# Stored data for newform 350.2.e.g, downloaded from the LMFDB on 19 April 2024. {"label": "350.2.e.g", "space_label": "350.2.e", "level": 350, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021872675684702, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 245128741540716460, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [9, 3, 1]], [11, [0, 1]], [13, [-2, 1]], [17, [4, 2, 1]]], "qexp_display": "q+\\zeta_{6}q^{2}+(-3+3\\zeta_{6})q^{3}+(-1+\\zeta_{6})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1400, "analytic_conductor": 2.7947640707448134, "hecke_ring_index": 1, "level_radical": 70, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [350, 3, [127, 101], [3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [51, 151], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "1.910", "prec": 17}, {"__RealLiteral__": 0, "data": "0.326", "prec": 17}, {"__RealLiteral__": 0, "data": "10.874", "prec": 20}, {"__RealLiteral__": 0, "data": "2.727", "prec": 17}, {"__RealLiteral__": 0, "data": "97.378", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, -3, 0, -5], "traces": [0, 2, 1, -3, -1, 0, -6, -5, -2, -6, 0, 0, -3, 4, -4, 0, -1, -2, 6, 2, 0, 3, 0, -1, 3, 0, 2, 18, 1, -2, 0, -10, 1, 0, -4, 0, 12, -8, -2, -6, 0, -6, 15, -10, 0, 0, 1, 8, 6, 11, 0, -6, -2, -6, 9, 0, 5, -12, -1, -2, 0, 9, -20, 24, 2, 0, 0, -7, -2, 6, 0, 12, 6, -10, 8, 0, -4, 0, -12, 10, 0, -9, -3, 18, 12, 0, -5, 3, 0, 7, 0, -10, 2, -30, -8, 0, 3, 0, 13, 0, 0, 15, 6, -11, -4, 0, -12, -7, -9, -5, 0, 48, 4, 20, -6, 0, 1, -12, -4, 2, 0, 11, -9, 9, -10, 0, -6, 16, 1, 15, 0, -20, 0, -8, -14, 0, 2, 16, 3, -16, 0, -48, 6, 0, -6, 0, -20, 6, 16, 15, 0, -6, -2, 24, 0, 0, -6, -12, -10, -18, 0, 4, -18, 12, 3, 0, 9, 18, -3, -18, 0, 12, 5, 12, 6, 0, 0, -6, -7, 26, 0, 10, -8, -54, 1, 0, 30, 0, -16, -45, 0, 20, -3, 20, 0, 0, 2, 16, 0, -12, 0, -21, 30, 5, 12, 0, 11, -6, -2, 0, 0, -36, -6, -18, 7, 0, -18, 10, -10, -30, 0, -4, 24, 16, -1, 0, 10, 12, 6, -10, 0, 0, 2, -14, 12, 0, -2, -60, 10, -20, 0, -18, -11, 0, -18, 0, 18, 4, 10, -27, 0, -20, -30, 0, 8, 0, -1, 12, 30, 32, 0, 6, 20, 21, 0, 0, 2, -42, -7, -5, 0, -6, 4, 6, 32, 0, -3, -26, -8, 120, 0, 36, -24, 8, -6, 0, 0, 15, -12, 13, 0, 0, -10, -48, -33, 0, 8, 0, -15, -2, 0, 25, -12, 45, 2, 0, 12, 38, 0, 66, 0, -6, 6, 8, -24, 0, -20, 22, 18, 0, 0, 42, -1, -8, -9, 0, -12, -15, 6, -32, 0, -14, -9, -48, 9, 0, -15, 4, -9, -30, 0, 0, 24, -20, 10, 0, -12, 21, 3, -18, 0, 36, 0, -6, 6, 0, -14, 24, 52, 14, 0, 15, 5, -66, 2, 0, -27, -23, -1, 18, 0, 6, 60, 8, 0, 0, -8, -4, -36, -4, 0, -24, -20, -9, -6, 0, 40, 30, 0, 18, 0, 4, -11, 120, 8, 0, 0, -32, -24, 30, 0, -3, 21, -20, 15, 0, 4, 0, 6, 17, 0, 48, 22, 2, -12, 0, 2, 24, 0, -80, 0, 62, -18, 48, 6, 0, -36, -36, 14, 0, 0, -32, -9, 28, 50, 0, -5, 2, 30, -8, 0, -78, -8, -3, -24, 0, 8, -90, -5, 46, 0, 0, -10, -18, 24, 0, 12, 32, 10, -18, 0, -28, 0, -50, 1, 0, 14, 1, 24, 7, 0, -36, 2, 0, -30, 0, 8, 72, -10, -18, 0, -16, -36, -15, -22, 0, 0, 4, -9, -72, 0, -36, 9, 2, -4, 0, 20, -30, -54, -16, 0, -27, -10, 