# Stored data for newform 510.2.a.d, downloaded from the LMFDB on 10 December 2024. {"Nk2": 2040, "analytic_conductor": 4.0723705030853, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [5, 1], [17, 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": [510, 1, [341, 307, 241], [1, 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": [[7, [-2, 1]], [11, [0, 1]], [13, [-4, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798915666430, "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": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "510.2.a.d", "level": 510, "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": true, "level_primes": [2, 3, 5, 17], "level_radical": 510, "minimal_twist": "510.2.a.d", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\\cdots", "related_objects": ["EllipticCurve/Q/510/d"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "510.2.a", "trace_display": [1, -1, -1, 2], "trace_hash": 1289838764869720929, "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "1.998", "prec": 17}, {"__RealLiteral__": 0, "data": "0.083", "prec": 17}, {"__RealLiteral__": 0, "data": "5.024", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 1, 1, -1, 1, -1, -1, 2, 1, 1, -1, 0, -1, 4, 2, 1, 1, -1, 1, 4, -1, -2, 0, 4, -1, 1, 4, -1, 2, 2, 1, 0, 1, 0, -1, -2, 1, -2, 4, -4, -1, -4, -2, 10, 0, -1, 4, -8, -1, -3, 1, 1, 4, 2, -1, 0, 2, -4, 2, -2, 1, -14, 0, 2, 1, -4, 0, 2, -1, -4, -2, -6, 1, -4, -2, -1, 4, 0, -4, -12, -1, 1, -4, 8, -2, 1, 10, -2, 0, -10, -1, 8, 4, 0, -8, -4, -1, 8, -3, 0, 1, -4, 1, 8, 4, 2, 2, -12, -1, 6, 0, 2, 2, -6, -4, -4, 2, 4, -2, -2, 1, -11, -14, 4, 0, -1, 2, 16, 1, -10, -4, 12, 0, 8, 2, 1, -1, -18, -4, -12, -2, 8, -6, 0, 1, -2, -4, 3, -2, -12, -1, 8, 4, -1, 0, 0, -4, 4, -12, -2, -1, 8, 1, 24, -4, 0, 8, -8, -2, 3, 1, 4, 10, -2, -2, 2, 0, 2, -10, 18, -1, -10, 8, 14, 4, 2, 0, 0, -8, -2, -4, 12, -1, -8, 8, 4, -3, 6, 0, 16, 1, -2, -4, 4, 1, 4, 8, 4, 4, 0, 2, 12, 2, 6, -12, -10, -1, 0, 6, 4, 0, -4, 2, -16, 2, 1, -6, -12, -4, -2, -4, 0, 2, 14, 4, 8, -2, 12, -2, -24, 1, -30, -11, -1, -14, 3, 4, 16, 0, -8, -1, -2, 2, 0, 16, -1, 1, -14, -10, -4, -4, 2, 12, 24, 0, -2, 8, 10, 2, 10, 1, -8, -1, -8, -18, 0, -4, 10, -12, 0, -2, 