# Stored data for newform 126.2.f.c, downloaded from the LMFDB on 24 April 2024.
{"label": "126.2.f.c", "space_label": "126.2.f", "level": 126, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007542885679230, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 602921084665082157, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [25, -10, 9, 2, 1]]], "qexp_display": "q+(-1+\\beta _{2})q^{2}+(1-\\beta _{3})q^{3}-\\beta _{2}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "f", "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": "0.026", "prec": 17}, "analytic_rank_proved": true, "char_values": [126, 3, [29, 73], [2, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [43, 85], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "3.870", "prec": 17}, {"__RealLiteral__": 0, "data": "0.985", "prec": 17}, {"__RealLiteral__": 0, "data": "56.892", "prec": 20}, {"__RealLiteral__": 0, "data": "33.865", "prec": 20}, {"__RealLiteral__": 0, "data": "1399.739", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 4, -2, 2], "traces": [0, 4, -2, 4, -2, -2, -2, 2, 4, -4, 4, -4, -2, 0, 2, -14, -2, 8, 2, 20, -2, 2, -4, 2, 4, -4, 0, -20, -4, 4, 4, -12, -2, -4, -4, -4, 2, 8, -10, 24, -2, 0, 2, -4, 8, -22, -4, 0, -2, -2, -4, 8, 0, -24, 10, 8, 2, 20, 4, 4, 10, -18, 24, -2, 4, 24, -4, 16, -4, 2, 2, 20, -4, -8, -4, 20, -10, 4, 0, -6, 4, -28, 0, -4, -4, -4, -4, 28, -4, -48, -4, 0, 2, -12, 0, -22, -2, 4, 4, 4, 8, 10, -4, -28, 0, -4, 12, -48, 10, -8, -4, 8, 2, 22, 2, 2, -8, 48, -8, 4, -14, 14, -18, 48, -12, 36, -2, -12, -2, -28, 24, 22, 8, 10, -32, -2, 8, 4, -4, -14, 2, -48, -10, 0, 2, 40, 4, -2, -4, 12, -28, 10, 20, -8, -8, -12, -24, 2, -6, -24, -2, 4, 14, -40, 0, 8, -4, -8, 2, -22, 8, -20, 8, 16, -20, 4, -4, 4, 24, 24, 26, -12, 0, -6, 2, 44, 24, -8, 0, -10, 44, -18, 4, 26, 4, 0, -2, 8, 4, 8, -4, -8, 10, -4, -4, 48, 56, -2, 0, -20, -10, -16, 12, 20, 24, -40, -20, -24, 4, -8, -4, 0, -52, 32, -4, 52, -44, 6, -22, 22, 2, 4, 4, -28, 0, -96, 4, 18, 4, 6, 4, 8, -28, 4, 36, -2, 0, 24, -12, -4, -18, 60, 4, -8, 6, -28, -2, -36, 20, 4, -48, 44, -44, -42, -4, -12, 10, -48, 16, -44, -20, 48, -4, 0, 4, -8, 2, 8, 28, 12, -4, 38, 48, 46, -10, -94, 0, 0, 2, -52, -20, -20, 4, -30, 4, 4, 8, 20, -24, 0, 8, 4, 10, 70, -10, 60, 4, 52, 4, -28, -12, -32, 