# Stored data for newform 85.2.d.a, downloaded from the LMFDB on 15 February 2026. {"Nk2": 340, "analytic_conductor": 0.6787284171808833, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 17, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [85, 2, [52, 71], [2, 1]], "cm_discs": [], "conrey_index": 16, "dim": 6, "field_disc": -350464, "field_disc_factorization": [[-1, 1], [2, 8], [37, 2]], "field_poly": [2, -4, 4, 2, 2, -2, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 206191984725, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 2, 1, 2, 0]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "85.2.d.a", "level": 85, "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": true, "level_primes": [5, 17], "level_radical": 85, "minimal_twist": "85.2.d.a", "nf_label": "6.0.350464.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{2}q^{2}-\\beta _{5}q^{3}+(\\beta _{1}-\\beta _{2})q^{4}-\\beta _{3}q^{5}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "85.2.d", "trace_display": [-2, 0, 0, 0], "trace_hash": 2142924540792907337, "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "5.362", "prec": 17}, {"__RealLiteral__": 0, "data": "1.680", "prec": 17}, {"__RealLiteral__": 0, "data": "136.184", "prec": 24}, {"__RealLiteral__": 0, "data": "45.828", "prec": 20}, {"__RealLiteral__": 0, "data": "4701.283", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.517", "prec": 17}, "traces": [0, 6, -2, 0, 2, 0, 0, 0, -6, 2, 0, 0, 0, 8, 0, 0, -6, -2, -10, 0, 0, -8, 0, 0, 0, -6, -20, 0, 0, 0, 4, 0, 6, 4, 6, 4, 22, 0, 8, 0, 0, 0, 20, 28, 0, 0, 0, -20, 0, -14, 2, 16, 0, -28, 0, 8, 0, 0, 0, 8, 12, 0, 0, 0, -22, 0, 8, 12, -34, 0, -24, 0, -14, 0, 0, 0, 24, -28, 0, 0, 0, -26, 0, 4, 0, -12, 8, 32, 0, 4, 0, 0, 0, -36, 8, 0, 0, 0, 86, 0, -2, -20, 12, -44, 12, 0, -36, 0, 0, 0, -16, -40, 0, 0, 0, 16, 0, 0, 24, 16, -16, 42, 0, 48, 0, 0, 0, -12, 66, 0, 0, 0, -20, 0, -24, 12, 30, 48, -60, 0, 32, 0, 0, 0, -26, 24, 0, 0, 0, -4, 0, 24, -32, -34, 64, -20, 0, -28, 0, 0, 0, 88, -46, 0, 0, 0, -80, 0, -12, -30, 0, 24, 12, 0, -8, 0, 0, 0, -88, -16, 0, 0, 0, 72, 0, -16, -8, 12, -52, -24, 0, -64, 0, 0, 0, -20, -106, 0, 0, 0, 6, 0, 40, 0, 8, -4, 112, 0, 32, 0, 0, 0, 52, 100, 0, 0, 0, 20, 0, 32, 12, 20, -24, -100, 0, -2, 0, 0, 0, 52, 44, 0, 0, 0, -28, 0, -16, 12, -68, -48, -32, 0, 22, 0, 0, 0, 64, -40, 0, 0, 0, -80, 0, 28, 40, -28, 26, 56, 0, 40, 0, 0, 0, -44, 8, 0, 0, 0, 92, 0, 4, 0, 58, -48, 20, 0, -32, 0, 0, 0, -12, -60, 0, 0, 