# Stored data for newform 150.2.g.b, downloaded from the LMFDB on 23 April 2024. {"label": "150.2.g.b", "space_label": "150.2.g", "level": 150, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504011977785494, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 1569939420183803312, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [-2, 1]]], "qexp_display": "q+(1-\\zeta_{10}+\\zeta_{10}^{2}-\\zeta_{10}^{3})q^{2}+\\zeta_{10}^{3}q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 25, "char_orbit_label": "g", "char_is_real": false, "Nk2": 600, "analytic_conductor": 1.1977560303192059, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "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": "0.008", "prec": 17}, "analytic_rank_proved": true, "char_values": [150, 5, [101, 127], [5, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [31, 61, 91, 121], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "4.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "52.292", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1259.576", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [1, 1, 5, 8], "traces": [0, 4, 1, 1, -1, 5, -1, 8, 1, -1, 5, -2, 1, -6, 2, 0, -1, -12, -4, 0, 0, 2, -8, -6, 4, -5, 6, 1, -2, 0, -5, -12, -4, -8, -3, 10, -1, 13, -10, 6, 5, -12, -2, 4, 8, 5, 6, -2, 1, -12, 5, -18, -6, -21, -1, 10, 2, 20, 0, 20, -5, -2, -18, -2, -1, -15, -2, 18, 18, 6, 10, 28, 1, 14, 22, 5, -20, -4, 9, 0, 5, -1, 2, -6, 2, -15, 6, -5, 2, -5, -5, -12, -6, 12, 2, 30, -1, 18, -3, -12, -5, 38, 3, -6, -9, 0, 21, 8, 1, 30, -20, -13, -2, -21, 10, -30, 5, 9, 0, -24, 5, -33, -13, 12, -12, -25, -8, -22, 1, -4, 15, -2, 12, 0, 12, 5, -3, -32, -6, -30, 0, 12, -28, 48, -1, -10, 1, -3, 13, -30, -5, 8, -10, -12, -16, 30, -9, 58, 0, -24, -5, -12, 1, -6, -12, -10, 6, -12, 8, -23, -30, 0, 4, 29, -10, -10, -12, -20, 0, -10, -5, 38, 12, -13, 6, -20, 18, -24, -12, 2, 20, 8, 1, 14, -18, 0, 3, 23, 2, 20, 5, 12, 27, 0, 12, -15, 6, 24, 9, 0, -10, 8, 24, 22, -18, 0, -1, -24, 30, 1, 10, 63, -2, 24, -8, 20, 6, -12, 0, 45, 0, -16, 10, 29, 6, 20, 20, 0, -6, 60, 5, 3, 33, -4, 13, -15, 13, -30, -18, -24, 0, -32, -2, 48, -8, -30, -1, -42, 4, 26, 0, 5, -8, 14, -2, -90, -20, 0, -12, -5, 0, -42, -12, 12, 2, 40, -24, 33, -30, -12, 10, 13, 28, -6, -22, 20, -18, -24, 1, 53, -15, -3, -1, -66, 3, 20, 2, -8, -40, -36, -20, 8, 22, -8, 0, 20, 12, -92, 16, -24, 0, -32, -6, -46, 7, 10, 0, 18, -6, -10, -5, 22, 12, 0, 4, -30, -64, -30, -13, -4, -20, 38, 24, -2, -8, 0, 2, 58, -22, 21, 30, -24, 0, -80, -4, 30, -4, 8, -5, 10, 10, 6, 2, -26, -20, 100, 0, -36, 10, -30, 0, -61, 27, -27, -12, 40, -2, 18, 24, 13, 20, -42, 12, -46, 84, 25, -28, 15, -2, 20, -20, -8, 12, -26, -1, 20, 6, -6, 3, 60, 30, 18, -3, 12, -23, 0, 8, -62, 30, 40, 20, -82, -12, 18, 8, -5, 0, 36, -12, 55, 15, 32, 24, 40, 6, -30, 6, -30, -40, 60, -10, 18, -8, -12, 6, 15, -12, -4, -22, 42, 10, -12, -4, 19, -36, 10, 30, 60, 14, -40, 20, 3, -63, 4, 2, -15, 6, 25, -2, -30, 5, 56, -21, -18, -28, -30, 0, -32, -45, -3, -30, -7, -4, 34, 5, 0, -4, -2, -6, 36, 40, 22, 20, 8, 0, 50, 36, 24, 60, -10, 0, -27, 42, 12, 27, 30, -1, -32, 2, 6, -15, 28, -13, -30, 30, -20, -12, 56, -6, -80, -25, -8, 2, -16, 2, 30, -48, -2, 8, -55, -15, 28, 1, -10, -8, -60, 6, 36, 44, -4, -30, -27, 0, 24, -12, 10, 16, 36, -8, -13, -30, -20, -40, -42, -5, 30, 12, -40, -20, 6, 5, 33, 42, 22, 12, -15, 18, -2, -32, -22, -40, 60, -6, 0, -18, -35, 30, -42, 12, -6, 10, 24, 12, 4, 12, -30, -4, -2, 12, -20, 30, -42, -42, -8, 4, -30, 4, 58, 82, 1, -10, -12, -42, 78, -14, 0, 11, -42, -3, -120, -20, 12, -2, 34, 