24, -20, -4, 4, 12, -12, 36, 8, -2, -48, -2, 40, 14, -96, 20, -8, 0, 0, 20, 20, 8, -8, 16, -8, 2, -12, -22, 46, -4, 48, 34, -4, -4, -10, 16, 0, -8, -32, -8, 24, 8, 12, -8, -34, 24, 4, -12, 4, -22, 48, 6, 14, 0, -20, -30, 8, -4, 96, -88, -12, -12, 4, -8, 36, 0, -96, -10, -8, -22, -12, -18, -4, -2, 4, -52, -44, -8, 40, 48, 4, -2, 34, -4, 60, -8, 96, -4, -2, -4, 30, -32, 0, -20, 62, 8, -8, 8, 8, 48, -44, -28, 8, 4, 8, 0, -26, -20, -54, 14, -36, 32, -96, -24, -8, 14, 18, 24, 0, 20, 48, 10, 8, 12, 40, 4, 10, 28, -24, 8, 2, 0, 20, 44, 0, 32, 12, 2, 4, -44, 0, 22, 10, 6, -24, 20, -14, -44, -40, -4, -26, -8, 22, 4, 60, 14, 40, -48, 32, 48, -34, 4, -8, -30, -44, -8, 24, -12, 20, 10, -96, 8, 4, 14, -56, -2, -28, -18, -40, -2, -12, -48, 8, -48, -8, 24, 10, -4, -8, -18, -80, -30, 0, -2, 100, 4, -22, 6, 24, 8, -4, 4, -100, 72, -28, 8, 0, 4, -8, 24, -96, -52, -28, 22, 28, -42, -24, -4, 44, 24, -4, -20, -96, 48, 24, 16, 24, 22, 8, 22, 24, -24, -12, -4, 76, 24, -24, -8, 42, 16, -4, 2, 6, 8, 68, -14, -32, -24, 96, 2, -8, 38, 26, 0, 46, -92, -14, 20, 60, 44, -48, 0, 6, 0, -8, -4, 16, 26, 2, -20, 4, 28, 24, -8, -72, 60, 2, -2, -60, 4, 8, -4, 0, 20, -8, 12, 8, 0, 48, 20, -4, -8, -64, -20, 14, -50, -12, -10, 20, -30, 192, 4, 0, -26, 0, 4, -28, 56, -26, 24, -10, 64, -24, 0, 14, -20, 4, 2, 16, -26, 92, -6, 8, -12, 6, -12, 0, -16, -20, 4, -34, 24, 20, -2, -40, -20, -144, -28, -16, 48, -24, 20, 0, -68, 34, 0, 8, 0, 20, -28, -14, 20, 48, -4, -44, -92, 8, -8, 8, -8, -36, -4, -22, 24, 44, 44, 0, -44, -4, -4, 18, -24, 168, -14, -104, 2, 82, -4, 48, 14, -58, -32, -4, 0, -26, 28, 0, -32, -28, 4, 88, 0, -56, -4, -96, 12, -10, 4, -16, 68, 54, -48, 12, 4, 48, -12, 54, -2, 0, -4, -56, -24, -16, 6, -40, -28, -32, 0, 92, 40, -8, 36, 30, 8, 10, 2, -64, 0, -24, 44, 144, -12, -72, -12, 12, -8, 4, 16, -24, -30, -42, 0, 60, 48, -20, 20, -24, 4, -8, -22, -4, 6, -4, 36, -44, 8, 0, -2, -20, 4, -84, 26, 28, 52, 48, 4, 52, 40, 48, -48, -20, -8, 4, 4, -34, -44, -36, -4, -66, -30, 44, 4, -48, -48, 36, -4, -18, 22, 0, 8, 48, -60, 8, 40, -2, 0, -44, 10, -104, -28, -8, -4, 48, -8, -28, -4, 4, -16, 0, -96, -40, 52, -32, -28, -56, -4, -48, -2, 64, -4, 80, 0, -4, 28, -80, 40, 60, 108, 80, -4, 2, -36, 38, -16, 44, 96, 28, 12, 34, -8, 4, -34, 14, -36, -122, -48, 60, -48, 20, 20, 0, -24, 