0, 32, 0, -72, 54, 22, -16, 72, 0, 44, 0, 0, 0, -8, 116, 0, 0, 0, -104, 0, -64, 12, 42, 4, -92, 0, 28, 0, 0, 0, -36, 32, 0, 0, 0, -40, 0, -24, -84, -56, 74, -8, 0, -64, 0, 0, 0, 16, 12, 0, 0, 0, -32, 0, 2, -24, -16, 48, -16, 0, -48, 0, 0, 0, -80, -28, 0, 0, 0, 84, 0, -16, -12, -20, -32, -16, 0, -50, 0, 0, 0, -60, -64, 0, 0, 0, 40, 0, 76, 48, -40, 0, 64, 0, 88, 0, 0, 0, 136, 20, 0, 0, 0, 12, 0, 116, -12, 32, 34, -84, 0, 20, 0, 0, 0, 40, 6, 0, 0, 0, 44, 0, 56, 56, -36, -36, -60, 0, -68, 0, 0, 0, 20, -44, 0, 0, 0, -20, 0, -52, 12, 2, 48, 176, 0, 8, 0, 0, 0, -56, -72, 0, 0, 0, 48, 0, -4, -106, 40, -36, 72, 0, -48, 0, 0, 0, 10, -56, 0, 0, 0, 20, 0, -64, 0, 56, -44, 4, 0, 100, 0, 0, 0, -92, 64, 0, 0, 0, -16, 0, -72, 0, 64, 52, -40, 0, 20, 0, 0, 0, -26, 40, 0, 0, 0, -80, 0, 72, -40, 16, -24, 12, 0, 36, 0, 0, 0, 64, -16, 0, 0, 0, -56, 0, -44, 12, 4, 56, -122, 0, -4, 0, 0, 0, -88, 32, 0, 0, 0, 28, 0, 8, 0, -4, 20, -102, 0, -16, 0, 0, 0, 0, -80, 0, 0, 0, 28, 0, -16, -24, -74, 36, 24, 0, -24, 0, 0, 0, 92, 116, 0, 0, 0, -96, 0, 0, -20, 32, -132, -76, 0, -36, 0, 0, 0, 60, 8, 0, 0, 0, 72, 0, -42, 48, -58, -24, -16, 0, 16, 0, 0, 0, 20, 52, 0, 0, 0, -72, 0, 76, 48, -40, -52, 108, 0, -48, 0, 0, 0, 92, 16, 0, 0, 0, 40, 0, 52, 16, -18, -44, 184, 0, 56, 0, 0, 0, 8, -32, 0, 0, 0, 6, 0, -24, 52, 8, -60, -8, 0, -28, 0, 0, 0, -80, 48, 0, 0, 0, 68, 0, 112, 20, 8, 148, -2, 0, 20, 0, 0, 0, -40, -28, 0, 0, 0, 72, 0, -52, 8, -16, 64, 16, 0, -64, 0, 0, 0, 40, -20, 0, 0, 0, -34, 0, -56, -40, 28, -8, -60, 0, -16, 0, 0, 0, -68, -8, 0, 0, 0, -92, 0, -56, 56, -56, 60, -112, 0, 20, 0, 0, 0, -44, 4, 0, 0, 0, -32, 0, 96, 4, -40, 28, 80, 0, 8, 0, 0, 0, 54, -56, 0, 0, 0, 60, 0, -22, 12, -32, -96, -60, 0, -20, 0, 0, 0, 32, 0, 0, 0, 0, -32, 0, -92, 12, 44, -160, -4, 0, 108, 0, 0, 0, -64, -104, 0, 0, 0, 68, 0, -56, -72, -16, 80, -24, 0, 100, 0, 0, 0, -40, -32, 0, 0, 0, -120, 0, 36, -16, 148, 16, 54, 0, -64, 0, 0, 0, 52, 160, 0, 0, 0, 16, 0, -124, 24, 96, -6, -12, 0, 72, 0, 0, 0, -80, -64, 0, 0, 0, -128, 0, -72, 36, -56, 40, 156, 0, 12, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 64, -136, 126, 88, 52, 0, -32, 0, 0, 0, 14, 64, 0, 0, 0, 80, 0, -4, -40, -6, -56, -68, 0, -264, 0, 0, 0, 8, 16, 0, 0, 0, 84, 0, 16, -20, -56, 156, 32, 0, -32, 0, 0, 0, -4, 88, 0, 0, 0, 0, 0, 206, -124, -100, 8, -144, 0, -8, 0, 0, 0, 68, -88, 0, 0, 0, 152, 0, 152, -22, -68, 64, 0, 0, -24, 0, 0, 0, 44, -44, 0, 0, 0, 164, 0, 20, 100, 24, -48, -16, 0, 44, 0, 0, 0, -112, -68, 