# Stored data for newform 418.2.a.g, downloaded from the LMFDB on 24 April 2024. {"label": "418.2.a.g", "space_label": "418.2.a", "level": 418, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021597797777826, "dim": 3, "is_polredabs": true, "nf_label": "3.3.621.1", "trace_hash": 1607218763882623315, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [-3, -6, 0, 1]]], "qexp_display": "q-q^{2}+\\beta _{1}q^{3}+q^{4}+(-1-\\beta _{1}-\\beta _{2})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1672, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 3.33774680448952, "hecke_ring_index": 1, "level_radical": 418, "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": [418, 1, [343, 287], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 11, 19], "conrey_indexes": [1], "field_disc": 621, "field_disc_factorization": [[3, 3], [23, 1]], "field_poly": [-3, -6, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.022", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "24.139", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "284.192", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [11, 1], [19, 1]], "trace_display": [-3, 0, -3, -6], "traces": [0, 3, -3, 0, 3, -3, 0, -6, -3, 3, 3, -3, 0, 0, 6, -9, 3, -9, -3, -3, -3, -15, 3, -15, 0, 12, 0, 9, -6, 6, 9, -3, -3, 0, 9, 0, 3, -6, 3, -15, 3, -9, 15, -21, -3, -27, 15, -12, 0, 27, -12, 3, 0, -9, -9, 3, 6, 0, -6, -3, -9, 24, 3, 0, 3, -6, 0, 0, -9, 3, 0, 21, -3, -3, 6, 36, -3, 6, 15, -6, -3, -9, 9, -33, -15, 24, 21, 6, 3, 6, 27, 36, -15, 36, 12, 3, 0, 12, -27, -3, 12, 0, -3, 3, 0, 63, 9, -3, 9, -3, -3, 6, -6, -24, 0, 30, 6, 6, 3, -3, 9, 3, -24, -30, -3, -24, 0, -18, -3, 33, 6, 9, 0, 6, 0, -9, 9, 6, -3, 15, 0, 42, -21, 0, 3, -45, 3, 18, -6, 6, -36, -24, 3, -24, -6, -24, -15, 15, 6, -51, 3, 9, 9, 0, -9, 9, 33, 18, 15, -3, -24, -3, -21, 27, -6, -69, -3, 21, -6, -3, -27, 0, -36, -6, 15, 36, -36, 9, -12, -18, -3, -21, 0, 15, -12, 45, 27, -36, 3, -51, -12, 21, 0, 15, 3, 66, -3, -30, 0, 3, -63, -27, -9, -57, 3, -21, -9, -39, 3, 3, 3, -21, -6, 18, 6, 39, 24, -15, 0, -3, -30, 15, -6, -54, -6, -54, -3, -12, 3, 18, -9, -3, -3, -18, 24, -6, 30, 0, 3, -15, 24, 30, 0, 15, 18, 18, 3, 48, -33, -30, -6, 45, -9, 21, 0, 30, -6, 18, 0, -12, 9, 0, -9, -12, -6, -12, 3, 0, -15, 24, 0, 9, -42, 33, 21, 9, 0, 21, -3, -6, 45, 12, -3, 24, -18, -30, 6, -9, -6, -21, 36, 18, 24, -18, -3, -54, 24, -30, 6, -27, 24, -15, 15, 0, -15, 99, -6, -39, 51, -6, -3, 27, -9, 9, -9, -45, 0, -33, 9, 6, -9, 42, -33, -36, -18, 36, -15, 9, 3, 0, 24, 3, 3, -69, 21, 36, -27, -18, 6, 18, 69, 0, 3, -15, -21, 39, 6, 75, 3, 24, 27, 3, 0, 0, 36, 18, 6, -24, -15, -66, -36, 99, 36, -6, -9, -99, 12, 27, 18, -30, 3, 36, 21, -3, 0, 0, -15, 21, 12, -27, -45, 63, -27, 36, 36, 84, -3, -39, 51, 15, 12, 0, -21, -45, 0, 54, -15, 6, -3, -9, -66, -3, 3, -3, 30, 27, 0, -27, -3, 30, 63, 51, 27, 54, 9, -27, 57, -6, -3, 15, 21, -66, 9, 18, 39, -36, -3, 15, -3, -54, -3, 6, 21, -18, 6, -54, -18, 54, -6, -66, -39, 9, -24, -42, 15, -27, 0, 9, 3, -27, 30, 24, -15, -60, 6, -99, 54, -18, 6, -78, 54, 45, 3, 21, 12, -12, -3, -30, -18, 21, 9, -42, 3, 105, 3, 48, 18, -9, -24, -60, 6, -15, -30, -51, 0, 27, -3, 12, 15, 36, -24, 12, -30, 18, 0, 48, -15, -42, -18, -54, -18, -15, -3, -9, -48, -69, 33, 12, 30, 51, 6, -24, -45, 27, 9, -114, -21, 18, 0, 24, -30, 30, 6, 3, -18, 