# Stored data for newform 600.2.d.g, downloaded from the LMFDB on 28 March 2024. {"label": "600.2.d.g", "space_label": "600.2.d", "level": 600, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021803956208216, "dim": 8, "is_polredabs": true, "nf_label": "8.0.214798336.3", "trace_hash": 1702044541972765603, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [1, 0, 156, 0, 134, 0, 28, 0, 1]], [11, [1600, 0, 1344, 0, 336, 0, 32, 0, 1]], [13, [9, 32, -22, 0, 1]], [37, [64, 128, -64, 0, 1]]], "qexp_display": "q-\\beta _{6}q^{2}-q^{3}+(-1-\\beta _{1}+\\beta _{3}+\\beta _{6}+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 40, "char_orbit_label": "d", "char_is_real": true, "Nk2": 2400, "analytic_conductor": 4.791024121276823, "hecke_ring_index": 4, "level_radical": 30, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [600, 2, [151, 301, 401, 577], [2, 1, 2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [349], "field_disc": 214798336, "field_disc_factorization": [[2, 12], [229, 2]], "field_poly": [16, -16, 0, -4, 9, -2, 0, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.023", "prec": 17}, {"__RealLiteral__": 0, "data": "6.992", "prec": 17}, {"__RealLiteral__": 0, "data": "1.180", "prec": 17}, {"__RealLiteral__": 0, "data": "247.807", "prec": 24}, {"__RealLiteral__": 0, "data": "292.458", "prec": 24}, {"__RealLiteral__": 0, "data": "13833.622", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, -8, 0, 0], "traces": [0, 8, -2, -8, -4, 0, 2, 0, -8, 8, 0, 0, 4, 0, 6, 0, 8, 0, -2, 0, 0, 0, 20, 0, 8, 0, -2, -8, 24, 0, 0, 8, -12, 0, -12, 0, -4, 0, 14, 0, 0, 0, -6, -8, 12, 0, 20, 0, -8, 0, 0, 0, 24, 8, 2, 0, 8, 0, -20, 0, 0, 0, 26, 0, 32, 0, -20, 24, 36, 0, 0, -40, -8, 0, -8, 0, -20, -24, 2, 16, 0, 8, -16, -32, -24, 0, -18, 0, -8, 0, 0, 0, 28, -8, 4, 0, 12, 0, -40, 0, 0, 0, 12, 0, -20, 0, -32, -32, 4, 0, 0, 0, -40, 0, -14, 0, 20, 0, 52, -72, 0, 24, -46, 0, -28, 0, 6, 0, -16, 8, 0, 0, -12, 48, -6, 0, 16, 0, -20, 0, 0, 0, 16, 0, 8, 0, 44, 0, 40, 0, 0, -24, -52, 0, -44, 0, -24, -48, 28, -8, 0, -48, -2, 24, 60, 0, 4, 0, -8, -16, 0, 0, 56, -8, 20, 0, -24, 0, -64, 0, 0, 0, 38, 0, 8, 0, -26, 16, 16, 0, 0, 56, -32, 0, 70, 0, 8, 64, 20, -8, 0, -24, -64, -16, -36, 0, -44, 0, -40, 32, 0, 0, 44, 40, -32, 0, 8, 0, -78, 0, 0, 0, 8, 0, -44, 0, -32, 48, 20, 0, 0, 24, -16, 0, -2, 0, 88, -16, 4, 72, 0, 40, -22, -8, 4, 0, 16, 0, -76, 32, 0, 0, 24, -112, -60, 0, 16, 0, 18, 0, 0, 0, 56, 0, 8, 0, 54, 0, 64, 0, 0, 0, -72, 0, -20, 0, -28, 96, 40, 8, 0, 48, -4, 56, 52, 0, -4, 0, -12, -24, 0, 0, 8, 112, 40, 0, -88, 0, -44, 0, 0, 0, 54, 0, 32, 0, -12, -8, 36, 0, 0, -80, 20, 0, 114, 0, -72, -64, 32, 64, 0, 32, -84, 48, -4, 0, -58, 0, -48, -32, 0, 0, 8, 0, 48, 0, 40, 0, 44, 0, 0, 0, 14, 0, -88, 0, 76, 64, -20, 0, 0, 0, -24, 0, -52, 0, 88, 72, -12, -88, 0, -80, -30, -24, 60, 0, 46, 0, -64, 0, 0, 0, 28, 48, -64, 0, -32, 0, -6, 0, 0, 0, -44, 0, 16, 0, 106, -8, 0, 0, 0, 0, 56, 0, -20, 0, 12, -144, 38, -48, 0, -16, 6, -56, 12, 0, 68, 0, -16, 24, 0, 0, 56, -176, 20, 0, -52, 0, -12, 0, 0, 0, 6, 0, 40, 0, -16, -40, 4, 0, 0, 136, -8, 0, 98, 0, -12, 152, -44, 88, 0, 0, 36, 48, -40, 0, -70, 0, -8, -48, 0, 0, -24, 24, 32, 0, 52, 0, 42, 0, 0, 0, 44, 0, -64, 0, -80, -144, 24, 0, 0, 48, -40, 0, -28, 0, 44, 8, -8, 80, 0, 0, 54, 48, -28, 0, 2, 0, 64, -24, 0, 0, -60, -144, -150, 0, 16, 0, -4, 0, 0, 0, -16, 0, 8, 0, 24, 16, -88, 0, 0, -32, -8, 0, -32, 0, -56, 48, 40, 8, 0, 0, -20, -40, 4, 0, -16, 0, 24, -72, 0, 0, -80, 136, 64, 0, -144, 0, 44, 0, 0, 0, -52, 0, -8, 0, -38, 16, -32, 0, 0, -104, -8, 0, 34, 0, -56, -160, 26, -40, 0, -16, 20, 16, -16, 