# Stored data for newform 126.2.e.d, downloaded from the LMFDB on 24 April 2024.
{"label": "126.2.e.d", "space_label": "126.2.e", "level": 126, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511073793572990, "dim": 6, "is_polredabs": true, "nf_label": "6.0.309123.1", "trace_hash": 2139367506979617448, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [9, -12, 31, 26, 21, 5, 1]]], "qexp_display": "q+q^{2}+(\\beta _{3}-\\beta _{4}-\\beta _{5})q^{3}+q^{4}+(\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "e", "char_is_real": false, "Nk2": 504, "analytic_conductor": 1.0061150654681328, "hecke_ring_index": 1, "level_radical": 42, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.008", "prec": 17}, "analytic_rank_proved": true, "char_values": [126, 3, [29, 73], [2, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [25, 121], "field_disc": -309123, "field_disc_factorization": [[-1, 1], [3, 3], [107, 2]], "field_poly": [3, -12, 19, -15, 10, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.746", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "137.034", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6142.874", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [6, -2, -5, 4], "traces": [0, 6, 6, -2, 6, -5, -2, 4, 6, -4, -5, -1, -2, -2, 4, -2, 6, -4, -4, -3, -5, -10, -1, -7, -2, -2, -2, 7, 4, -5, -2, 28, 6, -19, -4, -19, -4, -9, -3, 9, -5, -12, -10, 18, -1, 29, -7, -6, -2, -12, -2, 26, -2, 9, 7, 14, 4, 2, -5, -8, -2, -8, 28, 31, 6, 24, -19, -10, -4, -1, -19, 14, -4, -25, -9, 44, -3, 52, 9, -14, -5, -40, -12, 8, -10, 14, 18, 31, -1, -9, 29, 4, -7, 0, -6, -4, -2, -28, -12, -41, -2, -11, 26, -6, -2, -22, 9, -15, 7, -7, 14, 2, 4, 1, 2, -22, -5, -27, -8, 10, -2, -20, -8, -12, 28, 12, 31, -26, 6, -43, 24, -14, -19, -31, -10, -20, -4, 16, -1, -28, -19, 18, 14, -6, -4, 16, -25, -32, -9, 0, 44, 35, -3, -2, 52, -39, 9, 66, -14, -45, -5, -11, -40, -30, -12, 35, 8, 10, -10, 29, 14, 28, 18, 52, 31, -9, -1, 7, -9, 0, 29, 94, 4, -27, -7, 2, 0, 76, -6, 38, -4, -60, -2, -48, -28, -24, -12, 62, -41, -18, -2, 43, -11, 53, 26, 54, -6, 25, -2, 28, -22, 33, 9, 35, -15, 11, 7, 25, -7, 37, 14, -36, 2, -21, 4, -68, 1, -21, 2, -4, -22, -17, -5, 23, -27, 24, -8, -51, 10, -15, -2, 3, -20, -2, -8, -11, -12, 5, 28, -16, 12, -108, 31, -32, -26, -118, 6, 9, -43, -64, 24, -43, -14, 33, -19, -18, -31, 33, -10, 10, -20, 4, -4, 15, 16, 7, -1, 9, -28, -3, -19, -7, 18, 38, 14, -13, -6, 21, -4, -53, 16, 34, -25, 27, -32, -35, -9, 11, 0, 30, 44, -10, 35, 19, -3, 45, -2, 14, 52, 29, -39, -8, 9, -40, 66, 37, -14, 42, -45, -76, -5, 33, -11, -8, -40, -29, -30, 25, -12, -39, 35, 72, 8, 52, 10, 22, -10, -41, 29, 85, 14, -39, 28, 61, 18, 80, 52, -78, 