# Stored data for newform 280.2.g.b, downloaded from the LMFDB on 19 April 2024. {"label": "280.2.g.b", "space_label": "280.2.g", "level": 280, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504011977785624, "dim": 6, "is_polredabs": true, "nf_label": "6.0.5161984.1", "trace_hash": 1135545947907137977, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4, 0, 32, 0, 13, 0, 1]]], "qexp_display": "q-\\beta _{5}q^{3}+(\\beta _{1}-\\beta _{5})q^{5}+\\beta _{4}q^{7}+(-1+\\cdots)q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "g", "char_is_real": true, "Nk2": 1120, "analytic_conductor": 2.235811256595851, "hecke_ring_index": 1, "level_radical": 70, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [280, 2, [71, 141, 57, 241], [2, 2, 1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [169], "field_disc": -5161984, "field_disc_factorization": [[-1, 1], [2, 10], [71, 2]], "field_poly": [8, -20, 25, -4, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.691", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "177.051", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7918.262", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 14, 0, 0, 0, -18, 0, 0, 0, -8, 0, -2, 0, 0, 0, -10, 0, 0, 0, -6, 0, 20, 0, 0, 0, -2, 0, 0, 0, 10, 0, 36, 0, 0, 0, -28, 0, 0, 0, -6, 0, 42, 0, 0, 0, -12, 0, 0, 0, -12, 0, 48, 0, 0, 0, -22, 0, 0, 0, -36, 0, 8, 0, 0, 0, -40, 0, 0, 0, -34, 0, 30, 0, 0, 0, 14, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, -4, 0, -8, 0, 0, 0, -8, 0, 0, 0, -10, 0, -12, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, -24, 0, 0, 0, 32, 0, -4, 0, 0, 0, 26, 0, 0, 0, -4, 0, 34, 0, 0, 0, 36, 0, 0, 0, 52, 0, 10, 0, 0, 0, -16, 0, 0, 0, 76, 0, -12, 0, 0, 0, -18, 0, 0, 0, -60, 0, -16, 0, 0, 0, 4, 0, 0, 0, -24, 0, -44, 0, 0, 0, -12, 0, 0, 0, 38, 0, -18, 0, 0, 0, 20, 0, 0, 0, -68, 0, -76, 0, 0, 0, 40, 0, 0, 0, 24, 0, 2, 0, 0, 0, -8, 0, 0, 0, -36, 0, -74, 0, 0, 0, 28, 0, 0, 0, -92, 0, -14, 0, 0, 0, 70, 0, 0, 0, 78, 0, 12, 0, 0, 0, 0, 0, 0, 0, 128, 0, -44, 0, 0, 0, 44, 0, 0, 0, -36, 0, -36, 0, 0, 0, 84, 0, 0, 0, 52, 0, -40, 0, 0, 0, 10, 0, 0, 0, 56, 0, -106, 0, 0, 0, 32, 0, 0, 0, 4, 0, -54, 0, 0, 0, 60, 0, 0, 0, 148, 0, 0, 0, 0, 0, -20, 0, 0, 0, 14, 0, -64, 0, 0, 0, 16, 0, 0, 0, -114, 0, 0, 0, 0, 0, 64, 0, 0, 0, 18, 0, -56, 0, 0, 0, -20, 0, 0, 0, 116, 0, 28, 0, 0, 0, -48, 0, 0, 0, -56, 0, -134, 0, 0, 0, -16, 0, 0, 0, -40, 0, -26, 0, 0, 0, 4, 0, 0, 0, -160, 0, 20, 0, 0, 0, 18, 0, 0, 0, 24, 0, -108, 0, 0, 0, -26, 0, 0, 0, 102, 0, 116, 0, 0, 0, -20, 0, 0, 0, -32, 0, -38, 0, 0, 0, 8, 0, 0, 0, -16, 0, -64, 0, 0, 0, 100, 0, 0, 0, 60, 0, 74, 0, 0, 0, 96, 0, 0, 0, 94, 0, 14, 0, 0, 0, -54, 0, 0, 0, 60, 0, 8, 0, 0, 0, 8, 0, 0, 0, -14, 0, 36, 0, 0, 0, 32, 0, 0, 0, -110, 0, -16, 0, 0, 0, -28, 0, 0, 0, 20, 0, -4, 0, 0, 0, 56, 0, 0, 0, -20, 0, 60, 0, 0, 0, -50, 0, 0, 0, 60, 0, 90, 0, 0, 0, -96, 0, 0, 0, -62, 0, -46, 0, 0, 0, 28, 0, 0, 0, -92, 0, -12, 0, 0, 0, 26, 0, 0, 0, 86, 0, 72, 0, 0, 0, -6, 0, 0, 0, -46, 0, -152, 0, 0, 0, 0, 0, 0, 0, -14, 0, 38, 0, 0, 0, -4, 0, 0, 0, -8, 0, -120, 0, 0, 0, -48, 0, 0, 0, -128, 0, 102, 0, 0, 0, 84, 0, 0, 0, 44, 0, 104, 0, 0, 0, -104, 0, 0, 0, 104, 0, -24, 0, 0, 0, -136, 0, 0, 0, -96, 0, 212, 0, 0, 0, 28, 0, 0, 0, 10, 0, -8, 0, 0, 0, -76, 0, 0, 0, 30, 0, 142, 0, 0, 0, -188, 0, 0, 0, -196, 0, 188, 0, 0, 0, -50, 0, 0, 0, 12, 0, -18, 0, 0, 