal": false, "conrey_index": 449, "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, 2], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [-1, 0], [0, 0], [-5, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 8], [0, 0], [-2, 0], [0, 0], [2, 0], [0, 0], [0, -7], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [3, 0], [0, 0], [-4, 0], [0, 0], [0, -10], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [0, -6], [0, 0], [-1, 0], [0, 0], [-16, 0], [0, 0], [0, -10], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [-4, 0], [0, 0], [-6, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [0, -13], [0, 0], [14, 0], [0, 0], [-5, 0], [0, 0], [0, -6], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [-13, 0], [0, 0], [-11, 0], [0, 0], [0, 16], [0, 0], [0, 0], [0, 0], [0, 6], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -8], [0, 0], [0, 0], [0, 0], [0, -12], [0, 0], [5, 0], [0, 0]]}