# Stored data for newform 273.2.c.b, downloaded from the LMFDB on 20 April 2024. {"label": "273.2.c.b", "space_label": "273.2.c", "level": 273, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503737099878673, "dim": 6, "is_polredabs": true, "nf_label": "6.0.350464.1", "trace_hash": 2085892039712002252, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, 11, 0, 7, 0, 1]]], "qexp_display": "q-\\beta _{4}q^{2}+q^{3}+(-\\beta _{1}+\\beta _{2})q^{4}+(-\\beta _{3}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 13, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1092, "analytic_conductor": 2.1799159751809545, "hecke_ring_index": 2, "level_radical": 273, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [273, 2, [92, 157, 106], [2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 7, 13], "conrey_indexes": [64], "field_disc": -350464, "field_disc_factorization": [[-1, 1], [2, 8], [37, 2]], "field_poly": [2, -4, 4, 2, 2, -2, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.509", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "152.923", "prec": 24}, {"__RealLiteral__": 0, "data": "45.488", "prec": 20}, {"__RealLiteral__": 0, "data": "6062.601", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 6, 0, 0], "traces": [0, 6, 0, 6, -2, 0, 0, 0, 0, 6, 16, 0, -2, -2, -2, 0, -6, 0, 0, 0, 0, 0, -16, 4, 0, -10, -20, 6, 0, -4, 16, 0, 0, 0, 0, -4, -2, 0, 24, -2, 24, 0, -2, -32, 0, 0, 0, 0, -6, -6, 0, 0, 10, -36, 0, -16, 6, 0, 0, 0, 0, 28, -8, 0, 22, 20, -16, 0, -24, 4, 0, 0, 0, 0, 16, -10, 0, -20, -20, -32, 0, 6, 8, 0, 0, 0, 0, -4, 32, 0, 16, 8, -44, 0, 36, 16, 0, 0, 0, 0, -10, -24, 0, 32, 0, -4, 0, 12, -2, 0, 0, 0, 0, 20, 24, 0, -36, -2, 12, 0, 24, -22, 0, 0, 0, 0, -2, 16, 0, -32, 12, 56, 0, 16, -8, 0, 0, 0, 0, -8, 4, 0, -64, -4, -6, 0, 32, -6, 0, 0, 0, 0, -40, 0, 0, 96, 10, -36, 0, -36, -8, 0, 0, 0, 0, -16, -68, 0, 6, -50, 40, 0, 48, 8, 0, 0, 0, 0, 16, 52, 0, 4, 14, 28, 0, 0, -8, 0, 0, 0, 0, -36, 22, 0, 8, 20, 2, 0, -16, -32, 0, 0, 0, 0, -24, -24, 0, 4, -6, 96, 0, 48, 12, 0, 0, 0, 0, 24, 104, 0, -8, 8, 16, 0, 6, -10, 0, 0, 0, 0, 16, -20, 0, -44, -20, -32, 0, -32, 8, 0, 0, 0, 0, 6, -124, 0, 8, 40, -88, 0, -56, 32, 0, 0, 0, 0, 26, -88, 0, -8, -36, -4, 0, -68, 32, 0, 0, 0, 0, 0, 16, 0, -64, 8, -44, 0, -44, -4, 0, 0, 0, 0, 36, 72, 0, 16, 68, 28, 0, -38, -80, 0, 0, 0, 0, -48, -16, 0, 36, -20, -10, 0, -104, -24, 0, 0, 0, 0, 28, 32, 0, 56, 0, 44, 0, -4, -8, 0, 0, 0, 0, 12, -20, 0, -2, -58, 0, 0, 16, 0, 0, 0, 0, 0, -68, 