0, 0, -24, 12, -27, -9, 18, 0, -60, 9, -24, 12, 24, 6, 54, 12, -6, -3, -42, 0, 0, 15, -6, -24, -24, 0, -3, -9, 24, 42, 24, -33, -45, -21, -27, -9, 9, 0, 9, -21, -51, 3, -24, 6, 45, -45, 102, -12, 9, 3, 45, -24, 12, 18, 3, 30, 6, -6, 6, 9, -36, 6, 9, 21, 45, -36, 63, -18, -36, -24, -3, 18, 24, 3, -108, 54, -18, -24, -24, 30, 117, -6, -39, 27, -12, -24, -45, 15, 0, -15, 21, 0, 0, 15, 54, -99, 54, 6, 45, 39, 60, -51, -57, 6, -39, 3, -18, -27, -6, 9, -36, -9, 9, 9, 3, 45, -39, 0, -3, 33, -36, -9, -18, -6, 63, 9, 3, -42, 81, 33, 0, 36, -63, 18, -6, -36, -24, 15, 15, -9, 36, -3, 60, 0, -108, -24, -15, -3, 48, -3, -90, 69, 0, -21, 81, -36, -78, 27, 0, 18, 57, -6, 54, -18, -6, -69, 12, 0, 6, -3, -90, 15, -12, 21, 3, -39, -84, -6, 24, -75, 6, -3, -30, -24, -15, -27, 114, -3, -9, 0, 42, 0, 15, -36, -54, -18, 54, -6, 30, 24, -135, 15, 0, 66, 9, 36, 15, -99, -84, -36, -12, 6, -27, 9, -45, 99, -126, -12, -42, -27, 90, -18, -27, 30, -3, -3, 3, -36, 99, -21, 72, 3, -9, 0, -33, 0, 36, 15, -33, -21, 96, -12, 90, 27, 9, 45, -21, -63, 18, 27, -135, -36, -39, -36, -75, -84, 48, 3, 42, 39, 180, -51, -45, -15, 12, -12, 54, 0, 3, 21, -36, 45, 114, 0, 15, -54, 9, 15, -99, -6, 114, 3, 21, 9, 27, 66, 54, 3, -87, -3, -36, 3, 63, -30, 63, -27, -42, 0, -42, 27, 42, 3, -9, -30, -69, -63, -3, -51, 3, -27, 0, -54, -6, -9, -12, 27, 66, -57, 78, 6, 27, 3, 45, -15, 18, -21, 159, 66, -3, -9, -117, -18, -39, -39, 6, 36, -78, 3, -48, -15, 189, 3, -42, 54, 15, 3, 105, -6, 90, -21, -54, 18, -24, -6, -78, 54, 9, 18, 12, -54, 90, 6, 111, 66, 12, 39, -3, -9, 21, 24, 114, 42, 75, -15, -48, 27, 54, 0, 33, -9, -54, -3, -63, 27, -120, -30, 6, -24, 54, 15, -6, 60, 69, -6, 30, 99, -27, -54, -87, 18, -24, -6, 15, 78, 72, -54, 51, -45, 72, -3, 0, -21, 78, -12, -21, 12, -99, 3, 12, 30, -72, 18, -6, -21, 78, -9, 18, 42, 0, -3, 3, -105, -12, -3, -3, -48, 33, -18, -48, 9, -42, 24, 12, 60, -6, -6, 24, 15, -81, 30, 66, 51, -72, 0, 96, -27, 9, 3, -126, -12, 96, -15, 72, -36, -18, 24], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "418.2.a.g", "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, 0, 0], [1, 0, 0], [-1, 0, 0], [0, 1, 0], [1, 0, 0], [-1, -1, -1], [0, -1, 0], [-2, -1, 1], [-1, 0, 0], [1, 1, 1], [1, 1, 1], [-1, 0, 0], [0, 1, 0], [0, -1, 1], [2, 1, -1], [-3, -3, 0], [1, 0, 0], [-3, 0, -1], [-1, -1, -1], [-1, 0, 0], [-1, -1, -1], [-5, -2, -2], [1, 0, 0], [-5, 0, -1], [0, -1, 0], [4, 3, 0], [0, 1, -1], [3, 0, 0], [-2, -1, 1], [2, 1, 2], [3, 3, 0], [-1, 3, 0], [-1, 0, 0], [0, -1, 0], [3, 0, 1], [0, 6, 3], [1, 1, 1], [-2, 0, -2], [1, 0, 0], [-5, 0, -2], [1, 1, 1], [-3, -3, -2], [5, 2, 2], [-7, 3, 1], [-1, 0, 0], [-9, -3, 0], [5, 0, 1], [-4, 4, 2], [0, 1, 0], [9, 1, -2], [-4, -3, 0], [1, -4, 1], [0, -1, 1], [-3, -4, 1], [-3, 0, 0], [1, 1, 1], [2, 1, -1], [0, -1, 0], [-2, -1, -2], [-1, 2, 1], [-3, -3, 0], [8, 0, 2], [1, -3, 0], [0, -6, -3], [1, 0, 0], [-2, 4, 1], [0, 1, 0], [0, 1, -3], [-3, 0, -1], [1, -6, 1], [0, -6, -3], [7, -5, -1], [-1, -1, -1], [-1, 0, -1], [2, 0, 2], [12, 7, 3], [-1, 0, 0], [2, 1, -1], [5, 0, 2], [-2, -2, -4], [-1, -1, -1], [-3, 0, -3], [3, 3, 2], [-11, -1, 1], [-5, -2, -2], [8, 2, 2], [7, -3, -1], [2, 5, -1], [1, 0, 0], [2, 2, 2], [9, 3, 0], [12, -1, 0], [-5, 0, -1], [12, 2, 3], [4, -4, -2], [1, 1, 1], [0, -1, 0], [4, 0, -4], [-9, -1, 2], [-1, -1, -1], [4, 3, 0]]}