# Stored data for newform 418.2.f.d, downloaded from the LMFDB on 25 April 2024.
{"label": "418.2.f.d", "space_label": "418.2.f", "level": 418, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511142513050018, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 555694435983326190, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [16, -8, 4, -2, 1]]], "qexp_display": "q+(-1+\\zeta_{10}-\\zeta_{10}^{2}+\\zeta_{10}^{3})q^{2}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "f", "char_is_real": false, "Nk2": 1672, "analytic_conductor": 3.33774680448952, "hecke_ring_index": 1, "level_radical": 418, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [418, 5, [343, 287], [2, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 11, 19], "conrey_indexes": [115, 191, 229, 267], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.893", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "41.343", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "774.218", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [-1, 2, 2, 9], "traces": [0, 4, -1, 2, -1, 2, 2, 9, -1, -1, 2, -1, -8, 12, 9, 6, -1, -7, -1, -1, 2, 12, -11, -18, 2, 1, -8, -4, -6, -16, 6, -2, 4, 2, 18, -3, -1, -4, -1, -24, -3, 2, 12, -14, 4, 2, -3, 0, 2, 16, 6, 4, -8, 12, 16, 7, -6, 2, -16, -2, -4, -23, -2, 9, -1, 16, -18, 20, -7, -24, 12, 24, -1, 14, -4, -12, 4, 24, 16, 18, -3, 11, 12, -26, -18, -11, -9, -48, -1, 36, 2, 12, 12, 4, -5, -3, 2, 2, 26, -11, -14, -18, 4, 2, 12, 6, 2, -6, -4, 4, -3, -32, -6, 0, 2, -9, 4, -8, -2, -27, -4, -41, 2, -24, -2, 23, -6, -24, -1, -32, -4, -26, 2, -6, -10, -12, -2, 22, 6, 20, 12, 10, -16, 12, 4, 12, 14, 58, -4, 26, -2, 22, -1, 18, -36, 4, -24, -33, -12, -24, 2, -63, 11, 26, -28, 16, -6, 42, -18, 29, 9, -1, 16, 32, -8, 6, 9, 64, -4, -16, -3, 22, 12, -44, 12, 8, -16, 38, 10, -24, -3, -23, 2, 46, 12, 8, 16, -72, 4, 18, 6, 0, 27, -36, 14, 16, 2, -3, -8, -1, 36, 28, 2, 32, -6, -7, -4, 18, 4, 112, -8, -56, 8, 18, 9, 6, -20, 0, 2, -45, -24, -18, 24, 34, -8, -5, 18, -36, 33, -28, -4, 40, 19, 40, -23, -42, -4, 12, -2, -58, 23, -15, -6, 12, -24, -18, -1, -18, 18, -24, -4, -16, -6, 8, 22, -4, -6, 28, 0, -38, 8, -52, -2, -24, -38, 16, 36, -2, 20, -2, -3, -24, 0, -23, 24, -4, -48, 12, -1, 18, -28, -4, 14, 50, 58, -16, 16, 36, -64, -24, -2, -69, -8, 36, -1, 21, -7, -56, -21, 56, 4, 44, 16, 7, 2, 12, -12, -16, 56, -16, 2, 12, -63, -2, 11, -52, -9, 12, 12, 0, -24, -12, -26, -4, -18, 10, 12, 46, 29, 40, 4, -22, 4, 3, 16, -42, -8, -21, 32, 55, 21, -32, -1, 66, -36, -8, -14, 54, 34, -12, -3, -1, -28, 2, -48, -28, -44, -11, -3, 12, -12, -48, 4, -32, -2, 24, -5, -48, 36, -4, 2, -72, -23, -26, -8, 57, -4, -9, 12, 34, 8, -6, -29, -38, 18, 24, -1, 70, 18, -18, 1, -18, 20, -16, 27, -22, -96, 16, -36, 34, 16, 6, 12, 48, 12, 32, 12, 20, 9, 6, 6, -28, -32, -5, 12, -3, 32, -3, 24, 16, -32, -58, -4, -20, -12, -24, -6, 12, -28, 12, -8, 26, 64, 69, 8, 18, -12, -12, 9, 22, -14, 32, 40, 16, 0, 36, 2, 22, 30, -8, -9, 70, -48, -38, 4, 12, -21, -38, 12, 30, -5, -4, -32, 16, 24, 6, 33, 2, 7, 17, 6, -32, -10, -144, 19, -24, -10, -10, 22, -52, 13, 21, -4, 8, -8, -3, 8, 24, -58, 15, -17, -84, 0, -72, -6, -54, 57, -88, -24, -42, 22, 84, -1, -4, -18, -14, 28, -15, -24, 16, -4, 34, 4, 54, 19, 48, -12, 36, -8, 34, -14, -2, 9, -104, 8, -18, 0, -68, 12, 81, 8, -23, -52, 16, -7, 2, -24, -28, 22, 2, -29, 24, 6, 18, 18, -16, -15, 55, -2, 8, -18, -56, -44, 18, 0, -20, 22, 66, -16, -34, -4, 38, 52, 76, 42, -27, -1, -18, -27, 88, -28, 9, 56, 72, -56, -4, 50, 0, -32, -2, 14, -36, -4, -66, -4, -66, 26, 