16, 0, 68, 24, 20, 0, 128, 24, 0, 0, 0, 0, 76, -36, 0, -58, -2, 72, 0, 12, 144, 0, 0, 0, 0, 24, -14, 0, -22, 28, -136, 0, -16, -52, 0, 0, 0, 0, 76, 8, 0, -4, -52, -2, 0, 32, 16, 0, 0, 0, 0, -16, -32, 0, -36, 12, 48, 0, 56, 20, 0, 0, 0, 0, 16, 106, 0, -8, 0, 80, 0, -52, 16, 0, 0, 0, 0, -72, -16, 0, 32, 76, -8, 0, -128, 4, 0, 0, 0, 0, -96, -64, 0, 76, -4, -16, 0, -6, 52, 0, 0, 0, 0, 32, -112, 0, -6, -56, 36, 0, 40, 152, 0, 0, 0, 0, 48, -44, 0, -20, -16, -40, 0, 160, 0, 0, 0, 0, 0, 36, 96, 0, -96, 10, 32, 0, -36, 36, 0, 0, 0, 0, -36, 56, 0, -8, 72, 32, 0, 154, -40, 0, 0, 0, 0, -16, 76, 0, -32, -80, -16, 0, -12, -68, 0, 0, 0, 0, -32, 6, 0, -128, -50, -24, 0, 40, -32, 0, 0, 0, 0, 48, 40, 0, 8, 36, 32, 0, -40, 104, 0, 0, 0, 0, -50, -96, 0, -48, -84, 16, 0, -8, 52, 0, 0, 0, 0, 32, 4, 0, -112, 14, -152, 0, 28, -232, 0, 0, 0, 0, 0, 64, 0, -8, 64, 44, 0, -76, -160, 0, 0, 0, 0, -80, -92, 0, -40, 100, -36, 0, 20, 22, 0, 0, 0, 0, 16, 8, 0, 104, 20, 88, 0, 2, -160, 0, 0, 0, 0, -16, -40, 0, -32, -80, -28, 0, -116, 64, 0, 0, 0, 0, -96, -120, 0, 200, 76, -24, 0, -64, -24, 0, 0, 0, 0, 32, 4, 0, -12, -6, 158, 0, 96, 60, 0, 0, 0, 0, 48, 4, 0, 12, 2, -240, 0, -64, -52, 0, 0, 0, 0, 16, 56, 0, -56, 68, 24, 0, 12, 104, 0, 0, 0, 0, 4, -8, 0, 160, 8, 36, 0, 16, 72, 0, 0, 0, 0, 6, 76, 0, -10, -26, -24, 0, 0, 56, 0, 0, 0, 0, 96, 2, 0, 0, 12, 16, 0, -16, -20, 0, 0, 0, 0, 8, -44, 0, 156, -20, -64, 0, -32, 128, 0, 0, 0, 0, -32, -56, 0, 8, -56, 36, 0, -40, 32, 0, 0, 0, 0, -76, 252, 0, -32, 2, 6, 0, 32, -124, 0, 0, 0, 0, 64, 8, 0, 48, 40, 12, 0, -88, -64, 0, 0, 0, 0, -56, -104, 0, 32, -8, 144, 0, 36, -136, 0, 0, 0, 0, 48, 236, 0, 36, 36, 26, 0, -56, -88, 0, 0, 0, 0, 32, -8, 0, 16, -36, -8, 0, -4, 6, 0, 0, 0, 0, -68, -120, 0, 32, -4, -96, 0, 0, 40, 0, 0, 0, 0, 132, -136, 0, -8, -104, 0, 0, 4, 16, 0, 0, 0, 0, -32, -64, 0, -56, 8, -64, 0, -44, 64, 0, 0, 0, 0, -44, 52, 0, -4, -78, 0, 0, 112, -240, 0, 0, 0, 0, 42, -88, 0, 40, 72, 36, 0, 36, 72, 0, 0, 0, 0, -4, 16, 0, 184, 68, -8, 0, 28, -96, 0, 0, 0, 0, -38, -56, 0, -80, -104, 8, 0, 176, 96, 0, 0, 0, 0, 112, -32, 0, 80, 16, -48, 0, 40, -16, 0, 0, 0, 0, -80, 36, 0, -66, -20, -28, 0, -10, 0, 0, 0, 0, 0, -104, 48, 0, -24, 36, -68, 0, -72, 184, 0, 0, 0, 0, 72, -16, 0, -200, -12, 28, 0, 24, 32, 0, 0, 0, 0, -60, 56, 0, -96, 0, 148, 0, 44, 40, 0, 0, 0, 0, -4, 336, 0, -8, 56, 232, 0, 32, 28, 0, 0, 0, 0, 92, -32, 0, -166, -24, 12, 0, -112, -20, 0, 0, 0, 0, 56, -2, 0, 40, -58, -268, 0, 0, 48, 0, 0, 0, 0, 16, -112, 