# Stored data for newform 370.2.g.a, downloaded from the LMFDB on 24 April 2024.
{"label": "370.2.g.a", "space_label": "370.2.g", "level": 370, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 412350415218, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 752187711420176950, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [2, 2, 1]]], "qexp_display": "q+iq^{2}+(-1-i)q^{3}-q^{4}+(2+i)q^{5}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 185, "char_orbit_label": "g", "char_is_real": false, "Nk2": 1480, "analytic_conductor": 2.9544648747873743, "hecke_ring_index": 1, "level_radical": 370, "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": "0.233", "prec": 17}, "analytic_rank_proved": true, "char_values": [370, 4, [297, 261], [3, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 37], "conrey_indexes": [43, 327], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "2.057", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.813", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "92.483", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c4", "trace_display": [0, -2, 4, 2], "traces": [0, 2, 0, -2, -2, 4, 2, 2, 0, 0, -2, 0, 2, 0, -2, -2, 2, 8, 2, 10, -4, 0, -4, 0, -2, 6, 4, -8, -2, 6, 6, 14, 0, 4, 0, 2, 0, -12, -10, -4, 2, 0, 4, 0, 0, 2, 0, -14, -2, 0, -8, -8, 0, 2, -8, -4, 2, 0, 6, 2, 2, -6, -14, 2, -2, 4, 4, -6, -8, 0, -6, -16, -2, -18, 2, 2, -10, -4, -4, 2, 4, 10, 0, -10, 0, 16, 8, -12, 4, -10, 4, 4, 0, 0, 14, 10, 2, 16, 10, 4, -6, 0, 8, 28, -4, 4, 2, -22, 8, 14, -8, 10, 2, -24, 20, 0, -6, -4, -2, 8, -6, 14, 6, 0, -14, 4, 2, -6, 0, -8, 8, -26, -4, 0, -6, -24, 0, -14, 0, -8, -2, 0, 0, 8, 0, 18, 18, -10, 12, 0, 14, 0, 10, 0, -4, 14, 4, 18, -2, -4, -2, 0, 0, 4, 0, 12, -10, -44, -4, 18, -8, 10, 0, 6, 0, -2, 0, 0, -10, -18, -2, -44, 4, 0, 0, -22, 28, 0, 14, -16, -30, 2, 2, 0, 0, -12, 0, 26, 0, 22, 8, 12, 16, 12, 8, 0, 0, 0, 0, -20, 8, 8, -2, 16, 22, 8, 8, 0, -14, 0, 4, 0, -14, 6, -2, 8, 0, 12, 0, 0, 0, 8, -6, 14, 0, -14, -2, 0, -8, -6, -2, 2, 0, 14, 6, 10, 0, 20, 14, 20, -22, -10, -2, 0, 6, -8, 2, 24, -8, -10, -4, -6, 26, 22, -4, 6, -20, 20, 6, 0, -8, 16, 8, -8, 14, -16, 0, 0, 0, 14, 6, 2, -28, -28, 16, 20, 0, 0, 2, -2, 6, -16, 18, -38, -10, 2, -2, -16, -48, 0, -2, 8, 20, -16, 10, -6, 8, -30, 4, -28, -42, -34, 4, 0, -18, 6, -2, 38, 0, 12, -4, 0, 0, 40, -10, 16, 0, 0, 0, 0, 4, -46, 10, -2, 0, -18, 0, -18, 0, 24, -16, -28, 10, 24, -8, 0, -6, 0, 12, 0, -14, 16, -4, 0, 4, -32, 10, 0, -18, 0, -4, 0, 0, -14, -4, -18, -12, 10, 0, 0, 16, 4, 0, 30, -16, 18, -14, -12, 0, 0, -10, 0, 2, 0, -2, -12, 36, -8, -16, -50, -4, 0, -10, 0, -26, 2, -4, 30, 22, 20, 6, -14, 0, 28, 0, 20, 0, 4, -8, -26, 0, 0, -28, 0, 0, -30, 4, 8, -20, 0, -4, 18, 0, -14, -2, 24, -16, 0, 22, -8, 16, -2, -8, -22, -28, -24, -14, 0, -36, 54, 8, -10, 16, -42, -10, -30, 6, 48, -2, 22, 6, 0, 24, -20, 0, 12, -20, 0, -24, -32, 0, 2, 0, 0, 6, 28, -14, 28, 4, -12, 42, 0, 2, 16, 4, -10, -8, -2, 6, 26, 6, -4, 2, 0, -14, 32, -14, 4, -6, -4, 20, 24, 0, 24, 20, 8, 14, -16, 0, -26, -4, 44, 10, 0, -2, 