10, -24, 0, 0, 27, -8, -35, 0, 10, -2, 18, -12, 0, 15, 0, -8, -72, 0, 18, -6, 4, 40, 0, 42, -20, 0, 22, 0, 24, 10, -12, -21, 0, 7, 78, -10, 0, 0, -5, 6, -15, 2, 0, 30, -74, 16, 54, 0, -2, -6, -40, -52, 0, 8, -4, 60, -20, 0, 0, 18, 11, 24, 0, 16, 9, -12, 18, 0, 10, 0, -120, 12, 0, -6, -16, -13, 60, 0, -45, 0, 0, 10, 0, -24, -56, -39, -40, 0, -24, -8, 42, 0, 0, -30, -36, 2, -36, 0, -44, 20, 84, -6, 0, -45, 5, 4, -3, 0, 16, -12, 18, 19, 0, 0, -40, 33, 20, 0, -9, -12, -28, 12, 0, -8, 0, -12, 32, 0, -48, -10, 54, -22, 0, 36, 22, 0, -36, 0, 35, 21, 40, -5, 0, -4, 21, 9, 0, 0, 120, -24, 42, 15, 0, 3, 120, 8, 60, 0, 41, 14, -12, -18, 0, -96, 1, -9, -24, 0, 0, -12, -40, 2, 0, 9, -2, -60, 0, 0, 36, 0, 25, 12, 0, -37, 60, 5, -12, 0, 20, -24, 0, 42, 0, -3, 6, -9, 84, 0, -2, 18, 16, 0, 0, -12, -15, 12, 9, 0, 60, -7, 20, -6, 0, 26, 30, -14, -20, 0, 44, 30, -54, -5, 0, -33, 58, 10, -54, 0, 10, 27, -16, -46, 0, -2, 0, -18, 32, 0, -24, 30, 6, 30, 0, -8, -54, 0, 28, 0, -4, 8, 30, -2, 0, 9, 12, -2, 0, 0, 50, -48, 5, -40, 0, 9, -4, -3, 68, 0, -72, 20, -18, -30, 0, 0, -120, 36, -6, 0, 0, 2, -18, -13, 0, 60, 21, -8, 63, 0, -50, 0, 18, 32, 0, -12, 16, 24, -32, 0, 42, 3, 0, 42, 0, -40, -15, -15, -25, 0, 12, -1, 36, 0, 0, -6, -10, 34, 48, 0, 42, -48, -45, 11, 0, 10, 74, -6, -34, 0, -78, 4, 4, 48, 0, 0, -90, -40, 64, 0, -56, 31, -54, 18, 0, 96, -44, 12, 24, 0, -8, -18, 20, 9, 0, 7, -4, 0, 0, 0, -9, -64, -11, 9, 0, 14, -78, 40, 0, 0, -14, 5, 0, 4, 0, 60, -14, 8, 72, 0, -6, -12, -8, -4, 0, 3, 9, -48, -40, 0, 0, -8, -16, -45, 0, -4, 12, 23, 10, 0, -12, 0, -15, -20, 0, 18, -25, 12, -180, 0, 16, 6, 0, -32, 0, 20, 80, -36, -26, 0, -57, -14, 24, 0, 0, -25, -66, -1, -27, 0, 26, 28, -18, -1, 0, 12, 112, 35, -48, 0, -14, 36, 3, 4, 0, 0, -3, 30, -20, 0, -132, -2, -72, 36, 0, 10, 0, -36, -16, 0, -69, 16, -42, -18, 0, -12, -34, -11, 12, 0, 0, 0, 40, 8, 0, 9, 36, -36, 0, 0, 60, -18, 25, -9, 0, 4, 120, -8, 5, 0, 26, 10, 84, -24, 0, -27, 34, 16, -72, 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, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "70.2.i.a", "char_is_minimal": true, "conrey_index": 51, "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], [-3, 3], [-1, 1], [0, 0], [-3, 0], [-3, 1], [-1, 0], [0, -6], [0, 0], [0, 0], [0, -3], [2, 0], [-1, -2], [0, 0], [0, -1], [-2, 2], [6, -6], [0, 2], [0, 0], [6, -9], [0, 0], [0, -1], [3, -3], [0, 0], [0, 2], [9, 0], [2, -3], [-1, 0], [0, 0], [-10, 10], [1, -1], [0, 0], [-2, 0], [0, 0], [6, 0], [0, -8], [-2, 2], [-6, 6], [0, 0], [-3, 0], [9, -3], [-5, 0], [0, 0], [0, 0], [1, -1], [0, 8], [3, 0], [8, -5], [0, 0], [0, -6], [-2, 2], [-6, 6], [0, 9], [0, 0], [3, -1], [-6, 0], [0, -1], [-2, 2], [0, 0], [0, 9], [-10, 0], [6, 12], [1, 0], [0, 0], [0, 0], [-7, 7], [0, -2], [3, 0], [0, 0], [6, 0], [0, 6], [-10, 10], [8, -8], [0, 0], [-2, 0], [0, 0], [-6, 0], [0, 10], [0, 0], [-9, 9], [0, -3], [9, 0], [3, 6], [0, 0], [0, -5], [3, -3], [0, 0], [0, 7], [0, 0], [-6, 2], [1, 0], [0, -30], [-8, 8], [0, 0], [0, 3], [0, 0], [5, 3], [0, 0], [0, 0]]}