28, 10, -80, -4, -52, 12, -12, -20, 48, -8, -52, -20, 18, -20, 4, -24, -90, -4, 0, -4, -40, 0, -20, 20, 48, 8, -6, 0, 28, -64, 48, -24, 60, 2, 24, -2, -48, -8, -48, 0, -20, 22, -30, 10, 24, -12, 110, 48, -6, 2, -8, -14, 60, 22, 44, 20, -44, 2, 52, -26, 48, 4, 88, -44, 28, -8, 0, -84, -10, 14, 40, -20, 16, 48, 104, -16, 52, 48, -2, -4, 0, -8, 20, 16, -56, 12, 48, -44, -84, 4, 104, 36, 84, 6, -40, 20, -4, -14, -10, 192, 48, -16, 2, -2, -10, 14, 40, 28, -108, -2, -28, 14, -96, -18, 36, 68, 48, 4, 8, 24, -12, 48, 68, 8, -48, 24, -8, 52, 32, -12, -52, 10, -28, 8, -70, 16, -40, 36], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "126.2.f.c", "char_is_minimal": true, "conrey_index": 43, "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, 0, 1, 0], [1, 0, 0, -1], [0, 0, -1, 0], [0, -1, -1, -1], [-1, 1, 1, 0], [1, 0, -1, 0], [1, 0, 0, 0], [-1, 0, 0, -2], [1, 2, 0, -1], [-2, 0, 2, 0], [0, -1, -1, 1], [0, 2, 0, 2], [0, 0, 1, 0], [-4, -2, 1, 0], [-1, 0, 1, 0], [2, 0, 0, 0], [1, 2, -1, 0], [5, 2, 0, -1], [-1, -1, 1, 2], [1, -1, -1, 0], [0, 0, -2, 0], [0, 0, 1, 0], [1, 0, 0, -1], [-2, -2, 2, 4], [0, -4, 0, 2], [-5, 0, 0, -1], [-1, 0, 0, 0], [2, -2, -2, 4], [3, 2, -4, -2], [0, 0, -6, 0], [0, 0, -1, 0], [-2, 2, 2, 0], [-2, 0, 2, 0], [-1, -2, 0, 1], [0, -2, 1, 2], [2, -8, 0, 4], [-5, -1, 5, 2], [8, 2, -4, 2], [0, -1, -1, -1], [0, 4, 0, 4], [0, 1, 1, -1], [-2, 2, 2, -4], [2, 0, 0, 0], [-8, -1, 5, 3], [-1, 0, 0, 0], [0, 4, 0, -8], [-1, 1, 1, 0], [0, 0, -1, 0], [0, -2, -2, -2], [2, 0, 0, -2], [0, 2, 0, -4], [-6, 4, 0, -2], [5, 1, -5, 0], [2, 4, 0, -2], [1, 0, -1, 0], [7, 2, -4, -6], [0, -2, 2, -2], [0, 0, 2, 0], [1, 0, 3, 2], [-9, -1, 9, 2], [6, 0, 0, 0], [-1, -2, 1, 0], [1, 0, 0, 0], [12, 2, -12, -4], [0, -2, -2, 2], [0, -2, 8, -2], [0, 0, -2, 0], [0, 1, 1, -1], [1, 1, -1, -2], [5, 4, 0, -2], [-1, 0, 0, -2], [-2, 4, 0, -2], [-2, 4, 2, -8], [2, 0, 6, 4], [0, -1, -5, -1], [0, 0, 2, 0], [-4, -4, 8, 2], [-3, -2, 3, 4], [1, 2, 0, -1], [-7, 0, 0, 4], [0, -8, 0, 4], [-2, 0, 2, 0], [-1, 0, 0, 1], [0, -2, -2, -2], [0, 2, -2, 2], [6, -4, 2, 4], [-2, 0, 2, 0], [-12, 4, 0, -2], [3, -2, -8, -1], [0, 4, 0, -2], [1, 0, -1, 0], [0, -6, -6, 6], [0, 4, 0, 4], [0, -6, -11, -6], [0, -1, -1, 1], [2, 2, -2, -4], [1, 0, 0, 0], [2, 4, -2, 0], [2, 4, 0, -2]]}