0, 0, -88, -96, 0, 120, -104, 0, 0, 0, 0, 20, 64, 0, -152], "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, 13, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "273.2.c.b", "char_is_minimal": true, "conrey_index": 64, "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], [0, 0, 0, 0, -1, 0], [1, 0, 0, 0, 0, 0], [0, -1, 1, 0, 0, 0], [0, 0, 0, -1, 1, 1], [0, 0, 0, 0, -1, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, -1], [1, 0, 0, 0, 0, 0], [3, 1, 1, 0, 0, 0], [0, 0, 0, -3, -1, 1], [0, -1, 1, 0, 0, 0], [0, 0, 1, 2, -2, 1], [0, 0, 1, 0, 0, 0], [0, 0, 0, -1, 1, 1], [-1, -2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 2, 2, -2], [0, 0, 0, 1, -1, 1], [0, 0, 0, -1, 0, 0], [-1, -1, 5, 0, 0, 0], [0, 2, -2, 0, 0, 0], [0, 0, 0, 1, 0, -1], [-3, -2, -4, 0, 0, 0], [-3, -2, 1, 2, 1, -1], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1], [-2, 0, -4, 0, 0, 0], [3, 1, 1, 0, 0, 0], [0, 0, 0, 4, 0, -4], [0, 0, 0, 0, 3, -2], [0, 0, 0, -3, -1, 1], [0, 0, 0, 2, -2, 0], [-1, -1, -1, 0, 0, 0], [0, -1, 1, 0, 0, 0], [0, 0, 0, -2, 2, -2], [2, 2, -6, 0, 0, 0], [0, 0, 1, 2, -2, 1], [5, 1, 3, 0, 0, 0], [0, 0, 0, 5, -1, 3], [0, 0, 1, 0, 0, 0], [-4, 0, 4, 0, 0, 0], [0, 0, 0, 3, 5, -3], [0, 0, 0, -1, 1, 1], [0, 0, 0, -2, -4, 2], [0, 0, 0, -1, 3, -1], [-1, -2, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, -10, 1, 4], [0, 2, 0, 0, 0, 0], [1, 1, -2, 4, 2, 1], [-6, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [-4, -2, -4, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 0, 0, 2, 2, -2], [0, 0, 0, -8, -2, 4], [0, 0, 0, -3, 1, 1], [0, 0, 0, 1, -1, 1], [4, 8, -2, 0, 0, 0], [-4, 0, -8, 0, 0, 0], [0, 0, 0, -1, 0, 0], [2, -1, -5, 0, 0, 0], [4, 4, 2, -3, 1, 1], [-1, -1, 5, 0, 0, 0], [0, 0, 0, 6, -2, 2], [-4, 2, 0, 0, 0, 0], [0, 2, -2, 0, 0, 0], [0, 0, 0, -3, 1, 1], [0, 0, 0, -1, -3, -5], [0, 0, 0, 1, 0, -1], [0, 0, 0, -6, 2, 4], [2, 2, -2, 0, 0, 0], [-3, -2, -4, 0, 0, 0], [0, 0, 0, -6, -6, 2], [-3, -1, 1, 0, 0, 0], [-3, -2, 1, 2, 1, -1], [-6, 0, -2, 0, 0, 0], [0, 0, 0, 9, -5, -1], [1, 0, 0, 0, 0, 0], [1, -1, -1, 0, 0, 0], [0, 0, 0, 5, -7, 5], [0, 0, 0, 0, 1, -1], [0, 0, 0, -8, 4, 0], [0, 0, 0, 8, 8, -4], [-2, 0, -4, 0, 0, 0], [5, 3, -1, 0, 0, 0], [0, 0, 0, -3, 3, -5], [3, 1, 1, 0, 0, 0], [2, -1, 2, 0, 1, 0], [-6, 0, 4, 0, 0, 0], [0, 0, 0, 4, 0, -4], [5, 3, -3, 0, 0, 0], [4, 0, 4, 0, 0, 0], [0, 0, 0, 0, 3, -2], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 0], [0, 0, 0, -3, -1, 1], [0, -3, 5, 0, 0, 0]]}