# Stored data for newform 57.2.e.b, downloaded from the LMFDB on 01 November 2025.
{"Nk2": 228, "analytic_conductor": 0.4551472915212982, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [57, 3, [20, 40], [3, 1]], "cm_discs": [], "conrey_index": 7, "dim": 6, "field_disc": -954288, "field_disc_factorization": [[-1, 1], [2, 4], [3, 3], [47, 2]], "field_poly": [27, -9, -6, 3, -2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [9, -15, 28, -1, 6, -1, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503874538831929, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "57.2.e.b", "level": 57, "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": [3, 19], "level_radical": 57, "minimal_twist": "57.2.e.b", "nf_label": "6.0.954288.1", "prim_orbit_index": 3, "qexp_display": "q+(-\\beta _{4}+\\beta _{5})q^{2}-\\beta _{3}q^{3}+(-2-\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "57.2.e", "trace_display": [1, -3, -2, -2], "trace_hash": 608500418467347334, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.809", "prec": 17}, {"__RealLiteral__": 0, "data": "2.397", "prec": 17}, {"__RealLiteral__": 0, "data": "134.715", "prec": 24}, {"__RealLiteral__": 0, "data": "159.576", "prec": 24}, {"__RealLiteral__": 0, "data": "5526.663", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.010", "prec": 17}, "traces": [0, 6, 1, -3, -5, -2, 1, -2, -6, -3, 4, 0, 10, 1, 3, -2, -5, 0, -2, 4, 44, 1, -18, -14, 3, -5, -42, 6, -17, -4, -8, 30, 17, 0, 0, -18, -5, -6, 41, -2, 24, 4, 3, 3, -12, 4, 40, 18, -5, -4, -46, 0, -5, 6, 1, -12, -42, -5, -16, 0, -22, -13, 23, 1, -30, 12, -18, -9, 0, 28, 24, 18, 3, -19, -1, 10, 27, 24, 21, -11, -10, -3, -8, -8, 34, 0, 17, 8, 12, 16, 4, -7, 2, -15, 12, 2, -34, 2, 14, 0, -15, -22, 0, -18, 27, -18, 24, -20, -5, 18, -24, 3, -5, -24, -25, -32, -44, 1, 18, 0, 24, 30, -38, 4, -13, 0, -6, -28, -21, 3, 48, 14, 24, -32, 86, -2, 0, -18, -20, 29, 36, -36, -42, 36, 10, 80, 13, 2, 5, -12, 23, 32, 12, 0, -6, 2, -5, -25, -21, -12, -16, 30, 1, 42, -88, -12, -44, -12, 21, -4, 0, 1, -34, -28, 8, -5, 36, 0, 4, -28, -22, -18, -54, 26, -36, 2, 23, 0, 30, -2, -76, -36, 15, 23, 70, -6, 34, 112, 36, 29, 33, 18, -100, -36, 0, 40, 23, -14, 82, -60, -48, -3, 66, 18, 10, 14, -6, -34, 2, -19, -48, 0, -1, 17, -9, -5, 42, 36, -24, -2, -56, -12, 48, -26, 21, -24, -24, -11, 0, -36, 20, -23, -59, -3, 9, 32, 16, 49, -42, 4, 36, -18, -17, -24, -32, 0, 27, 2, -34, 2, -42, -4, 2, -18, -6, -120, 39, -32, 17, 12, 4, 16, 0, 14, 60, 36, 2, 20, 10, -15, 24, 38, -6, -28, -12, 26, -84, 36, 17, 51, 56, 2, 138, 4, 14, 12, 6, 0, -6, 54, -15, 11, -44, 44, -87, -44, 0, -8, 36, 9, 44, 