8, -30, -25, -20, 36, 40, -5, -2, 12, 18, 18, -120, 8, -52, 0, -10, -30, -42, 3, -11, -38, 10, 4, -7, -36, -20, 0, 6, -38, -10, 6, -25, 16, 0, -22, 21, -10, 68, 0, -8, 22, -50, -24, 18, 0, -22, 0, -2, -22, -16, -12, -20, -30, 58, 1, -80, 30, 24, -6, 64, -15, 20, 13, -26, 4, -10, 20, 38, -18, 27, 6, 60, -13, 0, 8, 6, 30, -74, -2, -21, -8, 5, 2, -22, 24, 36, 15, -28, 24, -36, 10, -35, -20, 30, -6, 9, 30, -12, 4, -24, -8, -30, 0, 81, -25, 66, -10, 58, -6, 30, 8, -30, 26, 76, 20, -10, 10, 0, 5, 108, 6, 90, 40, 60, 40, -50, -5, -12, -39, -3, -22, 0, 12, -32, -18, -1, 30, 18, 22, 34, 2, 0, 6, 36, 12, -30, 35, -30, 42, -36, -12, -5, -14, -6, -24, 16, 25, 68, -12, -18, 15, -10, 2, -102, -20, 12, -30, 88, -22, 60, 8, -30, 6, 60, -4, 30, -40, -13, -1, 4, -4, 90, 42, -26, 45, -50, 0, -124, -108, 0, 3, 80, 8, 78, -12, -14, 0, -42, -8, 78, 62, -15, 20, 23, 20, 96, 5, 10, -8, -22, -18, -60, -18, 30, -8, 75, -5, -32, 10, -8, 4, 90, -3, -20, 10, 18, -10, 78, 33, -56, 36, 10, 0, -22, -6, -35, -30, -18, -6, 36, -30, 0, 0, -18, 20, -60, 10, 9, -18, 2, 8, 20, 2, -66, 24, -4, -90, -132, 22, -51, -26, -20, 22, -32, -42, -60, 20, 24, -18, 24, -1, 95, -34, 82, -24, 0, -10, -72, 15, 3, 120, -50, 26, 58, -50, -44, -20, -102, 12, -56, -27, -20, -64, -62, 13, -44, -10, -2, -6, -160, -25, -100, 2, -54, -35, 60, -5, 108, -26, -8, -24, -5, 18, 108, 28, -27, 30, 38, -10, -12, 2, -20, -30, -4, 18, -10, -30, -8, 32, 18, 24, -110, 76, 24, 0, 60, 30, 0, -66, -38, 52, -150, 6, -17, 24, 46, 30, -47, -22, -12, -20, 10, 12, -22, 0, -6, 100, -8, -6, 84, 21, -10, -60, -20, 10, -64, 5, -113, -33, 18, 3, 15, -12, -52, -12, -30, -45, 78, 1, -60, -68, -45, -22, -12, -26, 10, 0, -15, -48, 84, -12, 70, 0, 24, 30, -36, -10, 48, 12, 112, -56, 0, 6, 18, 10, 22, -25], "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, 25, 4, 1, 5, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "150.2.g.b", "char_is_minimal": true, "conrey_index": 31, "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], [1, 0, 0, 0], [1, -1, 1, -1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 2, -1, 2], [0, 0, 1, 0], [2, 0, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [2, -1, 2, 0], [2, -4, 4, -2], [0, 1, 0, 0], [-3, 3, -3, 0], [2, -2, 2, -2], [-1, 0, -2, 2], [0, -1, 0, 0], [0, -3, 6, -3], [-1, 0, 0, 0], [0, -2, -4, -2], [1, 0, 2, -2], [0, 0, 0, 2], [-2, 2, 0, -2], [-6, 6, -6, 6], [1, 0, 0, 0], [-5, 5, -5, 5], [0, 0, -3, 3], [1, -1, 1, -1], [0, 0, 0, -2], [-1, 1, 0, 3], [-1, -1, 1, 1], [0, -6, 0, -6], [-1, 0, 0, 0], [0, -2, 4, -2], [-3, 6, -3, 0], [0, 4, -2, 4], [-1, 1, -1, 1], [3, 4, 3, 0], [-2, -4, -2, 0], [0, 3, -3, 0], [1, 1, -1, -1], [-5, 3, -5, 0], [0, 0, 2, 0], [2, 0, 2, -2], [0, 2, -4, 2], [2, -2, 0, -1], [0, 0, 0, 6], [2, -2, 0, -8], [1, -1, 1, -1], [-3, 0, 0, 0], [0, 0, 0, 5], [-3, 0, 3, -3], [0, -3, 3, 0], [-9, 9, 0, 6], [0, 0, 0, -1], [6, -8, 6, 0], [0, 0, -2, 0], [6, 0, 2, -2], [0, 1, 2, 1], [8, -4, 8, 0], [-2, 2, 0, 1], [4, -7, 7, -4], [-6, 0, -6, 0], [0, -2, 0, 0], [-1, 1, -1, 1], [-3, 3, 0, -6], [-2, 4, -2, 0], [0, 6, -6, 6], [3, 0, -3, 3], [0, 0, -6, 0], [4, -2, 4, 0], [10, -10, 0, -2], [0, 0, 0, 1], [8, -5, 5, -8], [7, 0, 3, -3], [0, 0, -5, 0], [-6, 0, -2, 2], [4, -8, 8, -4], [3, -3, 0, 0], [0, 0, 0, 0], [2, -2, 0, -1], [0, 0, 1, 0], [-2, 0, -5, 5], [0, 0, 6, 0], [0, 2, 0, 0], [3, -12, 12, -3], [2, 0, 0, -2], [-1, -2, -1, 0], [2, -4, 2, 0], [-3, 2, -2, 3], [0, -2, 1, -2], [-6, 6, -6, 0], [0, 0, 6, 0], [6, 0, 6, -6], [0, -2, -6, -2], [10, 0, 0, -10], [0, 0, 0, -1], [3, -3, 0, 9], [-3, 3, -3, 3], [-2, 0, 2, -2], [0, 0, 5, 0]]}