# Stored data for newform 175.2.a.c, downloaded from the LMFDB on 12 December 2024. {"Nk2": 700, "analytic_conductor": 1.3973820353724067, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, -1], [7, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [175, 1, [127, 101], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-2, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199288295599, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "175.2.a.c", "level": 175, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 7], "level_radical": 35, "minimal_twist": "35.2.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}-2q^{9}+\\cdots", "related_objects": ["EllipticCurve/Q/175/c"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "175.2.a", "trace_display": [2, 1, 0, -1], "trace_hash": 120277348501708116, "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.969", "prec": 17}, {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "1.899", "prec": 17}, {"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "4.691", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.016", "prec": 17}, "traces": [0, 1, 2, 1, 2, 0, 2, -1, 0, -2, 0, -3, 2, 1, -2, 0, -4, 7, -4, 0, 0, -1, -6, 6, 0, 0, 2, -5, -2, -5, 0, 2, -8, -3, 14, 0, -4, 2, 0, 1, 0, 2, -2, -4, -6, 0, 12, -3, -4, 1, 0, 7, 2, 6, -10, 0, 0, 0, -10, 10, 0, -8, 4, 2, -8, 0, -6, 2, 14, 6, 0, -8, 0, 6, 4, 0, 0, 3, 2, -5, 0, 1, 4, -4, -2, 0, -8, -5, 0, 0, 0, -1, 12, 2, -6, 0, -8, 7, 2, 6, 0, 12, 14, -19, 0, 0, 12, -8, -10, 5, 0, 2, 4, 6, 0, 0, -10, -2, 20, -7, 0, -2, -16, 2, 4, 0, 4, 2, 0, -4, 0, 22, -6, 0, 4, 0, 0, 12, 12, -10, 0, -3, -16, -3, 8, 0, 12, 1, 4, 10, 0, -13, 0, -14, 6, 0, 2, -18, -10, 6, 0, -6, 2, -14, 4, 0, -8, -3, 0, -12, 0, 0, -8, -9, -10, 0, 12, 10, 0, -20, 0, -18, -2, -8, 0, 0, 4, -21, -6, 5, 0, -3, -8, 16, 14, 0, 2, 2, 12, -10, 0, 2, 24, 5, 14, 0, -38, -12, -4, 0, 0, -13, 12, -8, -16, 0, 0, -2, 10, 6, 0, 7, 4, 21, 8, 0, 12, 17, 0, -10, 0, 3, 0, 16, -4, 0, 20, -5, -14, 15, 0, 22, -4, 16, -16, 0, 4, 0, 0, -4, 0, -18, 4, -18, 4, 0, 16, 22, -8, -2, 0, 10, 44, -24, 0, 0, 0, 0, 4, 10, 0, -8, -28, -1, 24, 0, 12, 2, -20, -4, 0, 7, -6, 11, -16, 0, -6, -2, 16, 32, 0, 7, 12, -9, 