22, 8, -28, -6, 4, 0, -8, 1, 1, -2, -8, -4, 22, 3, 2, -2, 0, -12, 16, -1, 20, 8, 4, 4, 14, -1, 10, 0, -8, 0, -10, -4, -16, 4, -2, -12, 30, -2, 0, -1, 12, 8, -4, 1, 4, 24, -6, -4, -16, 0, -16, 8, -2, -8, -2, -2, 12, 3, 6, 1, 0, 4, -20, 10, 4, -2, -20, -2, 2, 2, -4, 0, 18, 2, 6, -10, 2, 18, 20, -1, -3, -10, 11, 8, 4, 14, -2, 4, -4, 2, 4, 0, 8, 0, 1, -8, 8, -2, 28, -4, -16, 12, 16, -1, 0, -8, 10, 8, 12, 4, -4, -3, -12, 6, 12, 0, -10, 16, -8, 1, -24, -2, 0, -4, -1, 4, 0, 1, -26, 4, 18, 8, -4, 4, -8, 4, 12, 0, -4, 2, -34, 12, -8, 2, -1, 6, -28, -12, 0, -10, -34, -1, -34, 0, 2, 6, 16, 4, -12, 0, -3, -4, -8, 2, 10, -16, 12, 2, 40, 1, 0, -6, -8, -12, -8, -4, -34, -2, 1, -4, 0, 0, 16, 2, 0, 14, -36, 4, 4, 8, -4, -2, 0, 12, 4, -2, 2, -24, 2, 1, -8, -30, -8, -11, -8, -1, -22, -14, -24, 3, -14, 4, -2, 16, 0, 0, -12, -8, -12, -1, 8, -2, 28, 2, 4, 0, -3, 16, 4, -1, -8, 1, -4, -14, -8, -10, 0, -4, 2, -4, 16, 2, -18, 12, -2, 24, 0, 0, -7, -2, -2, 8, -16, 10, 12, 2, -18, 10, 0, 1, 2, -8, 10, -1, -6, -8, -36, -18, -14, 0, 8, -4, -24, 10, -2, -12, -46, 0, 40, -2, 0, 22, -32, 8, 6, -28, 2, -6, 42, 4, -12, 0, -12, -8, 4, 1, 22, 1, 8, -2, 16, -8, 0, -4, -4, 22, 8, 3, 0, 2, -6, -2, -30, 0, 2, -12, -16, 16, 12, -1, 38, 20, 2, 8, 11, 4, -14, 4, -4, 14, -32, -1, 24, 10, -4, 0, 6, -8, 44, 0, -4, -10, -20, -4, 1, -16, 0, 4, 2, -2, 32, -12, -12, 30, -16, -2, -12, 0, -6, -1, 40, 12, 16, 8, 10, -4, -8, 1, 0, 4, 0, 24, -14, -6, -12, -4, -4, -16, -6, 0, -30, -16, 4, 8, -8, -2, 8, -8, 16, -2, 0, -2, 8, 12, -1, 3, 38, 6, 16, 1, 12, 0, 12, 4, 18, -20, 2, 10, 8, 4, 12, -2, 0, -20, 12, -2, 4, 2, -14, 2, 24, -4, -8, 0, -8, 18, -8, 2, 26, 6, -12, -10, 0, 2, 0, 18, 24, 20, 26, -1, 16, -3, 30, -10, 2, 11, -24, 8, 1, 4, -10, 14, -16, -2, -3, 4, 0, -4, -16, 2, -16, 4, 0, 0, 12, 8, 8, 0, -24, 1, 20, -8, 2, 8, -8, -2, 52, 28, 0, -4, -54, -16, 12, 12, 1, 16, -8, -1, 14, 0, 14, -8, 42, 10, 0, 8, 4, 12, -16, 4, 0, -4, -2, -3, -4, -12, 8, 6, -24, 12, -12, 0, -56, -10, 2, 16, 6, -8, 8, 1, -10, -24, 0, -2, -8, 0, -10, -4, -28, -1, 52, 4, 8, 0, -24, 1, 40, -26, 8, 4, 30, 18, -50, 8, 0, -4, 52, 4, 2, -8, -10, 4, 3, 12, 8, 0, 0, -4, 14, 2, -25, -34, -22, 12, -3, -8, -22, 2, 28, -1, -8, 6, 42, -28, -4, -12, -2, 