16, 0, -18, 6, -60, 24, 0, 0, -80, 0, 56, 8, 28, 14, 0, -8, 0, 6, 0, 26, 16, -22, 56, 4, 46, 2, 2, 0, 0, 0, -22, 6, 36, 48, 20, 24, -6, 0, 44, 0, 14, 0, 0, 14, -6, -12, 60, 0, 0, -20, 6, 8, 0, 14, -16, 2, 16, 2, 0, 0, -48, 0, 10, 0, 14, 40, 40, -8, -4, 0, 0, 0, 24, 0, -36, -18, -20, 16, 4, -18, -8, -38, 0, 10, 0, -6, 0, -12, 58, 16, 8, 0, -44, 0, 0, -14, -84, 8, 6, 0, 28, -16, 0, -10, -12, 18, -28, 0, -34, -30, 0, 4, 30, 28, 8, -14, 0, 34, -20, -4, -14, 68, 40, -18, -48, 2, 38, 2, -8, 38, -6, 4, -20, -12, 0, 2, -36, -44, -28, 0, -24, -40, 0, 0, -4, 12, 28, -4, -24, 28, -26, 0, -18, 28, -40, -12, 42, -46, -16, 10, -20, -12, 0, 44, -12, -6, 12, 4, -46, -18, -56, -18, -26, -24, 16, 8, -12, -28, 0, -10, -14, 24, 24, 0, -4, 0, 0, -6, 4, -24, -16, 0, 0, 48, 0, 2, -38, -16, -50, 0, -28, 0, 16, 0, 54, 16, 2, 10, 0, 16, 16, 18, 0, 44, 0, 2, 28, -62, -4, 44, 42, 14, 0, -4, 0, 54, 0, 0, 46, -10, -30, 0, -12, 0, 8, 22, -40, 0, 46, -28, -48, -30, 10, 0, 0, 26, 0, -14, 0, 12, 20, 16, -56, -60, 0, 30, 0, -12, 0, -2, 8, 0, 4, -2, 78, -4, -24, 0, 50, 0, -14, 0, -4, 50, 0, 12, 0, 0, 0, 0, 18, -52, 26, -26, 0, -6, -24, 0, -12, 30, -8, -22, 0, 20, -56, -8, 10, 14, 36, -12, 0, 28, -48, -16, -66, -10, -88, -12, -16, 24, 8, -8, 40, -26, -4, 0, 60, -28, 62, 0, 28, -4, -36, 0, 30, -10, 20, 0, 0, -8, -88, 20, -112, 52, 48, -8, 0, -18, -4, -8, 36, -14, 14, 2, 28, -32, 0, -16, -88, 12, 30, -22, -96, 8, 66, -8, 0, 2, -10, -8, 6, -22, 2, 0, -4, 12, 12, 14, 0, 0, -18, 0, 66, 54, 76, -4, 0, 0, -76, 0, 4, 42, -46, 14, 0, -10, 0, -6, 0, 48, -54, 2, 0, -22, 84, -8, 8, 0, -16, 0, -88, -20, -84, -12, -16, 4, 82, 0, -20, 0, -12, 0, 0, -32, 14, 0, 60, 2, 0, -8, -28, -32, 0, 6, -68, 56, 50, -14, 0, 0, -16, 0, -22, 0, -68, 14, 100, 36, 0, 2, -32, 0, -20, 0, -36, -70, -76, 8, -2, 2, 6, 6, 0, -26, 0, 2, 0, -24, -22, -2, 36, 0, 68, 0, 0, -16, 104, -14, -8, 0, -28, -6, 0, 4, -20, -10, 14, 0, -42, 0, 26, 24, -28, -20, 0, -4, 6, -14, 92, 16, 66, -20, 40, -26, 56, 22], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 185, 6, 1, 4, 0]], "char_orbit_index": 7, "prim_orbit_index": 6, "minimal_twist": "370.2.g.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], [0, 1], [-1, -1], [-1, 0], [2, 1], [1, -1], [1, 1], [0, -1], [0, -1], [-1, 2], [0, 2], [1, 1], [0, -2], [-1, 1], [-1, -3], [1, 0], [4, 0], [1, 0], [5, 5], [-2, -1], [0, -2], [-2, 0], [0, 0], [-1, 1], [3, 4], [2, 0], [-4, 4], [-1, -1], [3, -3], [3, -1], [7, 7], [0, 1], [2, -2], [0, 4], [1, 3], [0, 1], [-6, -1], [-5, 5], [-2, 2], [1, -2], [0, 0], [2, 0], [0, -4], [0, -2], [1, -2], [0, 0], [-7, -7], [-1, -1], [0, -5], [-4, 3], [-4, -4], [0, 2], [1, -1], [-4, -4], [-2, 4], [1, -1], [0, -10], [3, 3], [1, 1], [1, 3], [-3, -3], [-7, 7], [1, -1], [-1, 0], [2, -4], [2, 2], [-3, 3], [-4, 0], [0, 0], [-3, 1], [-8, 0], [-1, 0], [-9, -9], [1, -6], [1, -7], [-5, -5], [-2, 2], [-2, -2], [1, 1], [2, 1], [5, 0], [0, 0], [-5, 5], [0, 2], [8, 4], [4, 0], [-6, 0], [2, 0], [-5, 5], [2, 1], [2, -2], [0, 0], [0, -14], [7, -7], [5, 15], [1, -1], [8, 0], [5, 0], [2, 0], [-3, -4]]}