# Stored data for newform 882.2.f.j, downloaded from the LMFDB on 25 April 2024. {"label": "882.2.f.j", "space_label": "882.2.f", "level": 882, "weight": 2, "hecke_orbit": 10, "hecke_orbit_code": 40532740277273458, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 763178405440580351, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [25, 10, 9, -2, 1]], [11, [4, 2, 1]], [13, [576, 0, 24, 0, 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": 3528, "analytic_conductor": 7.04280545827693, "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": "0.027", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 3, [785, 199], [2, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [295, 589], "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.869", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.892", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1399.738", "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, 0], "traces": [0, 4, -2, -4, -2, 2, 2, 0, 4, -4, -4, -4, 2, 0, 0, -14, -2, -8, 2, -20, 2, 0, -4, 2, -4, -4, 0, 20, 0, 4, 4, 12, -2, 4, 4, 0, 2, 8, 10, 24, 2, 0, 0, -4, 8, 22, -4, 0, 2, 0, -4, 8, 0, -24, -10, -8, 0, 20, 4, -4, 10, 18, -24, 0, 4, 24, 4, 16, 4, -2, 0, 20, -4, 8, -4, -20, 10, 0, 0, -6, -4, -28, 0, 4, 0, -4, -4, -28, -4, 48, 4, 0, 2, -12, 0, -22, 2, -4, 0, 4, 8, -10, -4, 28, 0, 0, 12, -48, -10, -8, 4, -8, 0, 22, 2, -2, -8, -48, 8, 0, -14, 14, 18, 48, 12, -36, 0, -12, -2, 28, 24, -22, -8, 0, -32, -2, -8, 4, 4, 14, 0, -48, -10, 0, 2, -40, -4, 0, -4, 12, 28, 10, -20, 8, 0, -12, -24, -2, -6, 24, 2, 0, 14, -40, 0, 8, 4, 8, 0, -22, 8, 20, 8, -16, 20, 0, -4, 4, -24, 24, -26, 12, 0, -6, 2, -44, 24, 8, 0, 0, 44, -18, -4, 26, -4, 0, 0, 8, 4, -8, -4, 8, -10, 0, -4, 48, -56, -2, 0, 20, 0, -16, 12, -20, 24, 40, 20, 0, 4, -8, 4, 0, 52, -32, 0, 52, -44, -6, -22, -22, -2, 0, 4, -28, 0, -96, -4, -18, 0, 6, 4, -8, -28, -4, -36, 0, 0, 24, 12, -4, 18, -60, 0, -8, 6, 28, -2, 36, -20, 0, -48, 44, 44, -42, 4, 12, 0, -48, 16, 44, -20, -48, 4, 0, 4, -8, -2, 8, -28, -12, 0, 38, 48, -46, -10, 94, 0, 0, 2, -52, 20, -20, -4, 30, 0, 4, 8, -20, -24, 0, -8, 0, 10, 70, 10, 60, -4, -52, 0, -28, -12, 32, 24, 20, 4, 0, 12, -12, -36, 8, 2, 48, 0, 40, 14, 96, 20, 8, 0, 0, 20, 20, -8, -8, -16, 8, 0, -12, -22, -46, -4, -48, -34, 0, -4, -10, -16, 0, 8, 32, 0, 24, 8, -12, -8, 34, -24, 0, -12, 4, 22, 48, -6, -14, 0, -20, -30, -8, -4, -96, 88, 0, -12, 4, 8, 36, 0, 96, 0, -8, -22, 12, -18, 4, 2, 0, -52, -44, 8, 40, -48, -4, 0, 34, -4, -60, -8, -96, 4, 0, -4, 30, 32, 0, 20, -62, 0, -8, 8, -8, 48, 44, 28, 0, 4, 8, 0, -26, 20, 54, 0, -36, 32, 96, -24, 8, -14, 0, 24, 0, -20, 48, -10, -8, 0, 40, 4, -10, 28, 24, -8, 0, 0, 20, -44, 0, -32, -12, 0, 4, -44, 0, 22, -10, -6, 0, 20, -14, 44, -40, 4, 26, 0, 22, 4, -60, 14, -40, 48, 0, 48, -34, -4, -8, 30, 44, 0, 24, -12, -20, 10, 96, -8, 0, 14, -56, 2, -28, 18, 40, 0, -12, -48, -8, -48, 8, -24, 0, -4, -8, 18, -80, 30, 0, 0, 100, 4, 22, 6, -24, -8, 0, 4, -100, -72, -28, -8, 0, 0, -8, 