# Stored data for newform 855.2.a.k, downloaded from the LMFDB on 20 September 2025.
{"Nk2": 3420, "analytic_conductor": 6.827209372819473, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [5, 1], [19, -1]], "atkin_lehner_string": "++-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [855, 1, [191, 172, 496], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 148, "field_disc_factorization": [[2, 2], [37, 1]], "field_poly": [1, -3, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [1, -3, -1, 1]], [7, [-34, -8, 4, 1]]], "hecke_orbit": 11, "hecke_orbit_code": 45035996307260247, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "855.2.a.k", "level": 855, "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": false, "level_primes": [3, 5, 19], "level_radical": 285, "minimal_twist": "855.2.a.j", "nf_label": "3.3.148.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(\\beta _{1}+\\beta _{2})q^{4}-q^{5}+(-2+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "855.2.a", "trace_display": [1, 0, -3, -4], "trace_hash": 1693393998555407197, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.860", "prec": 17}, {"__RealLiteral__": 0, "data": "0.405", "prec": 17}, {"__RealLiteral__": 0, "data": "22.969", "prec": 20}, {"__RealLiteral__": 0, "data": "9.319", "prec": 17}, {"__RealLiteral__": 0, "data": "276.447", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.009", "prec": 17}, "traces": [0, 3, 1, 0, 1, -3, 0, -4, 3, 0, -1, 4, 0, -6, 10, 0, -3, 16, 0, 3, -1, 0, 4, 10, 0, 3, 4, 0, 14, -2, 0, 8, -3, 0, 14, 4, 0, -20, 1, 0, -3, 10, 0, -10, 18, 0, 12, 6, 0, 11, 1, 0, -20, 8, 0, -4, 0, 0, 14, -6, 0, 6, -10, 0, -11, 6, 0, -2, 4, 0, -10, 10, 0, -4, -22, 0, 1, 14, 0, 12, 3, 0, -26, 6, 0, -16, -32, 0, 18, 40, 0, -4, 2, 0, 12, -3, 0, -2, -1, 0, 1, -6, 0, 16, -30, 0, -42, -8, 0, 2, -4, 0, -4, 20, 0, -10, -20, 0, -6, -14, 0, 3, 20, 0, 16, -3, 0, -18, -33, 0, -4, 14, 0, -4, 30, 0, 6, 26, 0, 32, -14, 0, -10, -50, 0, 2, -24, 0, -10, 24, 0, 8, 3, 0, 44, -8, 0, -28, -28, 0, 3, -6, 0, 8, -32, 0, 28, -26, 0, 45, -14, 0, -16, -24, 0, -4, -32, 0, 24, -6, 0, -26, -62, 0, 0, 20, 0, 10, 46, 0, -1, -12, 0, -10, -20, 0, -7, -8, 0, 0, 3, 0, -50, -2, 0, -10, 32, 0, 54, 4, 0, 32, -36, 0, -8, 10, 0, -10, -58, 0, -18, -2, 0, -12, -38, 0, -30, -18, 0, -6, -12, 0, -36, 14, 0, -6, 10, 0, 42, 6, 0, 18, 19, 0, 22, -11, 0, -6, 34, 0, -1, 18, 0, 2, -46, 0, 13, 16, 0, 8, 20, 0, -38, 2, 0, -8, 10, 0, 6, 20, 0, 20, 4, 0, 6, 4, 0, 6, 32, 0, 0, -28, 0, -8, -6, 0, -8, -78, 0, 53, -14, 0, -32, 44, 0, 6, -8, 0, 16, 10, 0, -28, 54, 0, -3, -6, 0, -8, 10, 0, 10, 14, 0, -24, -28, 0, -48, 20, 0, -56, 11, 0, 22, 16, 0, -6, -2, 0, 4, 46, 0, 52, -2, 0, 12, 2, 0, -4, -51, 0, -4, 50, 0, -2, 6, 0, 46, -2, 0, 46, 10, 0, -40, -10, 0, -10, 6, 0, 46, -16, 0, 3, 22, 0, 8, 4, 0, -22, 10, 0, 22, -94, 0, -14, 46, 0, 40, 106, 0, -60, -1, 0, 4, 8, 0, -14, 60, 0, 8, -46, 0, 72, 5, 0, -22, -12, 0, -2, 40, 0, -3, -10, 0, -94, -6, 0, -60, -18, 0, 30, 26, 0, 24, 16, 0, -6, 36, 0, 4, 40, 0, 22, 40, 0, 14, 16, 0, 30, -36, 0, 32, 0, 0, 62, 66, 0, -70, 10, 0, -32, -18, 0, -22, 2, 0, -40, -4, 0, -38, 38, 0, -28, -56, 0, -20, 4, 0, -20, -4, 0, -2, 8, 0, -34, 70, 0, -2, 34, 0, 40, -12, 0, 10, -10, 0, 3, 102, 0, 18, -26, 0, 4, -2, 