0, -164, 0, 0, 0, 72, 0, -36, 0, 0, 0, 32, 0, 0, 0, -100, 0, 44, 0, 0, 0, 12, 0, 0, 0, -54, 0, 64, 0, 0, 0, -36, 0, 0, 0, 30, 0, 136, 0, 0, 0, 72, 0, 0, 0, 18, 0, -22, 0, 0, 0, 16, 0, 0, 0, 68, 0, 64, 0, 0, 0, 36, 0, 0, 0, 96, 0, 22, 0, 0, 0, 52, 0, 0, 0, -54, 0, 196, 0, 0, 0, -14, 0, 0, 0, 68, 0, 14, 0, 0, 0, -90, 0, 0, 0, -14, 0, -112, 0, 0, 0, 18, 0, 0, 0, -62, 0, 168, 0, 0, 0, -32, 0, 0, 0, 0, 0, 18, 0, 0, 0, -28, 0, 0, 0, -140, 0, 148, 0, 0, 0, -172, 0, 0, 0, -200, 0, 20, 0, 0, 0, -52, 0, 0, 0, -64, 0, 0, 0, 0, 0, 40, 0, 0, 0, -80, 0, 44, 0, 0, 0, 96, 0, 0, 0, 38, 0, -136, 0, 0, 0, -40, 0, 0, 0, -10, 0, -20, 0, 0, 0, 44, 0, 0, 0, -84, 0, 2, 0, 0, 0, -88, 0, 0, 0, 76, 0, -52, 0, 0, 0, 22, 0, 0, 0, 100, 0, 132, 0, 0, 0, 4, 0, 0, 0, 210, 0, -72, 0, 0, 0, -36, 0, 0, 0, -48, 0, -44, 0, 0, 0, 38, 0, 0, 0, -150, 0, 108, 0, 0, 0, -46, 0, 0, 0, -122, 0, -24, 0, 0, 0, -84, 0, 0, 0, -4, 0, 174, 0, 0, 0, -80, 0, 0, 0, 36, 0, -60, 0, 0, 0, -44, 0, 0, 0, 8, 0, -88, 0, 0, 0, -104, 0, 0, 0, -226, 0, 102, 0, 0, 0, 24, 0, 0, 0, -20, 0, 8, 0, 0, 0, -6, 0, 0, 0, 194, 0, 112, 0, 0, 0, 28, 0, 0, 0, 148, 0, 8, 0, 0, 0, 44, 0, 0, 0, 0, 0, -18, 0, 0, 0, 96, 0, 0, 0, 40, 0, 44, 0, 0, 0, 54, 0, 0, 0, 104, 0, -108, 0, 0, 0, 108, 0, 0, 0, 160, 0, 104, 0, 0, 0, -144, 0, 0, 0, 228, 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": "280.2.g.b", "char_is_minimal": true, "conrey_index": 169, "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [-1, -1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [2, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, -2, 0, -2, -1], [0, 0, 0, 0, 0, 0], [-3, -1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [-2, -1, -1, -2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, -2, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0], [-2, -2, 0, -1, -1, -1], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, -6, 1], [0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 1, 0, 2, -1], [0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0], [0, -1, -1, -5, 0, 0], [0, 0, 0, 0, 0, 0], [6, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 2, -1, 2, -2, 2], [0, 0, 0, 0, 0, 0], [0, -3, 3, 0, -2, 3], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [6, 1, 1, -3, 0, 0], [0, 0, 0, 0, 0, 0], [0, -2, 2, 0, -2, 4], [0, 0, 0, 0, 0, 0], [-2, 3, 1, 0, 4, -1], [0, 0, 0, 0, 0, 0], [0, -2, 2, 0, 6, 2], [0, 0, 0, 0, 0, 0], [-2, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0], [8, -1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0], [-5, -1, 1, -4, -5, 1], [0, 0, 0, 0, 0, 0], [0, -2, 2, 0, -4, -2], [0, 0, 0, 0, 0, 0], [-4, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0], [0, -2, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0], [-6, -2, 0, 2, 2, 3], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 2, -1], [0, 0, 0, 0, 0, 0], [-4, 1, 1, 5, 0, 0], [0, 0, 0, 0, 0, 0], [3, -2, -2, -6, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 1, 0, 6, 6], [0, 0, 0, 0, 0, 0], [2, 1, 3, -1, -4, 2], [0, 0, 0, 0, 0, 0], [0, 3, -3, 0, -6, -3], [0, 0, 0, 0, 0, 0], [-2, -2, -2, -6, 0, 0], [0, 0, 0, 0, 0, 0], [2, 2, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, -2, 0, -8, -2], [0, 0, 0, 0, 0, 0], [-1, -2, 2, -1, 7, 3], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, -4, -3], [0, 0, 0, 0, 0, 0], [0, -4, -4, 2, 0, 0], [0, 0, 0, 0, 0, 0]]}