# Stored data for newform 550.2.a.j, downloaded from the LMFDB on 07 September 2025.
{"Nk2": 2200, "analytic_conductor": 4.391772111170421, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [5, -1], [11, -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": [550, 1, [177, 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": [[3, [1, 1]], [7, [-3, 1]], [13, [-4, 1]]], "hecke_orbit": 10, "hecke_orbit_code": 40532396679889446, "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": "550.2.a.j", "level": 550, "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": [2, 5, 11], "level_radical": 110, "minimal_twist": "110.2.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\\cdots", "related_objects": ["EllipticCurve/Q/550/j"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "550.2.a", "trace_display": [1, -1, 0, 3], "trace_hash": 100592759315300363, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.993", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.957", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.818", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.016", "prec": 17}, "traces": [0, 1, 1, -1, 1, 0, -1, 3, 1, -2, 0, 1, -1, 4, 3, 0, 1, 3, -2, -5, 0, -3, 1, 4, -1, 0, 4, 5, 3, 5, 0, 7, 1, -1, 3, 0, -2, -7, -5, -4, 0, -8, -3, -6, 1, 0, 4, 8, -1, 2, 0, -3, 4, 9, 5, 0, 3, 5, 5, 0, 0, -13, 7, -6, 1, 0, -1, -12, 3, -4, 0, -3, -2, -6, -7, 0, -5, 3, -4, 0, 0, 1, -8, 4, -3, 0, -6, -5, 1, -15, 0, 12, 4, -7, 8, 0, -1, -12, 2, -2, 0, 2, -3, 4, 4, 0, 9, -12, 5, -10, 0, 7, 3, -6, 5, 0, 5, -8, 0, 9, 0, 1, -13, 8, 7, 0, -6, 8, 1, 6, 0, 7, -1, -15, -12, 0, 3, -12, -4, 20, 0, -8, -3, 4, -2, 0, -6, -2, -7, -5, 0, 2, -5, -6, 3, 0, -4, 13, 0, -9, 0, 12, 1, -21, -8, 0, 4, 23, -3, 3, 0, 10, -6, 14, -5, 0, 1, 0, -15, 10, 0, -18, 12, 13, 4, 0, -7, 3, 8, 15, 0, -8, -1, -1, -12, 0, 2, -22, -2, 25, 0, 12, 2, 15, -3, 0, 4, -8, 4, -5, 0, -13, 9, 3, -12, 0, 5, 21, -10, 6, 0, 12, 7, 14, 3, 0, -6, -12, 5, 0, 0, -3, 5, 19, -8, 0, 0, 0, 9, 0, 0, -8, 1, -16, -13, 0, 8, -20, 7, -4, 0, 2, -6, 4, 8, 0, 1, 28, 6, -21, 0, -10, 7, 9, -1, 0, -15, 15, -12, 0, 0, 22, 3, -12, -12, 0, -4, 28, 20, -14, 0, -18, -8, -16, -3, 0, 4, -24, -2, -8, 0, 