# Stored data for newform 975.2.a.d, downloaded from the LMFDB on 25 April 2024. {"label": "975.2.a.d", "space_label": "975.2.a", "level": 975, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666895, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1284845842558847476, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]], [7, [-3, 1]]], "qexp_display": "q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{7}+3q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3900, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 7.785414197074838, "hecke_ring_index": 1, "level_radical": 195, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [975, 1, [326, 352, 301], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.975", "prec": 17}, {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "1.910", "prec": 17}, {"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "4.709", "prec": 17}], "related_objects": ["EllipticCurve/Q/975/d"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1], [13, 1]], "trace_display": [-1, -1, 0, 3], "traces": [0, 1, -1, -1, -1, 0, 1, 3, 3, 1, 0, -1, 1, -1, -3, 0, -1, 5, -1, -8, 0, -3, 1, 0, -3, 0, 1, -1, -3, 1, 0, 3, -5, 1, -5, 0, -1, 8, 8, 1, 0, -2, 3, -8, 1, 0, 0, 11, 1, 2, 0, -5, 1, 11, 1, 0, 9, 8, -1, 5, 0, 1, -3, 3, 7, 0, -1, -3, -5, 0, 0, 16, 3, 4, -8, 0, 8, -3, -1, 12, 0, 1, 2, 3, 3, 0, 8, -1, -3, 0, 0, -3, 0, -3, -11, 0, 5, 2, -2, -1, 0, 9, 5, 14, -3, 0, -11, -18, 1, -10, 0, -8, -3, 2, -8, 0, -1, -1, -5, 15, 0, -10, -1, 2, -3, 0, -3, -8, 3, 8, 0, 6, -1, -24, 3, 0, 15, 12, 0, -10, 0, -11, -16, 1, -1, 0, -4, -2, -8, 10, 0, -17, -24, 5, 3, 0, -1, 11, -12, -11, 0, 0, -1, 20, 2, 0, -3, -12, -9, 1, 0, -8, 8, 21, 1, 0, 1, -5, 0, 26, 0, 5, 3, -1, 0, 0, 3, -5, -11, -3, 0, 10, -7, -10, -2, 0, -2, 6, 1, 10, 0, 3, -9, 3, 5, 0, -14, 0, 1, 8, 0, -16, -11, -16, 18, 0, -3, 9, 10, -4, 0, -5, 8, 8, -15, 0, -2, -23, -8, -18, 0, 3, 3, 6, 1, 0, -5, -12, -15, -19, 0, 10, 10, -1, -1, 0, -2, 8, 9, -3, 0, -30, -3, 0, 8, 0, -17, 3, -8, 24, 0, 1, -6, -14, 3, 0, 24, 0, 3, 17, 0, -5, -5, 3, -12, 0, 0, -6, 10, 3, 0, -18, 11, 18, -16, 0, -1, -6, -5, 8, 0, -2, -4, -30, 2, 0, 24, 1, -10, 0, 0, -24, 17, -9, 8, 0, -5, 4, 3, -14, 0, 6, 3, 29, -11, 0, -12, 16, 11, -1, 0, 18, 0, -40, -1, 0, -20, 10, -6, 33, 0, -12, -3, 8, 12, 0, 3, -5, -1, -2, 0, -3, 8, -15, -24, 0, -21, 2, 1, 16, 0, 1, 5, -18, 5, 0, 0, -15, -26, 15, 0, 45, -5, 10, 3, 0, 1, 12, 0, -2, 0, 33, 3, 31, 5, 0, 33, -1, 3, -35, 0, 8, -10, 24, -3, 0, 10, -8, -2, -30, 0, 0, 6, -6, -6, 0, 1, -2, -10, 24, 0, 0, -3, -3, -9, 0, -3, -8, -15, 2, 0, -12, -14, 15, 0, 0, 5, 10, -8, -26, 0, 28, 16, 11, 33, 0, 16, 3, 18, -1, 0, -12, 1, 34, -9, 0, 10, 0, 4, 4, 0, 2, 5, 0, 8, 0, -8, -10, 21, -28, 0, 2, -2, 17, 23, 0, 24, 34, 