0, 24, -10, 8, -34, 32, -1, 2, -34, -1, 0, 0, 2, 8, 6, 8, 16, -2, 4, 10, -12, -22, 0, 48, -3, -2, -4, -2, -8, 20, 2, 32, 10, 0, -16, -32, 12, -18, 2, -16, 40, 0, 1, -2, 0, -20, -6, 10, -8, -8, -12, -4, -8, 18, -4, 0, -34, -14, -2, 24, 1, 32, -4, -10, 0, -24, 0, -2, 16, 8, 2, -20, 0, -12, 14, 10, -36, 0, 4, 54, 4, 16, 8, -10, -4, -16, -2, 2, 0, -4, 12, -16, 4, -30, -2, -34, 2, -12, -24, 0, 2, -36, 1, -31, -8, -12, -30, 8, -8, 20, -11, 4, -8, -6, -1, -24, -22, -4, -14, 18, -24, 0, 3, 6, -14, 56, 4, -6, -2, 16, 16, 40, 0, 24, 0, 16, -12, -16, -8, 14, -12, 2, -1], "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, 1, -1, 1, -1, -1, 2, 1, 1, -1, 0, -1, 4, 2, 1, 1, -1, 1, 4, -1, -2, 0, 4, -1, 1, 4, -1, 2, 2, 1, 0, 1, 0, -1, -2, 1, -2, 4, -4, -1, -4, -2, 10, 0, -1, 4, -8, -1, -3, 1, 1, 4, 2, -1, 0, 2, -4, 2, -2, 1, -14, 0, 2, 1, -4, 0, 2, -1, -4, -2, -6, 1, -4, -2, -1, 4, 0, -4, -12, -1, 1, -4, 8, -2, 1, 10, -2, 0, -10, -1, 8, 4, 0, -8, -4, -1, 8, -3, 0, 1, -4, 1, 8, 4, 2, 2, -12, -1, 6, 0, 2, 2, -6, -4, -4, 2, 4, -2, -2, 1, -11, -14, 4, 0, -1, 2, 16, 1, -10, -4, 12, 0, 8, 2, 1, -1, -18, -4, -12, -2, 8, -6, 0, 1, -2, -4, 3, -2, -12, -1, 8, 4, -1, 0, 0, -4, 4, -12, -2, -1, 8, 1, 24, -4, 0, 8, -8, -2, 3, 1, 4, 10, -2, -2, 2, 0, 2, -10, 18, -1, -10, 8, 14, 4, 2, 0, 0, -8, -2, -4, 12, -1, -8, 8, 4, -3, 6, 0, 16, 1, -2, -4, 4, 1, 4, 8, 4, 4, 0, 2, 12, 2, 6, -12, -10, -1, 0, 6, 4, 0, -4, 2, -16, 2, 1, -6, -12, -4, -2, -4, 0, 2, 14, 4, 8, -2, 12, -2, -24, 1, -30, -11, -1, -14, 3, 4, 16, 0, -8, -1, -2, 2, 0, 16, -1, 1, -14, -10, -4, -4, 2, 12, 24, 0, -2, 8, 10, 2, 10, 1, -8, -1, -8, -18, 0, -4, 10, -12, 0, -2, 22, 8, -28, -6, 4, 0, -8, 1, 1, -2, -8, -4, 22, 3, 2, -2, 0, -12, 16, -1, 20, 8, 4, 4, 14, -1, 10, 0, -8, 0, -10, -4, -16, 4, -2, -12, 30, -2, 0, -1, 12, 8, -4, 1, 4, 24, -6, -4, -16, 0, -16, 8, -2, -8, -2, -2, 12, 3, 6, 1, 0, 4, -20, 10, 4, -2, -20, -2, 2, 2, -4, 0, 18, 2, 6, -10, 2, 18, 20, -1, -3, -10, 11, 8, 4, 14, -2, 4, -4, 2, 4, 0, 8, 0, 1, -8, 8, -2, 28, -4, -16, 12, 16, -1, 0, -8, 10, 8, 12, 4, -4, -3, -12, 6, 12, 0, -10, 16, -8, 1, -24, -2, 0, -4, -1, 4, 0, 1, -26, 4, 18, 8, -4, 4, -8, 4, 12, 0, -4, 2, -34, 12, -8, 2, -1, 6, -28, -12, 0, -10, -34, -1, -34, 