12, -6, -16, -2, 0, -7, 5, -5, 16, 0, -18, 2, -2, -5, 0, -6, 8, 3, -4, 0, -13, -4, 14, 13, 0, 0, 23, -9, 5, 0, 12, 12, -15, 1, 0, -21, 10, -8, 24, 0, -18, 4, 14, 23, 0, -3, -7, 3, 6, 0, 7, 10, -15, -6, 0, 14, 18, -5, -10, 0, 20, 1, 14, 0, 0, -15, -9, 10, 0, 0, 6, -18, -1, 12, 0, 13, 8, 4, 16, 0, 27, -7, 4, 3, 0, 8, 20, 15, -10, 0, -8, -8, -6, -1, 0, -1, 12, -12, -30, 0, 12, 2, -7, -22, 0, -2, -22, 25, 15, 0, 27, 12, 28, 2, 0, 15, -7, -3, 20, 0, 12, 4, 0, -8, 0, 4, -20, -5, -20, 0, -28, -13, -16, 9, 0, 3, -39, -12, -4, 0, 32, 5, 14, 21, 0, -10, -20, 6, 10, 0, -4, 12, 4, 7, 0, 14, 5, 3, 30, 0, -8, -6, -2, -12, 0, 5, -27, 0, 15, 0, -13, -3, -16, 5, 0, 19, 3, -8, -36, 0, -13, 0, -6, 0, 0, 9, -18, 0, -10, 0, -28, -8, -12, 1, 0, -16, -22, -13, 21, 0, -33, 8, 15, -20, 0, 7, -9, -4, -40, 0, -23, 2, 24, -6, 0, 4, -3, 8, -20, 0, -18, 1, -25, 28, 0, 6, 8, -21, -14, 0, 22, -10, -16, 7, 0, 9, 21, -1, -7, 0, 0, -15, -32, 15, 0, -12, -10, 0, 2, 0, 17, 22, 18, 3, 0, -12, 8, -12, 26, 0, -25, -4, 0, 28, 0, 20, 28, -14, -24, 0, -3, -18, 4, -8, 0, -16, 3, -3, 20, 0, -3, 4, 8, -24, 0, -2, 8, -8, 1, 0, 12, 12, 9, -6, 0, -16, -7, -2, -35, 0, 22, -7, -6, 5, 0, -5, -25, 16, -5, 0, 2, -18, 24, 2, 0, -2, -7, -5, -15, 0, 32, -6, -6, 8, 0, 3, -12, -4, 20, 0, 20, -13, -45, -4, 0, 14, 5, 13, -21, 0, -43, 0, 13, 23, 0, -9, 8, 5, 6, 0, -33, 12, -1, 12, 0, -15, -12, 1, 0, 0, -21, -21, -21, 10, 0, -8, 12, 24, -35, 0, 12, -18, -12, 4, 0, 14, 20, 23, -14, 0, -13, -3, -1, -7, 0, 3, 8, 6, -36, 0, 12, 7, 49, 10, 0, -15, 0, -6, 36, 0, -8, 14, -6, 18, 0, -5, -24, -10, -19, 0, 27, 20, 35, 1, 0, 14, 6, 0, 10, 0, 0, -15, 28, -9, 0, 10, 0, 0, 15, 0, 12, 6, 8, -18, 0, -1, 18, 12, 13, 0, -18, 13, 14, 8, 0, 4, -12, 16, 40, 0, 20, 27, -1, -7, 0, 4, -8, 3, -36, 0, 27, 8, -2, 20, 0, 15, 18, -10, -4, 0, 12, -8, -30, -8, 0, -6, 0, -1, 30, 0, -28, -1, -11, 12, 0, -12, 21, -30, 40, 0, -3, 12, 25, 2, 0, -7, 38, -22, -9, 0, -18, -2, -52, -22, 0, 25, 18, 15, 24, 0, 30, 27, -6, 12, 0, 28, 0, 2, 10, 0, 37, 15, -22, -7, 0, -3, 30, 20, -24, 0, 22, 12, -26, 4, 0, 0, -22, -8, -20, 0, -28, 4, 6, -20, 0, -5, 35, -20, 0, 0, -4, -28, 18, -13, 0, -16, 3, 9, 16, 0, -28, 3, 44, -39, 0, -12, -17, -4, -10, 0, 24, 