54, 36, -46, -12, -10, -69, -10, -28, -38, 36, -36, -1, -168, 1, 40, -2, 62, 44, 8, 9, -8, -24, 20, -6, -12, -11, 96, 16, -36, 22, 22, 62, -28, 12, -48, 18, -56, 34, 48, -24, 128, 44, -16, 2, 80, 12, -61, 27, -46, -2, 12, -44, -72, 48, 24, -9, -2, -8, -13, 2, 14, -15, 108, -14, -20, 18, 72, 29, -3, -4, 132, -18, 24, 0, -18, 12, 92, 46, 4, -51, -42, 0, -78, 9, 0, 8, 36, -1, 16, 63, 90, -9, 56, -42, 30, -48, -36, -6, -5, 32, -6, -50, -68, -24, 54, 48, 16, -11, 0, -14, -108, 4, 10, -8, -12, -14, -6, 24, -4, -36, -14, -12, -5, 2, 42, -1, 20, 22, -64, -8, 62, 12, -13, 42, -38, 46, -19, -11, -26, -18, 0, -28, 78, -12, 16, 42, -48, 4, 38, 58, -6, -47, -36, 34, -6, 0, 30, 32, 36, 36, -18, -4, 66, 2, -90, -72, 24, 42, 9, 14, 64, 2, 62, 12, 16, 46, -46, 16, 12, 2, -72, 34, 12, -32, -16, -66, 16, -29, -64, 12, 54, 18, -16, -6, 0, 9, -184, -25, -32, -27, 98, 12, 5, 1, -4, 32, -56, -40, 36, -16, -64, -18, -18, 33, -90, -36, 44, -4, 18, 14, 16, -6, 12, -14, -22, 6, -18, -28, -72, -12, -78, 12, -68, -3, 4, -8, -103, 30, 36, -1, 32, -19, -12, -24, 93, -28, -92, -32, 22, 10, -111, -28, -44, -3, 48, -48, 25, -63, -3, -6, 76, 16, 14, -7, 96, 22, -62, -4, 56, -20, 54, -12, 18, -64, 80, -6, 12, -3, 18, -28, 58, -48, 120, 12, 48, 16, -95, -36, 32, -46, -70, 8, 36, 28, -44, -12, -5, -12, 2, -6, 48, -28, -32, 6, -136, -58, -192, -20, 6, -44, 64, 0, 27, 36, -30, -8, -41, -98, -2, 30, -96, -28, 66, 21, 32, 10, 192, -48, -56, -18, 2, -16, -69, -8, -29, -21, 22, 102, 49, -8, -119, 30, 36, 5, -20, 66, -54, 18, -72, 51, -22, -36, 112, 1, 32, -27, 66, 2, -19, 42, 32, -18, 57, 6, 27, 48, -6, -10, -42, -54, -166, -1, -36, -14, -38, -10, 15, -10, -56, 22, -42, 68, -14, 58, 4, 21, -130, -24, -36, -52, -30, 12, 138, -8, -16, -2, 24, 24, 9, 52, -33, 15, -16, -12], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 11, 3, 1, 5, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "418.2.f.d", "char_is_minimal": true, "conrey_index": 115, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 1, -1, 1], [0, 0, -2, 0], [0, 0, 0, -1], [1, -1, 1, 0], [0, 2, 0, 0], [3, -3, 0, 0], [0, 0, 1, 0], [-1, 1, -1, 1], [0, 0, -1, 1], [-2, 4, -1, 2], [-2, 0, 0, 0], [4, 0, 0, -4], [0, 3, -3, 3], [2, -2, 0, 0], [0, -1, 0, 0], [-1, -4, -1, 0], [0, 0, 0, -1], [0, 0, 1, 0], [0, 1, -1, 0], [0, 0, -6, 6], [-2, -1, 0, -2], [-3, 0, 3, -3], [2, -2, 2, -2], [0, -1, -3, -1], [-4, 4, 0, 4], [0, -4, 0, 0], [-3, 3, -3, 0], [-4, 4, 0, -4], [0, 2, -2, 2], [-2, 2, -2, 2], [1, 0, 0, 0], [2, 2, 2, -6], [5, 0, 1, -1], [3, -6, 6, -3], [0, 0, 1, 0], [0, 0, 0, -4], [0, -1, 0, 0], [-8, 0, -8, 0], [-1, 1, 0, 0], [0, -2, -6, -2], [0, 6, -6, 0], [-1, 0, 5, -5], [3, -2, 4, -2], [0, 0, -1, 1], [3, -6, 6, -3], [0, 1, 2, 1], [0, 0, 0, 2], [9, -11, 9, 0], [1, 3, 1, 0], [-2, 2, 0, 10], [0, -4, 0, -4], [8, -6, 6, -8], [4, 0, 0, 0], [-1, 3, -4, 4], [0, 0, 3, -3], [2, -2, 2, -2], [0, -4, 8, -4], [-4, 4, 0, 10], [-2, 2, -2, 0], [-9, 4, -9, 0], [0, 0, 0, -2], [0, 3, -3, 3], [-1, 1, -1, 1], [4, 0, 0, 0], [-4, 0, 4, 2], [6, 0, 2, -2], [-5, 4, -4, 5], [0, -6, 12, -6], [3, -3, 0, 3], [8, 0, 8, 0], [0, -1, 0, 0], [0, 0, 0, 14], [0, 0, 4, 0], [-8, 6, -6, 8], [1, 0, 0, 0], [0, 12, -9, 3], [8, 0, 8, -8], [6, 0, 0, -6], [0, -1, 1, -1], [0, 0, 0, 11], [2, 6, 2, 0], [-11, 7, -11, 0], [-6, 6, 0, 0], [0, -4, 3, -4], [1, -6, 6, -1], [-8, 0, 8, -8], [-1, -1, -1, 3], [8, 0, -2, 2], [0, 1, -1, 0], [0, 0, -12, 0], [3, -3, 0, 3], [0, 4, 0, 0], [-1, -2, -1, 0], [-1, 1, 0, 0], [0, 0, -2, 0], [6, -8, 8, -6], [2, 0, -9, 9], [-2, -1, 0, -2], [-4, 0, -1, 1]]}