# Stored data for newform 750.2.g.a, downloaded from the LMFDB on 19 April 2024.
{"label": "750.2.g.a", "space_label": "750.2.g", "level": 750, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 412350415598, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 80958868673058588, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [2, 1]]], "qexp_display": "q+(-1+\\zeta_{10}-\\zeta_{10}^{2}+\\zeta_{10}^{3})q^{2}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 25, "char_orbit_label": "g", "char_is_real": false, "Nk2": 3000, "analytic_conductor": 5.988780151596028, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [750, 5, [251, 127], [5, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [151, 301, 451, 601], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "4.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.487", "prec": 17}, {"__RealLiteral__": 0, "data": "52.268", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1259.454", "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, 0, -8], "traces": [0, 4, -1, -1, -1, 0, -1, -8, -1, -1, 0, -2, -1, 6, 2, 0, -1, 12, 4, 0, 0, 2, 8, 6, 4, 0, 6, -1, 2, 0, 0, -12, 4, 8, -3, 0, -1, -13, 10, 6, 0, -12, 2, -4, 8, 0, 6, 2, -1, -12, 0, -18, 6, 21, -1, 0, 2, -20, 0, 20, 0, -2, 18, 2, -1, 0, -2, -18, -18, 6, 0, 28, -1, -14, 22, 0, -20, 4, -9, 0, 0, -1, -2, 6, 2, 0, 6, 5, -2, -5, 0, -12, 6, -12, 2, 0, -1, -18, 3, -12, 0, 38, -3, 6, -9, 0, 21, -8, -1, 30, 0, -13, 2, 21, 10, 0, 5, -9, 0, -24, 0, -33, 13, -12, -12, 0, -8, 22, -1, -4, 0, -2, -12, 0, 12, 0, -3, 32, 6, -30, 0, 12, 28, -48, -1, 0, 1, 3, -13, -30, 0, 8, 10, 12, -16, 0, -9, -58, 0, -24, 0, -12, -1, 6, -12, 0, 6, 12, -8, -23, 0, 0, -4, -29, -10, 0, -12, 20, 0, -10, 0, 38, -12, 13, 6, 0, 18, 24, 12, 2, 0, 8, -1, -14, -18, 0, 3, -23, -2, 20, 0, 12, -27, 0, 12, 0, 6, -24, -9, 0, 0, 8, -24, -22, -18, 0, -1, 24, -30, 1, 0, 63, 2, -24, -8, 0, 6, 12, 0, 45, 0, -16, -10, -29, 6, 0, 20, 0, 6, 60, 0, 3, -33, 4, 13, 0, 13, 30, 18, -24, 0, -32, 2, -48, -8, 0, -1, 42, -4, 26, 0, 5, 8, -14, -2, 0, -20, 0, 12, -5, 0, -42, 12, -12, 2, 0, -24, -33, 30, -12, 0, 13, -28, 6, -22, 0, -18, 24, -1, 53, 0, -3, 1, 66, 3, 0, 2, 8, 40, -36, 0, 8, -22, 8, 0, 0, 12, 92, -16, -24, 0, -32, 6, 46, 7, 0, 0, -18, 6, -10, 0, 22, -12, 0, 4, 0, -64, 30, 13, -4, 0, 38, -24, 2, -8, 0, 2, -58, 22, 21, 0, -24, 0, 80, -4, 0, -4, -8, 5, 10, 0, 6, -2, 26, -20, 0, 0, 36, -10, -30, 0, -61, -27, 27, -12, 0, -2, -18, -24, 13, 0, -42, -12, 46, 84, 0, -28, -15, 2, 20, 0, -8, -12, 26, -1, 0, 6, 6, -3, 60, 0, 18, 3, -12, -23, 0, 8, 62, -30, 40, 0, -82, 12, -18, 8, 0, 0, -36, 12, 55, 0, 32, -24, -40, 6, 0, 6, 30, 40, 60, 0, 18, 8, 12, 6, 0, -12, 4, 22, 42, 0, -12, 4, -19, -36, 0, 30, -60, -14, -40, 0, 3, 63, -4, 2, 0, 6, -25, 2, -30, 0, 56, 21, 18, -28, 0, 0, 32, 45, -3, 0, -7, 4, -34, 5, 0, -4, 2, 6, 36, 0, 22, -20, -8, 0, 0, 36, -24, -60, -10, 0, -27, -42, -12, 27, 0, -1, 32, -2, 6, 0, 28, 13, 30, 30, 0, -12, -56, 6, -80, 0, -8, -2, 16, 2, 0, -48, 2, -8, -55, 0, 28, -1, 10, -8, 0, 6, -36, -44, -4, 0, -27, 0, -24, -12, 0, 16, -36, 8, -13, 0, -20, 40, 42, -5, 0, 12, 40, 20, 6, 0, 33, -42, -22, 12, 0, 18, 2, 32, -22, 0, 60, 6, 0, -18, 0, 30, 42, -12, -6, 0, 24, -12, -4, 12, 0, -4, 2, -12, -20, 0, -42, 42, 8, 4, 0, 4, -58, -82, 1, 0, -12, 42, -78, -14, 0, 11, 42, 3, -120, 0, 12, 2, -34, 8, 0, -25, 20, -36, 40, 