32, -36, 5, 0, 14, 8, 21, 0, 0, -48, -10, 24, -20, 0, 6, -2, 10, 16, 0, -18, -4, 9, 12, 0, 4, -32, 7, 24, 0, 1, 14, -40, 5, 0, 3, -16, 30, 35, 0, 27, -8, 18, -6, 0, -2, 23, -12, -4, 0, 37, 5, 4, -27, 0, 0, 21, 15, 50, 0, -8, -13, -12, -3, 0, -16, -8, 5, 15, 0, -10, 19, 13, 3, 0, -8, -42, -36, -14, 0, 17, -13, -32, 0, 0, -6, 53, 0, -24, 0, -23, 9, 29, -18, 0, 0, -5, -10, -36, 0, 18, -28, 24, -8, 0, -12, 13, 1, 15, 0, -28, -16, 60, -22, 0, -13, 28, 21, -15, 0, 20, -33, 14, 8, 0, 15, -24, -20, -24, 0, -8, 7, 18, -9, 0, -4, -2, -40, -35, 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, 1, -1, 1, 0, -1, 3, 1, -2, 0, 1, -1, 4, 3, 0, 1, 3, -2, -5, 0, -3, 1, 4, -1, 0, 4, 5, 3, 5, 0, 7, 1, -1, 3, 0, -2, -7, -5, -4, 0, -8, -3, -6, 1, 0, 4, 8, -1, 2, 0, -3, 4, 9, 5, 0, 3, 5, 5, 0, 0, -13, 7, -6, 1, 0, -1, -12, 3, -4, 0, -3, -2, -6, -7, 0, -5, 3, -4, 0, 0, 1, -8, 4, -3, 0, -6, -5, 1, -15, 0, 12, 4, -7, 8, 0, -1, -12, 2, -2, 0, 2, -3, 4, 4, 0, 9, -12, 5, -10, 0, 7, 3, -6, 5, 0, 5, -8, 0, 9, 0, 1, -13, 8, 7, 0, -6, 8, 1, 6, 0, 7, -1, -15, -12, 0, 3, -12, -4, 20, 0, -8, -3, 4, -2, 0, -6, -2, -7, -5, 0, 2, -5, -6, 3, 0, -4, 13, 0, -9, 0, 12, 1, -21, -8, 0, 4, 23, -3, 3, 0, 10, -6, 14, -5, 0, 1, 0, -15, 10, 0, -18, 12, 13, 4, 0, -7, 3, 8, 15, 0, -8, -1, -1, -12, 0, 2, -22, -2, 25, 0, 12, 2, 15, -3, 0, 4, -8, 4, -5, 0, -13, 9, 3, -12, 0, 5, 21, -10, 6, 0, 12, 7, 14, 3, 0, -6, -12, 5, 0, 0, -3, 5, 19, -8, 0, 0, 0, 9, 0, 0, -8, 1, -16, -13, 0, 8, -20, 7, -4, 0, 2, -6, 4, 8, 0, 1, 28, 6, -21, 0, -10, 7, 9, -1, 0, -15, 15, -12, 0, 0, 22, 3, -12, -12, 0, -4, 28, 20, -14, 0, -18, -8, -16, -3, 0, 4, -24, -2, -8, 0, 12, -6, -16, -2, 0, -7, 5, -5, 16, 0, -18, 2, -2, -5, 0, -6, 8, 3, -4, 0, -13, -4, 14, 13, 0, 0, 23, -9, 5, 0, 12, 12, -15, 1, 0, -21, 10, -8, 24, 0, -18, 4, 14, 23, 0, -3, -7, 3, 6, 0, 7, 10, -15, -6, 0, 14, 18, -5, -10, 0, 20, 1, 14, 0, 0, -15, -9, 10, 0, 0, 6, -18, -1, 12, 0, 13, 8, 4, 16, 0, 27, -7, 4, 3, 0, 8, 20, 15, -10, 0, -8, -8, -6, -1, 0, -1, 12, -12, -30, 0, 12, 2, -7, -22, 0, -2, -22, 25, 15, 0, 27, 12, 28, 2, 0, 15, -7, -3, 20, 0, 12, 4, 0, -8, 0, 4, -20, -5, -20, 0, -28, -13, -16, 9, 0, 3, -39, -12, -4, 0, 32, 5, 14, 21, 0, -10, -20, 