16, -54, -30, -41, 36, -14, 42, -12, -24, 22, 10, 72, 0, 10, -41, 53, 18, -48, -6, 48, -86, 20, 3, -84, -52, -5, -27, -28, 12, 0, -96, -16, -46, 3, 16, -40, -54, -44, 50, -66, 1, 18, 92, -36, -12, 8, 0, -16, 4, -48, -18, 44, -15, -37, -50, 19, 15, -52, -8, -4, 54, 26, 60, 0, 0, -18, -12, 3, 58, 28, 56, 48, -28, -21, 48, 7, -6, 108, -42, 48, 0, 36, 14, 58, 18, -12, 3, 82, 7, 102, 20, -43, -31, -50, -2, -96, 0, 0, -58, 112, 36, 95, 12, -20, 16, -27, -58, 54, 8, -18, 6, -1, 18, -72, 0, 84, 35, -58, -72, -40, -18, -5, -25, 21, -40, -196, -70, -26, -25, -60, 2, 0, 36, -10, 16, -53, -12, -14, -32, 23, 24, -12, -16, 24, 60, 39, 118, 21, 0, -28, -24, -6, -6, 40, 2, 94, -80, 10, 35, -24, -25, 6, 48, 42, 51, 0, 6, -24, 2, 8, -1, -114, -60, -5, -56, -2, -24, -3, -21, -4, 10, 44, 0, 48, 24, -61, -30, -44, -7, 24, 24, -84, -36, 21, 56, 216, -4, -84, 50, 0, -31, 118, 4, 152, 86, 17, 0, -3, -28, -168, 152, 8, 21, 28, 10, -30, 0, 36, -71, -84, 0, 55, -24, -2, -68, -69, 14, -30, -120, 44, -27, -120, 36, 0, 80, 27, 23, -54, -13, -12, 52, 72, 29, -110, 2, 135, -42, -46, 74, -66, 0, -40, -28, 30, -24, 52, 1, -30, -48, -4, -18, 96, 18, -48, 26, 15, -44, 34, 23, -80, -24, -140, 36, 63, -6, -98, -16, -68, 80, -48, -56, 5, -12, -18, 0, -72, -58, 72, 84, -66, 26, 3, -9, 24, 10, 50, 22, 19, 72, 16, -6, 0, 10, -12, -80, 108, -28, 23, -18, 268, -14, 70, -24, -41, 49, -148, 84, -18, 0, 24, -31, -39, -3, 120, 112, 66, -30, 96, -36, -12, -94, 10, 105, -30, -28, 0, -24, 3, 48, 27, 17, -67, 92, -4, -28, 20, 38, 36, -56, 24, -14, -39, 0, 120, -114, 2, 32, -120, 17, -112, 60, 18, -78, -55, -5, 136, -52, 42, -58, 0, -18, -42, 132, -3, 72, -39, 1, -31, 18, -56, -216, -8, -12, 36, -212, -96, 0, 43, -26, -71, 54, -42, -4, -96, 12, -4, -6, 12, -39, 144, 22, 6, -46, 0, -120, -26, 18, 28, 10, -10, -154, -71, 46, 14, -20, -59, 21, 57, 6, -152, 0, 9, -76, 230, 32, 104, -60, -8, -65, -44, 28, 144, 72, 21, 48, 38, 4, 0, 156, 36, 41, -60, 36, 96, 40, -17, -27, -51, 48, 192, -136, 16, 62, 66, 0, 50, 72, -54, 55, -60, -4, -138, 54, 17, -61, 126, -1, -264, -4, 84, -96, 0, -4, -26, 34, -4, 30, -88, -18, 120, 72, -6, -25, -49, 60, 111, 132, -51, 0, 7, 16, -10, -24, 17, 120, -126, 12, 78, 164, -8, 24, -36, 16, 18, -46, 0, -79, -140, -7, 80, -12, -30, -40, 126, -72, 6, 80, -4, -114, -104, -10, -41, 0, -5, 216, -120, 30, -10, -18, 24, 7, -10, -76, -238, -64, -6, -50, -60, -28, 0, 14, 6, 11, 6, -28, -156, 18, 42, 27, -2, 36, 132, -52, 17, 32, 58, -102, -121, -24, 56, 95, -78, -4, -124, -48, -69, 39, 97, -2, 36, 4, -28, 19, 0, -24, 96, -28, -3, -28, 4, 0, 90, -6, 12, -40, 9, 54, 4, 4, 30, 0, 48, 