# Stored data for newform 80.2.j.a, downloaded from the LMFDB on 25 April 2024.
{"label": "80.2.j.a", "space_label": "80.2.j", "level": 80, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 618508845136, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 637039166408952706, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4, 0, 1]]], "qexp_display": "q+(1-i)q^{2}+2iq^{3}-2iq^{4}+(1+2i)q^{5}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 80, "char_orbit_label": "j", "char_is_real": false, "Nk2": 320, "analytic_conductor": 0.638803216170243, "hecke_ring_index": 1, "level_radical": 10, "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": "0.251", "prec": 17}, "analytic_rank_proved": true, "char_values": [80, 4, [31, 21, 17], [2, 1, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [43, 67], "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": "1.924", "prec": 17}, {"__RealLiteral__": 0, "data": "0.172", "prec": 17}, {"__RealLiteral__": 0, "data": "10.966", "prec": 20}, {"__RealLiteral__": 0, "data": "2.261", "prec": 17}, {"__RealLiteral__": 0, "data": "88.250", "prec": 20}], "related_objects": ["Genus2Curve/Q/6400/g"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c4", "trace_display": [2, 0, 2, -6], "traces": [0, 2, 2, 0, 0, 2, 4, -6, -4, -2, 6, -2, 8, -4, -12, -8, -8, 2, -2, 6, 8, 12, -4, -2, 8, -6, -4, 0, -12, 14, -4, 0, -8, 4, 4, 6, 0, -12, 12, 0, 4, 0, 0, 8, -4, -2, 0, 14, 0, 0, 2, -4, 0, 0, 8, 2, 0, -12, 0, -6, 8, -2, 4, 6, 0, -4, 0, 8, 4, -4, -12, 0, 4, -6, -12, -16, 12, 0, -8, -16, -8, -22, -8, 0, -24, -2, 8, 28, 0, 12, -6, 12, 4, -8, 0, -6, -16, -22, 22, 2, 16, -10, 0, -10, 8, 36, 16, 0, 16, -10, -4, 0, 24, 26, 0, -6, -28, 4, 0, 0, 24, 0, -4, 16, 8, -22, 12, 14, 16, 0, -12, -14, -8, 0, 8, -16, 0, 18, -8, 18, -36, 28, 0, 4, 8, 42, -12, -44, 0, -2, -28, 16, 0, -2, 12, -8, -16, 0, -16, -32, -24, 12, -22, 0, -16, 12, 4, -6, -48, -18, 4, -6, 0, -12, 56, 42, 8, -12, 12, -10, -8, 6, 24, 4, 8, -12, -8, 0, -28, 24, 12, 0, -32, -30, -44, 16, 44, 12, 4, 0, 28, 0, 0, -84, 8, 16, 0, 2, 16, 0, 48, -38, 32, 0, -12, 8, 16, 12, 0, 12, -12, -4, -24, 18, 48, 6, 0, 24, 24, -2, -8, -24, -56, 18, 4, 42, 12, 0, -12, 0, 32, -28, -18, 0, -4, -44, 16, -12, 8, -8, -26, 22, 12, 4, 0, -12, 32, 26, 16, 36, -16, -14, 0, 14, -16, -32, -36, 0, 0, -2, -8, 0, -8, -24, 0, 14, -8, 36, 0, 0, -48, 0, 56, 24, 0, -36, 8, -24, 8, 0, 56, 44, -12, 0, -44, -18, 24, 8, -4, 4, -24, -24, 16, -20, -24, 2, -4, -8, 24, -20, -4, 32, -16, 26, 40, -6, 0, 0, -32, -28, -32, 24, 12, 0, 0, 12, -28, -20, -16, -84, 16, -42, 8, 12, -12, 8, -48, -22, -18, 52, 12, 4, -12, 24, -16, 4, -12, 0, 56, 6, 36, 0, 16, 26, -24, 0, 0, 24, -20, 0, -4, 0, 0, 36, 24, 6, 0, -42, 8, 0, -36, 48, 0, 0, -4, 8, -56, -28, 0, -30, 36, 28, 36, 10, -32, -24, 0, -8, -44, 46, 8, -4, 44, -28, 12, -16, 4, 0, 20, 72, 24, -4, 16, 0, 20, -22, -84, 12, 16, 76, 8, 36, 20, 36, 0, -8, 16, 36, -12, -34, 24, -10, 0, -14, 32, -14, 0, 0, -24, -8, 24, 0, 0, 10, 0, -28, 20, -12, 0, 0, -16, 0, -8, -8, -48, 12, 36, 4, 48, 0, -2, -8, -52, 0, 24, -12, 48, -14, -4, -8, -4, -42, -24, -38, -56, -8, 36, -56, 0, -24, 56, -80, 24, -8, -32, -42, -24, 0, 0, 64, 16, 24, -28, 0, -36, 22, -20, -30, 0, 56, -22, -18, 