# Stored data for newform 350.2.e.f, downloaded from the LMFDB on 25 April 2024. {"label": "350.2.e.f", "space_label": "350.2.e", "level": 350, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518273048314206, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 710933321913564879, "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": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "1.910", "prec": 17}, {"__RealLiteral__": 0, "data": "0.148", "prec": 17}, {"__RealLiteral__": 0, "data": "10.874", "prec": 20}, {"__RealLiteral__": 0, "data": "0.785", "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]]}