2, 0, 0, 15, 20, 6, 0, 4, -26, 12, 0, 0, -28, 7, 6, -19, 0, 12, 0, 21, -36, 0, -10, 12, 12, 15, 0, -8, -12, 0, 2, 0, -28, 5, 0, 3, 0, 12, -8, -4, -6, 0, 4, -18, -24, 6, 0, -6, 0, -1, 0, 0, -18, -18, -10, -20, 0, -5, 24, 11, 20, 0, 0, -7, -40, -20, 0, -19, -36, -2, -2, 0, -16, -3, -24, -4, 0, -6, 4, -24, -42, 0, 0, -5, 10, 20, 0, 2, -6, 16, 0, 0, 32, 8, 14, 5, 0, 42, 0, 22, 4, 0, 12, 7, -20, 0, 0, -3, 4, 2, 24, 0, 10, -6, 0, 20, 0, 12, -38, -10, -24, 0, -8, -10, 0, 30, 0, -3, -26, 6, 0, 0, -16, 8, -16, -3, 0, -23, 20, 26, -4, 0, 10, 0, 12, 30, 0, -2, 14, -4, 4, 0, 42, 10, 8, -5, 0, -6, 12, -13, 34, 0, 0, -38, -20, -35, 0, 12, 6, 36, 20, 0, 32, 27, -4, -2, 0, -18, 0, 12, -10, 0, -14, -12, 30, -30, 0, 2, 44, -6, -4, 0, 32, 42, 0, -14, 0, 7, 4, -35, 0, 0, -8, 8, -8, -35, 0, -3, -36, -9, 0, 0, -36, -12, 4, -30, 0, -6, 32, 0, 44, 0, -8, 9, -4, -9, 0, -28, 20, -4, 44, 0, -48, 14, 12, 13, 0, -20, 0, 2, 0, 0, 0, -20, 20, -3, 0, 27, -16, -18, -56, 0, -2, 32, 24, 16, 0, 0, 0, 5, 4, 0, -20, -28, -8, -4, 0, -21, 14, -24, -6, 0, 22, -1, 0, -30, 0, 12, -6, -3, -4, 0, 16, -43, 64, 16, 0, 4, 14, -18, 0, 0, -18, 12, 2, 0, 0, 2, -8, 41, 30, 0, 20, -10, 12, 25, 0, -8, 8, -4, -26, 0, 24, 27, 0, 5, 0, -3, -28, -44, 14, 0, 0, 22, -38, 10, 0, -30, 24, 0, -4, 0, 42, 0, -36, 14, 0, 37, 0, -13, 24, 0, 12, 1, 30, 16, 0, 22, -16, 1, -12, 0, 0, -8, 0, -30, 0, -2, -28, -4, 10, 0, -8, -12, 6, -15, 0, 12, 24, 7, 0, 0, -8, -30, -6, 21, 0, 24, 8, -24, -36, 0, -24, -43, 12, -7, 0, 17, -12, 16, 0, 0, -2, -10, 16, 6, 0, -8, -18, -6, -36, 0, 0, 14, -40, 16, 0, -13, -10, 0, 24, 0, 22, -12, 20, 35, 0, 10, 0, 12, -14, 0, -40, 15, -40, 30, 0, 19, -38, 22, -36, 0, -4, -28, 0, 13, 0, -28, -16, 1, -6, 0, -48, -6, -8, -35, 0, 0, -12, -14, 0, 0, -48, 8, -42, 8, 0, -33, 12, -18, -10, 0, 10, 32, 40, -18, 0, 2, 4, -5, -6, 0, 32, 10, 16, 0, 0, 22, 32, 21, 16, 0, 0, -2, 10, 0, 0, 24, 84, 25, -4, 0, 44, 17, 4, -24, 0, -6, 0, -8, 14, 0, -20, -13, 0, -21, 0, 0, -6, -18, 4, 0, 4, 10, 0, 45, 0, -38, 10, -8, -12, 0, -28, 0, 40, 2, 0, -23, 24, 26, 0, 0, -20, -18, -24, -30, 0, 2, -8, 7, -20, 0, 0, -10, 60, 30, 0, -4, -6, 7, -26, 0, 12, 2, -24, 11, 0, 12, -16, -54, 16, 0, 0, 42, -6, 40, 