0, 2, 6, 16, 4, -12, 0, -3, -4, -8, 2, 10, -16, 12, 2, 40, 1, 0, -6, -8, -12, -8, -4, -34, -2, 1, -4, 0, 0, 16, 2, 0, 14, -36, 4, 4, 8, -4, -2, 0, 12, 4, -2, 2, -24, 2, 1, -8, -30, -8, -11, -8, -1, -22, -14, -24, 3, -14, 4, -2, 16, 0, 0, -12, -8, -12, -1, 8, -2, 28, 2, 4, 0, -3, 16, 4, -1, -8, 1, -4, -14, -8, -10, 0, -4, 2, -4, 16, 2, -18, 12, -2, 24, 0, 0, -7, -2, -2, 8, -16, 10, 12, 2, -18, 10, 0, 1, 2, -8, 10, -1, -6, -8, -36, -18, -14, 0, 8, -4, -24, 10, -2, -12, -46, 0, 40, -2, 0, 22, -32, 8, 6, -28, 2, -6, 42, 4, -12, 0, -12, -8, 4, 1, 22, 1, 8, -2, 16, -8, 0, -4, -4, 22, 8, 3, 0, 2, -6, -2, -30, 0, 2, -12, -16, 16, 12, -1, 38, 20, 2, 8, 11, 4, -14, 4, -4, 14, -32, -1, 24, 10, -4, 0, 6, -8, 44, 0, -4, -10, -20, -4, 1, -16, 0, 4, 2, -2, 32, -12, -12, 30, -16, -2, -12, 0, -6, -1, 40, 12, 16, 8, 10, -4, -8, 1, 0, 4, 0, 24, -14, -6, -12, -4, -4, -16, -6, 0, -30, -16, 4, 8, -8, -2, 8, -8, 16, -2, 0, -2, 8, 12, -1, 3, 38, 6, 16, 1, 12, 0, 12, 4, 18, -20, 2, 10, 8, 4, 12, -2, 0, -20, 12, -2, 4, 2, -14, 2, 24, -4, -8, 0, -8, 18, -8, 2, 26, 6, -12, -10, 0, 2, 0, 18, 24, 20, 26, -1, 16, -3, 30, -10, 2, 11, -24, 8, 1, 4, -10, 14, -16, -2, -3, 4, 0, -4, -16, 2, -16, 4, 0, 0, 12, 8, 8, 0, -24, 1, 20, -8, 2, 8, -8, -2, 52, 28, 0, -4, -54, -16, 12, 12, 1, 16, -8, -1, 14, 0, 14, -8, 42, 10, 0, 8, 4, 12, -16, 4, 0, -4, -2, -3, -4, -12, 8, 6, -24, 12, -12, 0, -56, -10, 2, 16, 6, -8, 8, 1, -10, -24, 0, -2, -8, 0, -10, -4, -28, -1, 52, 4, 8, 0, -24, 1, 40, -26, 8, 4, 30, 18, -50, 8, 0, -4, 52, 4, 2, -8, -10, 4, 3, 12, 8, 0, 0, -4, 14, 2, -25, -34, -22, 12, -3, -8, -22, 2, 28, -1, -8, 6, 42, -28, -4, -12, -2, 0, 24, -10, 8, -34, 32, -1, 2, -34, -1, 0, 0, 2, 8, 6, 8, 16, -2, 4, 10, -12, -22, 0, 48, -3, -2, -4, -2, -8, 20, 2, 32, 10, 0, -16, -32, 12, -18, 2, -16, 40, 0, 1, -2, 0, -20, -6, 10, -8, -8, -12, -4, -8, 18, -4, 0, -34, -14, -2, 24, 1, 32, -4, -10, 0, -24, 0, -2, 16, 8, 2, -20, 0, -12, 14, 10, -36, 0, 4, 54, 4, 16, 8, -10, -4, -16, -2, 2, 0, -4, 12, -16, 4, -30, -2, -34, 2, -12, -24, 0, 2, -36, 1, -31, -8, -12, -30, 8, -8, 20, -11, 4, -8, -6, -1, -24, -22, -4, -14, 18, -24, 0, 3, 6, -14, 56, 4, -6, -2, 16, 16, 40, 0, 24, 0, 16, -12, -16, -8, 14, -12, 2, -1]}