18, -5, 0, 42, -3, 9, -1, 0, -6, -32, 1, -9, 0, -11, 15, 8, 12, 0, -15, 11, 19, -15, 0, -8, -10, 0, 10, 0, 1, -37, 3, -20, 0, -26, -2, 5, -8, 0, -3, 48, 3, -41, 0, 12, 30, -26, 9, 0, 0, -1, 8, -10, 0, 12, 11, 8, -3, 0, -8, -11, -24, -21, 0, -26, -1, -26, -6, 0, 14, 15, -1, -23, 0, 5, 24, 2, 0, 0, -9, -26, -17, -2, 0, 12, 5, -5, -25, 0, -3, 22, -12, 1, 0, -8, 0, 36, 6, 0, 10, 18, -3, 8, 0, 5, 18, 24, 11, 0, -18, 3, 48, 15, 0, 32, -1, -10, 6, 0, 7, -10, -8, 10, 0, 9, 2, -11, 12, 0, 30, 45, 2, -24, 0, -6, -8, -26, -1, 0, -10, -10, 0, 46, 0, 5, 24, -3, 17, 0, 9, -38, 40, -3, 0, -11, -5, -14, -4, 0, -9, -6, 14, -4, 0, 0, -6, 0, -1, 0, -29, -8, -11, 40, 0, -44, 36, 16, -16, 0, 11, -2, 1, 16, 0, -15, -18, 12, 0, 0, 40, -16, 3, -5, 0, -9, -20, -35, -10, 0, 2, 4, -33, -4, 0, -2, 12, 5, 9, 0, -8, 0, 12, -8, 0, -1, 15, -45, 5, 0, -1, 18, 2, 6, 0, 23, 3, -9, 8, 0, 15, 18, 8, -11, 0, -29, -21, -3, -2, 0, -3, -10, -16, -6, 0, 31, -1, -64, -7, 0, 18, 27, 5, -14, 0, 12, 0, 0, 15, 0, -26, 19, -15, 6, 0, 42, -45, -10, -5, 0, -10, 2, -9, 1, 0, -40, 1, 20, -12, 0, 0, 3, 2, 7, 0, -8, -33, -13, -9, 0, -31, 3, 5, -54, 0, 40, -11, 30, 1, 0, 3, -23, 35, 0, 0, -24, -8, -30, -10, 0, -24, -5, 17, -40, 0, -3, 10, -18, 8, 0, 6, -24, 30, 16, 0, -16, 0, -1, -2, 0, 6, -17, -6, 14, 0, 6, -3, -1, 2, 0, -10, 43, -24, 55, 0, 0, 0, -4, -3, 0, 3, -17, 27, -2, 0, -33, -3, 5, 8, 0, 5, 64, -2, -3, 0, 0, 12, -28, 42, 0, -15, -1, 0, 51, 0, 6, -7, 10, -10, 0, -8, -3, 26, -8, 0, -28, -28, 18, 16, 0, -11, -30, -11, -18, 0, 0, 16, -24, -3, 0, -54, 38, 1, 4, 0, 6, 12, 7, 5, 0, -34, -8, -9, -12, 0, 3, -30, 2, 0, 0, 4, -24, -4, 30, 0, -25, -2, -16, 5, 0, 0, -12, -24, -24, 0, -1, -8, -88, 10, 0, 9, 0, 28, 3, 0, 55, -2, 24, 6, 0, -17, -24, 23, 9, 0, 56, -8, -3, -34, 0, 18, 18, 5, 22, 0, -4, -42, -16, -3, 0, -9, 14, -5, -26, 0, -16, -6, -6, 32, 0, -3, -45, 9, -29, 0, -56, 11, 0, -5, 0, -8, -21, 12, -4, 0, -16, 45, -37, -11, 0, 19, 1, 15, 36, 0, -22, 8, -18, -10, 0, 0, -37, -30, 40, 0, 54, 1, -30, 37, 0, -1, -28, 20, 0, 0, -10, 26, 21, 6, 0, -5, -33, -8, 0, 0, 20, -15, 12, -48, 0, 3, -3, 41, -8, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "975.2.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-1], [-1], [-1], [0], [1], [3], [3], [1], [0], [-1], [1], [-1], [-3], [0], [-1], [5], [-1], [-8], [0], [-3], [1], [0], [-3], [0], [1], [-1], [-3], [1], [0], [3], [-5], [1], [-5], [0], [-1], [8], [8], [1], [0], [-2], [3], [-8], [1], [0], [0], [11], [1], [2], [0], [-5], [1], [11], [1], [0], [9], [8], [-1], [5], [0], [1], [-3], [3], [7], [0], [-1], [-3], [-5], [0], [0], [16], [3], [4], [-8], [0], [8], [-3], [-1], [12], [0], [1], [2], [3], [3], [0], [8], [-1], [-3], [0], [0], [-3], [0], [-3], [-11], [0], [5], [2], [-2], [-1], [0]]}