0, 0, 0, -40, 0, 116, 80, -8, -36, 84, 0, 144, 0, 0, 0, 208, -24, 0, 0, 0, -52, 0, -8, 56, -12, -136, -60, 0, 112, 0, 0, 0, 36, 26, 0, 0, 0, -52, 0, 20, -38, 40, -56, -104, 0, -108, 0, 0, 0, -124, -44, 0, 0, 0, 32, 0, -72, 24, -24, -16, 72, 0, -36, 0, 0, 0, -152, -36, 0, 0, 0, -48, 0], "weight": 2, "weight_parity": 1, "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, 1, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 1, -1, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 2, -1], [-1, -1, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 1], [1, -1, -1, 0, 0, 0], [0, 0, 0, -3, -3, 2], [0, 1, 0, 0, 0, 0], [-1, -2, 0, 0, 0, 0], [0, -2, 1, -2, 0, 1], [-1, -1, 2, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1], [-1, 1, 1, 0, 0, 0], [0, 0, 0, -2, -2, 1], [0, 0, 0, 4, -4, 1], [0, 0, 0, -3, 1, 0], [-1, 0, 0, 0, 0, 0], [-3, -1, 1, 0, 0, 0], [0, 0, 0, 2, 0, -2], [0, 0, 0, 4, 4, -1], [0, 0, 0, 4, 0, 2], [1, 0, 1, 0, 0, 0], [0, 0, 0, -3, -1, -2], [0, 2, -3, 0, 0, 0], [1, -1, 1, 0, 0, 0], [0, 1, -3, -1, 3, 0], [0, 1, -2, 0, 0, 0], [3, 0, -2, 0, 0, 0], [0, 0, 0, -2, -2, -2], [2, 0, 2, 0, 0, 0], [0, 0, 0, -4, 2, -2], [0, 0, 0, 1, 0, -1], [0, 0, 0, -2, 4, 2], [3, 1, -1, 0, 0, 0], [5, 1, 1, 0, 0, 0], [0, 0, 0, 1, 3, -2], [0, 0, 0, 0, -1, 1], [0, 0, 0, 7, 1, -4], [-3, -3, 1, 0, 0, 0], [0, 0, 0, -6, 2, -1], [0, -3, 7, 0, 0, 0], [0, 0, -1, 0, 0, 0], [3, 1, 1, -5, 1, -2], [-1, 3, -3, 0, 0, 0], [-6, 2, -4, 0, 0, 0], [0, 0, 0, 2, -4, 0], [1, 0, -1, 0, 0, 0], [0, 0, 0, -1, -3, 0], [0, 0, 0, 6, -2, 2], [0, 0, 0, -2, -2, 0], [2, 0, 2, 0, 0, 0], [2, -1, 0, 0, 0, 0], [0, 0, 0, 4, -6, 6], [0, 0, 0, 4, 2, -1], [0, 0, 0, 4, 4, -1], [-2, 1, 5, 0, 0, 0], [0, 0, 0, -1, -1, -1], [1, 1, -1, 0, 0, 0], [1, 5, -3, 0, 0, 0], [-5, 1, 2, -2, -2, 1], [-1, -5, -3, 0, 0, 0], [-3, -2, 3, 0, 0, 0], [0, 0, 0, -3, 1, 6], [-2, 0, 1, 0, 0, 0], [0, 0, 0, -10, 0, 2], [0, 0, 0, 6, 2, -2], [0, 0, 0, 0, 0, 1], [4, -2, 0, 0, 0, 0], [-3, -3, 5, 0, 0, 0], [0, 0, 0, -2, 0, 2], [0, 0, 0, 5, -5, 2], [0, 0, 0, 1, 0, -2], [-6, 3, -5, 0, 0, 0], [0, 0, 0, -10, 0, 4], [-1, -3, -5, 0, 0, 0], [1, -3, 3, 0, 0, 0], [-2, -1, 0, 0, 1, -2], [3, 1, 5, 0, 0, 0], [6, -6, 2, 0, 0, 0], [0, 0, 0, 0, -2, 1], [-1, -5, -5, 0, 0, 0], [0, 0, 0, 1, 2, -1], [0, 0, 0, 2, 4, -4], [0, 0, 0, -6, -4, -1], [-7, 5, -3, 0, 0, 0], [-1, 1, -7, 0, 0, 0], [0, 0, 0, 0, 0, 2], [0, 0, 0, 3, 1, 2], [0, 0, 0, 6, 2, 4], [11, 7, -10, 0, 0, 0], [0, 0, 0, 1, 3, -2], [0, -1, 1, 0, 0, 0]]}