24, 96, -52, 28, -22, 0, -42, -24, 4, 44, -24, 4, 0, -96, 48, -24, 16, -24, -22, 0, 22, 24, 24, -12, 4, -76, 0, -24, -8, -42, 16, 4, -2, 0, 8, 68, 14, -32, 24, -96, 0, -8, 38, -26, 0, -46, 92, 0, 20, 60, -44, -48, 0, -6, 0, -8, -4, -16, 26, -2, 20, 0, 28, 24, 8, -72, -60, -2, 0, -60, 4, -8, -4, 0, -20, 0, 12, 8, 0, 48, -20, 4, 0, -64, -20, -14, -50, 12, 10, 0, -30, 192, -4, 0, 26, 0, 0, -28, 56, 26, 24, 10, -64, 0, 0, 14, 20, 4, -2, -16, 0, 92, -6, -8, -12, -6, 12, 0, -16, -20, -4, -34, -24, -20, 0, -40, -20, 144, -28, 16, -48, 0, 20, 0, 68, 34, 0, -8, 0, 20, -28, 14, 20, -48, 4, 0, -92, 8, 8, 8, 8, 36, 0, -22, 24, -44, 44, 0, 44, 0, -4, 18, 24, 168, 14, 104, 0, 82, -4, -48, 14, 58, 32, 0, 0, -26, -28, 0, 32, 28, 0, 88, 0, 56, -4, 96, -12, 0, 4, -16, -68, 54, 48, -12, 0, 48, -12, -54, -2, 0, 4, 0, -24, -16, -6, -40, 28, 32, 0, 92, 40, 8, 36, -30, -8, 0, 2, -64, 0, -24, -44, -144, 0, -72, -12, -12, -8, -4, -16, 0, -30, -42, 0, 60, -48, 20, 0, -24, 4, 8, -22, 4, -6, 0, 36, -44, -8, 0, 2, 20, 0, -84, 26, -28, 52, -48, -4, 0, 40, 48, 48, -20, 8, -4, 0, -34, -44, 36, -4, 66, 30, 0, 4, -48, 48, 36, 4, 18, 0, 0, 8, -48, -60, -8, -40, 0, 0, -44, -10, -104, 28, 8, 0, 48, -8, 28, -4, -4, 16, 0, -96, -40, -52, -32, 28, 56, 0, -48, -2, -64, -4, -80, 0, 0, 28, -80, -40, 60, -108, -80, 0, 2, -36, -38, -16, -44, -96, 0, 12, 34, 8, 4, 34, -14, 0, -122, -48, -60, -48, -20, -20, 0, -24, 28, -10, -80, 4, 52, 0, -12, -20, -48, -8, 52, 20, 0, -20, 4, 24, -90, 4, 0, 0, -40, 0, 20, 20, -48, -8, 0, 0, 28, 64, 48, 24, -60, 0, 24, -2, 48, -8, 48, 0, 0, 22, -30, -10, 24, 12, -110, 0, -6, 2, 8, -14, -60, -22, 0, 20, -44, -2, 52, 26, -48, 0, 88, -44, -28, -8, 0, 84, 0, 14, 40, 20, 16, -48, -104, 0, 52, 48, 2, -4, 0, 8, 0, 16, -56, -12, 48, 44, 84, 0, 104, 36, -84, 6, 40, -20, 0, -14, -10, -192, 48, 16, -2, 0, -10, 14, -40, 28, 108, 2, 0, 14, -96, 18, 36, -68, -48, 0, 8, 24, 12, 48, -68, -8, 0, 24, -8, -52, 32, 12, 52, 0, -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": 295, "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], [0, 0, 0, 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, 0, 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], [0, 0, 0, 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], [0, 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], [0, 0, 0, 0], [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, 0, 0, 0], [-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, 0, 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], [0, 0, 0, 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], [0, 0, 0, 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], [0, 0, 0, 0], [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, 0, 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], [0, 0, 0, 0], [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, 0, 0, 0], [1, 0, -1, 0], [0, 6, -6, -6], [0, 4, 0, 4], [0, 6, -11, 6], [0, -1, 1, 1], [-2, 2, 2, -4], [0, 0, 0, 0], [2, -4, -2, 0], [2, -4, 0, 2]]}