11, -132, -64, -44, -28, -18, -22, 84, -88, 51, 144, -15, 22, -5, -42, 0, -54, 24, -8, -18, -132, -72, 5, 29, 9, 16, 94, -88, 88, 140, -8, 52, 0, 27, 27, 138, 60, 132, -40, 82, 64, -36, -18, 66, 22, 7, 14, 16, -84, 0, -52, -12, 48, 18, 48, 212, -18, 22, 60, 42, 10, -89, 46, -36, -25, 138, 0, -392, 6, -5, 77, -40, -41, 102, 84, 53, -12, -32, -36, -26, 52, -48, -32, 0, 12, -239, -76, -24, 23, 67, 43, -30, -164, -40, -141, -77, -6, -24], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1], [0, 0, 0, -1, 0, 0], [-2, -1, -1, 2, 0, 0], [0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0], [-1, 0, -1, 0, 1, 0], [-1, 0, 0, 1, 0, 0], [1, 1, 1, -1, 0, -2], [1, 0, 1, 0, 2, 0], [2, 0, 1, 0, 0, 0], [1, 0, 0, -1, 0, 2], [0, -1, 0, 1, -1, 1], [-1, -1, -1, 1, 0, 0], [0, 0, 0, -1, 2, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -2], [7, 0, 1, 0, -2, 0], [0, 1, 0, 0, 0, 0], [0, 1, 0, -7, -2, 2], [-5, 1, 1, 5, 0, -2], [0, -1, 0, 1, -1, 1], [-1, 0, 0, 1, 0, 2], [-8, 0, -2, 0, -1, 0], [1, 0, 0, 0, 0, 0], [-5, 0, 0, 5, 0, 2], [-2, -2, -2, 2, 0, 0], [-1, 0, -1, 0, 2, 0], [4, 0, -1, 0, -2, 0], [6, 0, 0, -6, 0, 1], [0, 1, 0, -1, -2, 2], [0, 0, 0, 0, 0, 0], [0, -1, 0, -5, 2, -2], [0, 1, 0, -2, 0, 0], [-1, 0, 0, 0, 0, 0], [8, 1, 2, -1, 1, -1], [-1, 0, 0, 0, -2, 0], [0, -1, 0, 7, -4, 4], [0, -2, 0, 2, 0, 0], [1, 1, 1, -1, 0, -1], [0, -1, 0, 2, 2, -2], [-5, 1, 1, 5, 0, -4], [1, 0, 1, 0, 0, 0], [9, 0, 3, 0, 4, 0], [6, 0, 0, -6, 0, 0], [-1, 0, 0, 1, 0, 2], [-2, 0, -2, 0, -2, 0], [-8, 0, -2, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 6, -6], [3, 3, 3, -3, 0, 0], [0, 0, 0, 0, -1, 1], [0, -2, 0, -4, -2, 2], [-6, 0, 0, 0, 3, 0], [0, -1, 0, 0, 2, 0], [-2, 0, -2, 0, 4, 0], [0, -1, 0, 1, 2, -2], [0, 1, 0, -7, 2, -2], [-3, 2, 2, 3, 0, 2], [0, -1, 0, 7, -3, 3], [0, -1, -1, 0, 0, 0], [-6, 0, -1, 0, -2, 0], [1, 0, 1, 0, -4, 0], [-7, -1, -1, 7, 0, -2], [-4, 1, 1, 4, 0, -4], [0, 0, 0, 0, 0, 0], [5, 0, -1, 0, 2, 0], [7, 1, 1, -7, 0, -4], [0, 2, 0, 4, -4, 4], [1, 1, 1, -1, 0, -1], [0, 2, 0, -7, 0, 0], [0, 0, 0, 0, 1, -1], [1, 0, 0, 0, -2, 0], [5, -2, 0, -3, -6, 4], [3, 0, -3, 0, 0, 0], [0, -2, 0, 8, 1, -1], [0, -1, 0, -4, -2, 2], [-3, -3, -3, 3, 0, 4], [0, 0, 0, -1, 0, 0], [-2, -2, -2, 2, 0, 4], [0, 0, 0, 0, 4, 0], [5, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0], [7, 1, 1, -7, 0, 3], [2, 0, 2, 0, 0, 0], [3, 0, 3, 0, 0, 0], [5, -1, -1, -5, 0, 0], [0, -1, 0, 1, -2, 2], [-2, -1, -1, 2, 0, 2], [0, 3, 0, -3, -8, 8], [0, -1, 0, -4, 2, -2], [0, 0, 0, 0, -6, 0], [-2, 1, -2, 5, 2, 2], [-6, 0, 0, 0, -1, 0], [0, 2, 0, 2, 6, -6], [0, 0, 0, 6, 4, -4], [-1, -1, -1, 1, 0, -2], [0, 3, 0, -4, 6, -6]]}