0, 21, 2, 0, 10, 8, 0, 1, 60, 0, 38, 4, 0, -60, -36, 0, 12, -1, 0, -6, -26, 0, 6, 38, 0, -34, -38, 0, -48, 61, 0, -14, -16, 0, 86, -58, 0, 30, 52, 0, 42, -40, 0, -32, 4, 0, -17, 42, 0, 14, -2, 0, 8, -26, 0, 20, -2, 0, 62, -88, 0, -22, -2, 0, 28, 66, 0, 4, -2, 0, -100, 14, 0, -4, -34, 0, -28, 4, 0, 16, 26, 0, -20, 18, 0, 14, 66, 0, 68, -18, 0, -8, 10, 0, 0, 91, 0, 20, 14, 0, -22, -12, 0, -6, -2, 0, 8, 6, 0, -4, 30, 0, 14, -16, 0, -30, -58, 0, -14, -30, 0, -28, -3, 0, 42, -3, 0, -20, -114, 0, -40, 48, 0, -20, -36, 0, -32, -16, 0, 70, -50, 0, 3, -52, 0, -52, -134, 0, 20, -8, 0, 74, 18, 0, -4, 22, 0, 33, 48, 0, -18, 74, 0, 14, 6, 0, 20, 4, 0, 66, -32, 0, -14, 2, 0, 98, -34, 0, 30, 18, 0, -24, 4, 0, 42, -46, 0, -30, 30, 0, 32, 6, 0, -9, 44, 0, -8, -6, 0, -14, -76, 0, -26, -50, 0, -22, -34, 0, -28, 52, 0, -80, -32, 0, 30, 46, 0, 14, -20, 0, -20, -14, 0, -22, -44, 0, -22, 10, 0, 22, -12, 0, 50, 2, 0, 64, 50, 0, 24, 1, 0, -2, -2, 0, 104, 66, 0, 24, -98, 0, -68, -20, 0, -16, -20, 0, -52, 10, 0, -6, -96, 0, -24, -88, 0, 122, -28, 0, -12, -74, 0, -76, -8, 0, -38, 26, 0, -3, -18, 0, -132, 46, 0, -68, -36, 0, -94, -44, 0, 4, 40, 0, 8, 26, 0, 38, 10, 0, 8, 80, 0, 1, 28, 0, 58, -68, 0, 28, -126, 0, -18, -98, 0, 28, -8, 0, 8, -3, 0, 70, -44, 0, 6, 74, 0, 38, 40, 0, 28, 54, 0, -76, -8, 0, -10, 66, 0, 32, 22, 0, -34, 8, 0, 8, -58, 0, -54, -28, 0, -32, 60, 0, 26, 18, 0, -20, -62, 0, 65, 66, 0, -28, -45, 0, 34, -20, 0, 14, -94, 0, -26, 42, 0, -36, -40, 0, -8, 16, 0, 20, -116, 0, 24, -32, 0, -14, -56, 0, 76, -10, 0, 12, 4, 0, 64, -56, 0, 32, 104, 0, -48, -134, 0, -92, 56, 0, -44, -24, 0, -4, 6, 0, 6, 40, 0, -54, -122, 0, -8, -110, 0, -6, 26, 0, 66, -38, 0, 62, 60, 0, -26, -72, 0, 78, -106, 0, -88, 0, 0, -8, -32, 0, -20, -92, 0, 26, 138, 0, 11, 74, 0, -40, -10, 0, -106, -24, 0, -46, -4, 0, 10, -26, 0, -112, 26, 0, 32, 1, 0, 46, -56, 0, 12, 28, 0, -130, 20, 0, 19, 50, 0, 30, 10, 0, -8, 5, 0, 20, -30, 0, -36, 86, 0, -10, 12, 0, 28, 7, 0, -28, 58, 0, 8, 30, 0, -20, -78, 0, -68, -22, 0, 28, 0, 0, 20, 20, 0, -3], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0], [0, 1, 1], [-1, 0, 0], [0, 0, 0], [-2, 2, 1], [1, 0, 1], [0, 0, 0], [0, -1, 0], [1, 1, 2], [0, 0, 0], [-2, 0, -3], [3, 1, 2], [0, 0, 0], [-1, 0, -2], [5, 1, -1], [0, 0, 0], [1, 0, 0], [0, -1, -1], [0, 0, 0], [0, 4, 1], [3, 1, -1], [0, 0, 0], [1, 0, 0], [3, -5, 0], [0, 0, 0], [4, 2, -1], [-1, 1, -4], [0, 0, 0], [3, -1, 3], [0, -3, -2], [0, 0, 0], [3, 5, 1], [2, -2, -1], [0, 0, 0], [-6, -2, 1], [0, 1, 0], [0, 0, 0], [-1, 0, -1], [5, -5, -2], [0, 0, 0], [-2, -4, 1], [5, 3, 0], [0, 0, 0], [3, 3, 1], [1, 3, 5], [0, 0, 0], [4, -1, -1], [0, 1, 0], [0, 0, 0], [-6, -2, 1], [5, -7, -1], [0, 0, 0], [-1, -1, -2], [-1, 3, -2], [0, 0, 0], [6, -4, 1], [-2, 0, 2], [0, 0, 0], [1, 3, 1], [-5, 5, -1], [0, 0, 0], [-2, -5, 1], [2, 0, 3], [0, 0, 0], [-2, 4, -2], [-1, 7, 7], [0, 0, 0], [-3, -1, -2], [4, -2, 0], [0, 0, 0], [0, -4, -2], [-5, -7, -2], [0, 0, 0], [0, 1, 1], [3, 5, -3], [0, 0, 0], [6, -6, -4], [1, 0, 2], [0, 0, 0], [-8, -2, -5], [1, 3, -3], [0, 0, 0], [-5, -1, 1], [-9, -5, -4], [0, 0, 0], [6, 0, 1], [13, 1, -2], [0, 0, 0], [1, -7, 7], [-1, 5, 5], [0, 0, 0], [1, 9, 3], [-1, 0, 0], [0, 0, 0], [0, -2, 3], [-1, 2, -1], [0, 0, 0], [0, 1, 1]]}