0, -2, -46, -54, 40, 0, 52, 32, -4, 15, 0, 2, 0, -14, 0, 0, 12, 32, 60, -9, 0, 32, -4, 36, 14, 0, -8, -28, 0, -2, 0, -3, 42, 0, 20, 0, 0, 6, -10, -10, 0, 42, -12, 4, 0, 0, -26, -38, 34, -24, 0, 12, 0, 12, -76, 0, -20, -22, -70, -5, 0, 7, 24, -8, 6, 0, 72, 38, 40, -50, 0, 0, 32, 12, 54, 0, 0, -13, -4, 21, 0, -48, -36, 12, -40, 0, 24, 42, -10, 6, 0, 12, 0, 6, -24, 0, 30, 15, -60, -12, 0, -27, 4, 16, 44, 0, -12, -8, 0, 0, 0, 22, 32, 10, 84, 0, 32, 12, -28, 0, 0, -10, 14, 51, 0, 0, -70, 3, 0, -24, 0, -8, -16, 12, 16, 0, -8, -13, -70, -10, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 2, 1, 2, 0, 2, -1, 0, -2, 0, -3, 2, 1, -2, 0, -4, 7, -4, 0, 0, -1, -6, 6, 0, 0, 2, -5, -2, -5, 0, 2, -8, -3, 14, 0, -4, 2, 0, 1, 0, 2, -2, -4, -6, 0, 12, -3, -4, 1, 0, 7, 2, 6, -10, 0, 0, 0, -10, 10, 0, -8, 4, 2, -8, 0, -6, 2, 14, 6, 0, -8, 0, 6, 4, 0, 0, 3, 2, -5, 0, 1, 4, -4, -2, 0, -8, -5, 0, 0, 0, -1, 12, 2, -6, 0, -8, 7, 2, 6, 0, 12, 14, -19, 0, 0, 12, -8, -10, 5, 0, 2, 4, 6, 0, 0, -10, -2, 20, -7, 0, -2, -16, 2, 4, 0, 4, 2, 0, -4, 0, 22, -6, 0, 4, 0, 0, 12, 12, -10, 0, -3, -16, -3, 8, 0, 12, 1, 4, 10, 0, -13, 0, -14, 6, 0, 2, -18, -10, 6, 0, -6, 2, -14, 4, 0, -8, -3, 0, -12, 0, 0, -8, -9, -10, 0, 12, 10, 0, -20, 0, -18, -2, -8, 0, 0, 4, -21, -6, 5, 0, -3, -8, 16, 14, 0, 2, 2, 12, -10, 0, 2, 24, 5, 14, 0, -38, -12, -4, 0, 0, -13, 12, -8, -16, 0, 0, -2, 10, 6, 0, 7, 4, 21, 8, 0, 12, 17, 0, -10, 0, 3, 0, 16, -4, 0, 20, -5, -14, 15, 0, 22, -4, 16, -16, 0, 4, 0, 0, -4, 0, -18, 4, -18, 4, 0, 16, 22, -8, -2, 0, 10, 44, -24, 0, 0, 0, 0, 4, 10, 0, -8, -28, -1, 24, 0, 12, 2, -20, -4, 0, 7, -6, 11, -16, 0, -6, -2, 16, 32, 0, 7, 12, -9, 2, 0, 0, 15, 20, 6, 0, 4, -26, 12, 0, 0, -28, 7, 6, -19, 0, 12, 0, 21, -36, 0, -10, 12, 12, 15, 0, -8, -12, 0, 2, 0, -28, 5, 0, 3, 0, 12, -8, -4, -6, 0, 4, -18, -24, 6, 0, -6, 0, -1, 0, 0, -18, -18, -10, -20, 0, -5, 24, 11, 20, 0, 0, -7, -40, -20, 0, -19, -36, -2, -2, 0, -16, -3, -24, -4, 0, -6, 4, -24, -42, 0, 0, -5, 10, 20, 0, 2, -6, 16, 0, 0, 32, 8, 14, 5, 0, 42, 0, 22, 4, 0, 12, 7, -20, 0, 0, -3, 4, 2, 24, 0, 10, -6, 0, 20, 0, 12, -38, -10, -24, 0, -8, -10, 0, 30, 0, -3, -26, 6, 0, 0, -16, 8, -16, -3, 0, -23, 20, 26, -4, 0, 10, 