31, 8, -9, 18, -1, -15, 7, 2, -9, -50, 0, 19, 29, 36, 94, 47, 4, -38, -27, -87, -7, -48, 2, -66, 0, -58, 76, -69, -6, -42, 38, -4, -4, -48, -60, 38, -2, -44, -48, -26, -28, 28, -24, 40, -12, 64, 62, -21, -41, -38, -18, 31, -2, -18, 43, -25, -11, 41, 53, 55, 26, 54, 54, 25, -6, 32, 25, 8, -2, -2, 28, 12, -22, 28, 33, -15, 9, -176, 35, -14, -15, 27, 11, 9, 7, 30, 25, -14, -7, 22, 37, -68, 14, 20, -36, -82, 2, 54, -21, -21, 4, -26, -68, -33, 1, -14, -21, 51, 2, 98, -4, 104, -22, -8, -17, 35, -5, 0, 23, 25, -27, -60, 24, 26, -8, -38, -51, 8, 10, 48, -15, 56, -2, 8, 3, -5, -20, -50, -2, -12, -8, -121, -11, -3, -12, -40, 5, -23, 28, -44, -16, 35, 12, -80, -108, 42, 31, -2, -32, -49, -26, -3, -118, 27, 6, -13, 9, 11, -43, -12, -64, -62, 24, -39, -43, 27, -14, 31, 33, -6, -19, 28, -18, 47, -31, -15, 33, 60, -10, 21, 10, -16, -20, -32, 4, -93, -4, 4, 15, 19, 16, -33, 7, 74, -1, 79, 9, -31, -28, -11, -3, 14, -19, 88, -7, -40, 18, 76, 38, -98, 14, 42, -13, -32, -6, 3, 21, 100, -4, 41, -53, -1, 16, -29, 34, 84, -25, 3, 27, 53, -32, 11, -35, 8, -9, 75, 11, 130, 0, 17, 30, 156, 44, -21, -10, -7, 35, -13, 19, -53, -3, 23, 45, 21, -2, -5, 14, -12, 52, -7, 29, 11, -39, -76, -8, -48, 9, -17, -40, -65, 66, -8, 37, -90, -14, 38, 42, 48, -45, -26, -76, -23, -5, 8, 33, -36, -11, 44, -8, 96, -40, -49, -29, -3, -30, -57, 25, 22, -12, 23, -39, 14, 35, -22, 72, 66, 8, 22, 52, 5, 10, 14, 22, 99, -10, -27, -41, 56, 29, -78, 85, 0, 14, -3, -39, 45, 28, -50, 61, -50, 18, 54, 80, 6, 52, -28, -78, 142, 31, 48, 8, -46, -9, -164, 18, -45, -1, 18, -15, -118, 7, -30, 2, 42, -9, -39, -50, 9, 0, -150, 19, 54, 29, 71, 36, -154, 94, -124, 47, 23, 4, 65, -38, 94, -27, 40, -87, 7, -7, -64, -48, 1, 2, -24, -66, -33, 0, -21, -58, 13, 76, -81, -69, -101, -6, 9, -42, -200, 38, -2, -4, 25, -4, 32, -48, 36, -60, 70, 38, -39, -2, -13, -44, -42, -48, 49, -26, -47, -28, 82, 28, 6, -24, -68, 40, -44, -12, 2, 64, -92, 62, 69, -21, -49, -41, 41, -38, 27, -18, -39, 31, -66, -2, -21, -18, -136, 43, -59, -25, -14, -11, 52, 41, -64, 53, 24, 55, -28, 26, -42, 54, -48, 54, 62, 25, 8, -6, 55, 32, 12, 25, 2, 8, -25, -2, 164, -2, -158, 28, -36, 12, 35, -22, -2, 28, 77, 33, 38, -15, -63, 9, -71, -176, 58, 35, -66, -14, 13, -15, -12, 27, -54, 11, 69, 9, -32, 7, -83, 30, -10, 25, 81, -14, 17, -7, 56, 22, 90, 37, 35, -68, -36, 14, 186, 20, -36, -36, 7, -82, 93, 2, 13, 54, 124, -21, 0, -21, 21, 4, -42, -26, 33, -68, 66, -33, 73, 1, -78, -14, 34, -21, 89, 51, -3, 2, 100, 98, -27, -4, 122, 104, 23, -22, 13, -8, 9, -17, 14, 35, -59, -5, 84, 0, 21, 23, -11, 25, -116, -27, 84, -60, 52, 24, -80, 26, 48, -8, -97, -38, -74, -51, 26, 8, 90, 10, -4, 48, 90, -15, 23, 56, -13, -2, 26, 8, 3, 3, 