0, 28, -24, -2, 0, 0, -8, -58, -8, 12, 44, -58, 0, -30, 4, 0, -28, -34, -16, 0, 32, -24, 52, -30, 32, -28, 72, 0, -8, 0, 0, 40, 28, 12, 0, -4, -16, 0, -16, 6, -72, 0, 24, 24, -16, 20, 0, 22, 16, 30, -60, 12, -16, -30, 0, 56, -36, 2, 12, 84, 0, 48, 36, 48, -36, 0, -4, -16, -24, 8, 32, 0, 56, 78, 24, 66, 0, 12, -48, -50, 8, -72, 0, -2, 0, 18, -30, -60, 28, 12, 0, 16, 0, 4, 24, 0, 0, -12, -24, 0, 48, 34, 0, 24, -4, -40, 0, 0, 8, 0, -48, -8, 0, 36, -40, 46, -48, 0, -4, -28, -4, 0, -8, 16, 24, 50, -40, -14, 8, -8, 32, -36, 0, -14, 52, 24, 80, -12, 12, 48, 32, -76, 16, 42, 0, 0, -28, 0, -16, -60, 24, 0, 0, -32, 12, -30, 44, 12, -4, 24, -56, -4, -40, -42, 0, 6, -84, 22, 8, -50, -84, 8, 8, 72, 12, 0, -12, -36, 24, 0, 0, 2, -44, -32, 0, -84, 104, 0, 16, 0, 0, -8, -12, 54, 0, 4, -32, 0, -8, 42, 0, 0, 4, 54, 0, 8, 0, -36, -12, -26, -16, -36, 16, -28, 0, 60, -24, -2, 0, 16, -24, -4, 24, -4, -20, 0, -28, 64, 8, 60, -2, 0, -12, 14, 36, -14, 0, -26, -12, 8, -8, -60, 0, -44, 0, -8, 8, -42, -48, 24, 0, 62, 16, 2, 8, 0, -8, -36, -36, 0, -56, -44, 0, 16, -48, 4, 0, 0, 48, 0, 56, 60, 72, 2, 20, 12, 0, 0, -12, -52, 60, 0, -8, -16, 0, -72, 92, 24, -16, 0, -4, 56, 0, -80, -56, -8, 0, 28, -48, -156, 0, 4, -64, -32, 40, 0, 72, 28, -8, -12, -4, 0, 32, 12, -8, -4, 40, 52, -66, -18, 0, 120, 24, 56, 16, 24, 76, -12, -16, 30, 72, -42, 40, 4, 36, 0, -4, 54, -4, 0, 0, -22, 72, 6, -24, -16, -68, 0, -48, 0, 0, -64, 76, -18, 0, -54, 0, 0, -12, 12, 0, 0, 12, 6, -24, -54, 0, -38, 32, -48, 4, 10, -32, -12, 0, 60, -24, 16, 56, -16, 40, 22, -12, 54, -24, 0, 52, -48, -8, 92, -22, 0, -8, 12, -8, -46, -48, -84, 36, 22, 36, 84, 0, 10, 0, 8, 48, 28, -16, -16, 0, 48, -104, 18, 32, 0, 0, 10, 24, 0, 48, 4, 0, 12, -4, 84, 0, 0, 8, 0, -84, 0, 0, 36, -76, 10, 0, 0, -24, -66, 36, 0, -56, 8, -8, -6, -48, -52, 28, -2, -80, 8, 24, 72, -16, 56, -64, 12, -36, -32, -24, -62, -16, -72, 0, 0, 64, -108, -32, 54, 24, 0, 0, -90, 24, 66, -36, -24, -44, 62, -40, -108, -60, 32, 8, 34, 56, -12, 44, 10, -36, -10, -32, 12, 28, 0, -24, -8, 4, 0, -16, 84, 0, -40, 0, 44, -116, 0, 36], "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, 80, 10, 1, 4, 0]], "char_orbit_index": 10, "prim_orbit_index": 10, "minimal_twist": "80.2.j.a", "char_is_minimal": true, "conrey_index": 43, "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], [1, -1], [0, 2], [0, -2], [1, 2], [2, 2], [-3, -3], [-2, -2], [-1, 0], [3, 1], [-1, -1], [4, 0], [-2, 0], [-6, 0], [-4, 2], [-4, 0], [1, 1], [-1, 1], [3, 3], [4, -2], [6, -6], [-2, 0], [-1, 1], [4, -4], [-3, 4], [-2, 2], [0, 4], [-6, 6], [7, -7], [-2, 6], [0, 2], [-4, 4], [2, -2], [2, 0], [3, -9], [0, 2], [-6, 0], [6, 0], [0, -4], [2, -6], [0, -4], [0, -12], [4, 0], [-2, 2], [-1, -2], [0, 2], [7, -7], [0, -8], [0, 11], [1, 7], [-2, 2], [0, 4], [0, 8], [4, 4], [1, -3], [0, 12], [-6, 6], [0, -14], [-3, 3], [4, 8], [-1, -1], [2, 2], [3, 3], [0, 8], [-2, -4], [0, -4], [4, 0], [2, -2], [-2, -2], [-6, -12], [0, 0], [2, 2], [-3, -3], [-6, 6], [-8, -6], [6, -6], [0, 6], [-4, -4], [-8, 0], [-4, -8], [-11, 0], [-4, -4], [0, 2], [-12, -12], [-1, 3], [4, -4], [14, 14], [0, 4], [6, 0], [-3, -1], [6, 6], [2, 2], [-4, 0], [0, -14], [-3, 9], [-8, -8], [-11, -11], [11, 11], [1, 1], [8, 6]]}