6, 10, 0, -4, 12, 4, 7, 0, 14, 5, 3, 30, 0, -8, -6, -2, -12, 0, 5, -27, 0, 15, 0, -13, -3, -16, 5, 0, 19, 3, -8, -36, 0, -13, 0, -6, 0, 0, 9, -18, 0, -10, 0, -28, -8, -12, 1, 0, -16, -22, -13, 21, 0, -33, 8, 15, -20, 0, 7, -9, -4, -40, 0, -23, 2, 24, -6, 0, 4, -3, 8, -20, 0, -18, 1, -25, 28, 0, 6, 8, -21, -14, 0, 22, -10, -16, 7, 0, 9, 21, -1, -7, 0, 0, -15, -32, 15, 0, -12, -10, 0, 2, 0, 17, 22, 18, 3, 0, -12, 8, -12, 26, 0, -25, -4, 0, 28, 0, 20, 28, -14, -24, 0, -3, -18, 4, -8, 0, -16, 3, -3, 20, 0, -3, 4, 8, -24, 0, -2, 8, -8, 1, 0, 12, 12, 9, -6, 0, -16, -7, -2, -35, 0, 22, -7, -6, 5, 0, -5, -25, 16, -5, 0, 2, -18, 24, 2, 0, -2, -7, -5, -15, 0, 32, -6, -6, 8, 0, 3, -12, -4, 20, 0, 20, -13, -45, -4, 0, 14, 5, 13, -21, 0, -43, 0, 13, 23, 0, -9, 8, 5, 6, 0, -33, 12, -1, 12, 0, -15, -12, 1, 0, 0, -21, -21, -21, 10, 0, -8, 12, 24, -35, 0, 12, -18, -12, 4, 0, 14, 20, 23, -14, 0, -13, -3, -1, -7, 0, 3, 8, 6, -36, 0, 12, 7, 49, 10, 0, -15, 0, -6, 36, 0, -8, 14, -6, 18, 0, -5, -24, -10, -19, 0, 27, 20, 35, 1, 0, 14, 6, 0, 10, 0, 0, -15, 28, -9, 0, 10, 0, 0, 15, 0, 12, 6, 8, -18, 0, -1, 18, 12, 13, 0, -18, 13, 14, 8, 0, 4, -12, 16, 40, 0, 20, 27, -1, -7, 0, 4, -8, 3, -36, 0, 27, 8, -2, 20, 0, 15, 18, -10, -4, 0, 12, -8, -30, -8, 0, -6, 0, -1, 30, 0, -28, -1, -11, 12, 0, -12, 21, -30, 40, 0, -3, 12, 25, 2, 0, -7, 38, -22, -9, 0, -18, -2, -52, -22, 0, 25, 18, 15, 24, 0, 30, 27, -6, 12, 0, 28, 0, 2, 10, 0, 37, 15, -22, -7, 0, -3, 30, 20, -24, 0, 22, 12, -26, 4, 0, 0, -22, -8, -20, 0, -28, 4, 6, -20, 0, -5, 35, -20, 0, 0, -4, -28, 18, -13, 0, -16, 3, 9, 16, 0, -28, 3, 44, -39, 0, -12, -17, -4, -10, 0, 24, 32, -36, 5, 0, 14, 8, 21, 0, 0, -48, -10, 24, -20, 0, 6, -2, 10, 16, 0, -18, -4, 9, 12, 0, 4, -32, 7, 24, 0, 1, 14, -40, 5, 0, 3, -16, 30, 35, 0, 27, -8, 18, -6, 0, -2, 23, -12, -4, 0, 37, 5, 4, -27, 0, 0, 21, 15, 50, 0, -8, -13, -12, -3, 0, -16, -8, 5, 15, 0, -10, 19, 13, 3, 0, -8, -42, -36, -14, 0, 17, -13, -32, 0, 0, -6, 53, 0, -24, 0, -23, 9, 29, -18, 0, 0, -5, -10, -36, 0, 18, -28, 24, -8, 0, -12, 13, 1, 15, 0, -28, -16, 60, -22, 0, -13, 28, 21, -15, 0, 20, -33, 14, 8, 0, 15, -24, -20, -24, 0, -8, 7, 18, -9, 0, -4, -2, -40, -35, 0]}