0, -2, -12, -18, 18, 0, 8, 52, 0, -10, 0, -42, -3, 11, -38, 0, 4, 7, 36, -20, 0, 6, 38, 10, 6, 0, 16, 0, 22, 21, 0, 68, 0, 8, 22, 0, -24, -18, 0, -22, 0, -2, 22, 16, -12, 0, -30, -58, -1, -80, 0, 24, 6, -64, -15, 0, 13, 26, -4, -10, 0, 38, 18, -27, 6, 0, -13, 0, -8, 6, 0, -74, 2, 21, -8, 0, 2, 22, -24, 36, 0, -28, -24, 36, 10, 0, -20, -30, 6, 9, 0, -12, -4, 24, -8, 0, 0, -81, 25, 66, 0, 58, 6, -30, 8, 0, 26, -76, -20, -10, 0, 0, -5, -108, 6, 0, 40, -60, -40, -50, 0, -12, 39, 3, -22, 0, 12, 32, 18, -1, 0, 18, -22, -34, 2, 0, 6, -36, -12, -30, 0, -30, -42, 36, -12, 0, -14, 6, 24, 16, 0, 68, 12, 18, 15, 0, 2, 102, 20, 12, 0, 88, 22, -60, 8, 0, 6, -60, 4, 30, 0, -13, 1, -4, -4, 0, 42, 26, -45, -50, 0, -124, 108, 0, 3, 0, 8, -78, 12, -14, 0, -42, 8, -78, 62, 0, 20, -23, -20, 96, 0, 10, 8, 22, -18, 0, -18, -30, 8, 75, 0, -32, -10, 8, 4, 0, -3, 20, -10, 18, 0, 78, -33, 56, 36, 0, 0, 22, 6, -35, 0, -18, 6, -36, -30, 0, 0, 18, -20, -60, 0, 9, 18, -2, 8, 0, 2, 66, -24, -4, 0, -132, -22, 51, -26, 0, 22, 32, 42, -60, 0, 24, 18, -24, -1, 0, -34, -82, 24, 0, 0, -72, -15, -3, 120, 0, 26, -58, 50, -44, 0, -102, -12, 56, -27, 0, -64, 62, -13, -44, 0, -2, 6, 160, -25, 0, 2, 54, 35, 60, 0, 108, 26, 8, -24, 0, 18, -108, -28, -27, 0, 38, 10, 12, 2, 0, -30, 4, -18, -10, 0, -8, -32, -18, 24, 0, 76, -24, 0, 60, 0, 0, 66, 38, 52, 0, 6, 17, -24, 46, 0, -47, 22, 12, -20, 0, 12, 22, 0, -6, 0, -8, 6, -84, 21, 0, -60, 20, -10, -64, 0, -113, 33, -18, 3, 0, -12, 52, 12, -30, 0, 78, -1, 60, -68, 0, -22, 12, 26, 10, 0, -15, 48, -84, -12, 0, 0, -24, -30, -36, 0, 48, -12, -112, -56, 0, 6, -18, -10, 22, 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, 25, 4, 1, 5, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "150.2.g.b", "char_is_minimal": false, "conrey_index": 151, "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, 0, 0, 0], [0, 0, 1, 0], [-2, 0, 0, 0], [0, 0, 1, 0], [0, -1, 0, 0], [0, 0, 0, 0], [2, -4, 4, -2], [0, -1, 0, 0], [3, -3, 3, 0], [2, -2, 2, -2], [0, 0, 0, 0], [0, -1, 0, 0], [0, 3, -6, 3], [1, 0, 0, 0], [0, -2, -4, -2], [0, 0, 0, 0], [0, 0, 0, 2], [2, -2, 0, 2], [6, -6, 6, -6], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -3, 3], [-1, 1, -1, 1], [0, 0, 0, 2], [-1, 1, 0, 3], [0, 0, 0, 0], [0, -6, 0, -6], [1, 0, 0, 0], [0, 2, -4, 2], [-3, 6, -3, 0], [0, 0, 0, 0], [-1, 1, -1, 1], [-3, -4, -3, 0], [2, 4, 2, 0], [0, 3, -3, 0], [0, 0, 0, 0], [-5, 3, -5, 0], [0, 0, -2, 0], [-2, 0, -2, 2], [0, 2, -4, 2], [0, 0, 0, 0], [0, 0, 0, 6], [-2, 2, 0, 8], [-1, 1, -1, 1], [-3, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 3, -3], [0, 3, -3, 0], [9, -9, 0, -6], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, -2, 0], [-6, 0, -2, 2], [0, -1, -2, -1], [8, -4, 8, 0], [0, 0, 0, 0], [4, -7, 7, -4], [6, 0, 6, 0], [0, 2, 0, 0], [-1, 1, -1, 1], [0, 0, 0, 0], [-2, 4, -2, 0], [0, -6, 6, -6], [-3, 0, 3, -3], [0, 0, -6, 0], [0, 0, 0, 0], [10, -10, 0, -2], [0, 0, 0, -1], [-8, 5, -5, 8], [7, 0, 3, -3], [0, 0, 0, 0], [-6, 0, -2, 2], [-4, 8, -8, 4], [-3, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [2, 0, 5, -5], [0, 0, -6, 0], [0, 2, 0, 0], [0, 0, 0, 0], [2, 0, 0, -2], [1, 2, 1, 0], [-2, 4, -2, 0], [-3, 2, -2, 3], [0, 0, 0, 0], [-6, 6, -6, 0], [0, 0, -6, 0], [-6, 0, -6, 6], [0, -2, -6, -2], [0, 0, 0, 0], [0, 0, 0, -1], [-3, 3, 0, -9], [3, -3, 3, -3], [-2, 0, 2, -2], [0, 0, 0, 0]]}