80, -5, 6, -20, -38, -50, 45, -2, 21, -12, 6, -8, 54, -121, 39, -11, -22, -3, 54, -12, -31, -40, 39, 5, 7, -23, 0, 28, -52, -44, -37, -16, 111, 35, -25, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 63, 8, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 8, "minimal_twist": "126.2.e.d", "char_is_minimal": true, "conrey_index": 25, "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, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, -1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 2, -1], [0, 0, 0, 1, -1, -1], [0, 2, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0], [-1, -2, 0, 0, -2, 1], [0, 1, 0, 0, 2, -1], [0, -1, 1, -1, 0, -1], [0, 0, 0, 1, -1, -1], [-1, -1, -1, -1, -1, 1], [0, 2, 1, 0, 1, 0], [-2, -1, -2, -1, -2, 3], [1, 0, 0, 0, 0, 0], [-2, 0, 0, -2, 2, 4], [-1, -2, 0, 0, -2, 1], [-1, 1, 0, 1, -1, 0], [0, 1, 0, 0, 2, -1], [1, -1, -1, 2, 2, 0], [0, -1, 1, -1, 0, -1], [1, 0, 0, 1, 2, -2], [0, 0, 0, 1, -1, -1], [-2, -3, -4, -3, -2, 4], [-1, -1, -1, -1, -1, 1], [1, 2, 2, -2, 3, -2], [0, 2, 1, 0, 1, 0], [1, -4, 0, 1, 0, 2], [-2, -1, -2, -1, -2, 3], [6, -1, 1, 3, -1, 0], [1, 0, 0, 0, 0, 0], [-7, 4, 1, -4, 0, -1], [-2, 0, 0, -2, 2, 4], [-1, 1, 1, 1, 2, -4], [-1, -2, 0, 0, -2, 1], [-3, 2, 0, 2, -3, 0], [-1, 1, 0, 1, -1, 0], [1, 2, 2, 0, 1, -1], [0, 1, 0, 0, 2, -1], [-4, -1, 0, -1, -4, 0], [1, -1, -1, 2, 2, 0], [1, 1, 0, 1, -6, -3], [0, -1, 1, -1, 0, -1], [8, 1, 3, 3, 4, -2], [1, 0, 0, 1, 2, -2], [-1, -1, -3, -1, -1, 0], [0, 0, 0, 1, -1, -1], [-2, 1, 5, 2, 0, -1], [-2, -3, -4, -3, -2, 4], [8, 4, 0, 0, 10, -2], [-1, -1, -1, -1, -1, 1], [-1, 5, 0, -1, -1, -3], [1, 2, 2, -2, 3, -2], [4, -3, -4, 2, -3, 0], [0, 2, 1, 0, 1, 0], [3, -3, 0, 2, 1, 1], [1, -4, 0, 1, 0, 2], [1, -1, 4, 6, -1, 0], [-2, -1, -2, -1, -2, 3], [-5, 3, -2, -8, 3, 0], [6, -1, 1, 3, -1, 0], [4, -4, -4, -2, -3, 4], [1, 0, 0, 0, 0, 0], [4, 1, 3, 1, 1, 0], [-7, 4, 1, -4, 0, -1], [0, -3, -4, 2, -3, 0], [-2, 0, 0, -2, 2, 4], [-4, -2, -3, -3, -5, 4], [-1, 1, 1, 1, 2, -4], [4, -3, -4, 2, -3, 0], [-1, -2, 0, 0, -2, 1], [3, -4, 0, 3, 6, -2], [-3, 2, 0, 2, -3, 0], [7, 5, 5, 2, 2, -3], [-1, 1, 0, 1, -1, 0], [10, -1, -2, 3, -4, -3], [1, 2, 2, 0, 1, -1], [-4, 4, 7, -1, 4, 0], [0, 1, 0, 0, 2, -1], [-10, 4, -1, -2, -1, 0], [-4, -1, 0, -1, -4, 0], [-2, 3, 0, -2, -1, 1], [1, -1, -1, 2, 2, 0], [8, 4, 10, 4, 8, -10], [1, 1, 0, 1, -6, -3], [4, 2, -1, -5, 3, -2], [0, -1, 1, -1, 0, -1], [-4, -1, -3, -1, -4, 3], [8, 1, 3, 3, 4, -2], [-2, -1, -3, -2, -4, 2], [1, 0, 0, 1, 2, -2], [4, -4, -2, 4, -4, -5], [-1, -1, -3, -1, -1, 0], [-1, 1, 2, 0, 1, 0], [0, 0, 0, 1, -1, -1], [2, -2, 0, 2, 8, -2], [-2, 1, 5, 2, 0, -1], [-8, 5, 4, -1, 7, 3], [-2, -3, -4, -3, -2, 4]]}