0, 12, 30, 0, -2, 14, -4, 4, 0, 42, 10, 8, -5, 0, -6, 12, -13, 34, 0, 0, -38, -20, -35, 0, 12, 6, 36, 20, 0, 32, 27, -4, -2, 0, -18, 0, 12, -10, 0, -14, -12, 30, -30, 0, 2, 44, -6, -4, 0, 32, 42, 0, -14, 0, 7, 4, -35, 0, 0, -8, 8, -8, -35, 0, -3, -36, -9, 0, 0, -36, -12, 4, -30, 0, -6, 32, 0, 44, 0, -8, 9, -4, -9, 0, -28, 20, -4, 44, 0, -48, 14, 12, 13, 0, -20, 0, 2, 0, 0, 0, -20, 20, -3, 0, 27, -16, -18, -56, 0, -2, 32, 24, 16, 0, 0, 0, 5, 4, 0, -20, -28, -8, -4, 0, -21, 14, -24, -6, 0, 22, -1, 0, -30, 0, 12, -6, -3, -4, 0, 16, -43, 64, 16, 0, 4, 14, -18, 0, 0, -18, 12, 2, 0, 0, 2, -8, 41, 30, 0, 20, -10, 12, 25, 0, -8, 8, -4, -26, 0, 24, 27, 0, 5, 0, -3, -28, -44, 14, 0, 0, 22, -38, 10, 0, -30, 24, 0, -4, 0, 42, 0, -36, 14, 0, 37, 0, -13, 24, 0, 12, 1, 30, 16, 0, 22, -16, 1, -12, 0, 0, -8, 0, -30, 0, -2, -28, -4, 10, 0, -8, -12, 6, -15, 0, 12, 24, 7, 0, 0, -8, -30, -6, 21, 0, 24, 8, -24, -36, 0, -24, -43, 12, -7, 0, 17, -12, 16, 0, 0, -2, -10, 16, 6, 0, -8, -18, -6, -36, 0, 0, 14, -40, 16, 0, -13, -10, 0, 24, 0, 22, -12, 20, 35, 0, 10, 0, 12, -14, 0, -40, 15, -40, 30, 0, 19, -38, 22, -36, 0, -4, -28, 0, 13, 0, -28, -16, 1, -6, 0, -48, -6, -8, -35, 0, 0, -12, -14, 0, 0, -48, 8, -42, 8, 0, -33, 12, -18, -10, 0, 10, 32, 40, -18, 0, 2, 4, -5, -6, 0, 32, 10, 16, 0, 0, 22, 32, 21, 16, 0, 0, -2, 10, 0, 0, 24, 84, 25, -4, 0, 44, 17, 4, -24, 0, -6, 0, -8, 14, 0, -20, -13, 0, -21, 0, 0, -6, -18, 4, 0, 4, 10, 0, 45, 0, -38, 10, -8, -12, 0, -28, 0, 40, 2, 0, -23, 24, 26, 0, 0, -20, -18, -24, -30, 0, 2, -8, 7, -20, 0, 0, -10, 60, 30, 0, -4, -6, 7, -26, 0, 12, 2, -24, 11, 0, 12, -16, -54, 16, 0, 0, 42, -6, 40, 0, -2, -46, -54, 40, 0, 52, 32, -4, 15, 0, 2, 0, -14, 0, 0, 12, 32, 60, -9, 0, 32, -4, 36, 14, 0, -8, -28, 0, -2, 0, -3, 42, 0, 20, 0, 0, 6, -10, -10, 0, 42, -12, 4, 0, 0, -26, -38, 34, -24, 0, 12, 0, 12, -76, 0, -20, -22, -70, -5, 0, 7, 24, -8, 6, 0, 72, 38, 40, -50, 0, 0, 32, 12, 54, 0, 0, -13, -4, 21, 0, -48, -36, 12, -40, 0, 24, 42, -10, 6, 0, 12, 0, 6, -24, 0, 30, 15, -60, -12, 0, -27, 4, 16, 44, 0, -12, -8, 0, 0, 0, 22, 32, 10, 84, 0, 32, 12, -28, 0, 0, -10, 14, 51, 0, 0, -70, 3, 0, -24, 0, -8, -16, 12, 16, 0, -8, -13, -70, -10, 0]}