0, -26, 0, -16, 48, 0, 0, 36, -56, 40, 0, 32, 0, 46, 0, 0, 0, -70, 0, -80, 0, -60, -80, -8, 0, 0, -64, 80, 0, -20, 0, 32, 8, 36, -112, 0, 24, -2, 24, -140, 0, 64, 0, 92, 16, 0, 0, 36, 112, -26, 0, 96, 0, 44, 0, 0, 0, -12, 0, 40, 0, 38, -32, -48, 0, 0, 8, 88, 0, -8, 0, -44, -160, -40, -40, 0, -112, 32, 80, 100, 0, 60, 0, -8, -128, 0, 0, 8, -112, 78, 0, -16, 0, 52, 0, 0, 0, -8, 0, -16, 0, -8, 112, 4, 0, 0, 120, 44, 0, -26, 0, -56, 120, 32, 8, 0, -48, 76, -128, -20, 0, -142, 0, 136, 144, 0, 0, -44, -24, 100, 0, 16, 0, -24, 0, 0, 0, 2, 0, -24, 0, 44, 16, -88, 0, 0, 16, 48, 0, -4, 0, -32, -72, 16, 152, 0, -48, -12, -40, -4, 0, 22, 0, 20, 8, 0, 0, -4, -160, -46, 0, -40, 0, -16, 0, 0, 0, -48, 0, 76, 0, 22, -32, 32, 0, 0, -32, -32, 0, -92, 0, -24, 192, -138, 112, 0, 96, 60, 104, 20, 0, 192, 0, -16, -24, 0, 0, -40, 72, -18, 0, -44, 0, 88, 0, 0, 0, -120, 0, 176, 0, -56, -120, -136, 0, 0, 16, -8, 0, 78, 0, -4, -48, -54, -112, 0, 0, 40, 16, -64, 0, 22, 0, 64, -64, 0, 0, -4, 0, -16, 0, 72, 0, -22, 0, 0, 0, 20, 0, 32, 0, -76, 160, 28, 0, 0, -96, 136, 0, -40, 0, 108, -8, -120, 24, 0, -56, 160, -48, -36, 0, 4, 0, -40, -56, 0, 0, -52, 96, 42, 0, 216, 0, 4, 0, 0, 0, 20, 0, 12, 0, -34, 24, 48, 0, 0, 216, 40, 0, -76, 0, -8, -32, -2, -112, 0, 208, -40, 24, 44, 0, -96, 0, 88, 208, 0, 0, -56, -176, 44, 0, 0, 0, 32, 0, 0, 0, -32, 0, 32, 0, -54, -64, -156, 0, 0, 80, -32, 0, 60, 0, 20, -8, 12, 72, 0, 8, 32, 128, -36, 0, -12, 0, 120, -64, 0, 0, -148, 80, -20, 0, -20, 0, 170, 0, 0, 0, -114, 0, -176, 0, -60, 96, 72, 0, 0, 64, 40, 0, -32, 0, 44, -64, -124, 128, 0, 64, -48, -32, -52, 0, 84, 0, 48, -48, 0, 0, 4, 64, 38, 0, 24, 0, 58, 0, 0, 0, -152, 0, 48, 0, 152, 32, -104, 0, 0, -200, 164, 0, 64, 0, -8, 160, -118, 0, 0], "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, 40, 6, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 6, "minimal_twist": "600.2.k.d", "char_is_minimal": false, "conrey_index": 349, "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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, -1, 0, 1, 0, 1], [-1, 0, 0, -1, 0, -1, 0, -1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 0], [1, 1, 0, -1, 0, 0, -1, 0], [-1, -1, 2, 1, -1, 0, 1, 0], [1, 1, 2, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -2, -1, 1, -1, 1, 2], [0, 1, -1, -2, 0, 0, -1, 2], [0, 0, 0, 0, 0, 0, -1, 0], [0, -1, -1, 0, -2, -3, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, -1, 0, -1], [3, 1, 0, -1, -1, 1, -1, 0], [0, 2, 2, 0, 1, 0, 1, 1], [1, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -2, -4, 0, -2], [-1, 0, 0, 0, 0, 0, 0, 0], [3, -1, 2, 1, -2, 0, -1, -2], [0, 0, -2, -2, -1, -4, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 2, -1, 1, -1, 0, -2, 0], [0, 2, 0, 0, 0, 4, -2, 0], [0, -1, -1, 0, 0, 0, -1, 0], [-1, 1, 2, 3, -1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, 0, 0, 1, 0], [0, 0, -2, 2, 0, 0, 2, 2], [3, 1, -3, -1, 3, -3, -1, 0], [1, 1, -2, -1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 2, 2, -1, 0, 3, 1], [-1, -1, -2, -1, 1, -1, 0, 0], [-1, 0, -4, 2, 1, 0, 3, 3], [2, 0, 2, 2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, -1, -3, 3, -1, 0], [0, 0, -2, -2, -2, -2, 0, 0], [-1, -1, 2, 1, -1, 1, -1, -2], [0, 0, -6, -2, 4, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 2, 0, 0, 1, -2], [4, 0, -4, 0, 1, -3, 0, 0], [-2, -3, 3, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 1, 0, -5, -2, -1], [0, 1, 1, 0, 2, 3, -1, 2], [-1, 1, -2, 3, 1, -1, 1, 0], [0, 4, 0, -4, -2, -2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, -1, 1, 5, -3, 2], [3, -3, 1, 3, 1, 5, -1, -2], [0, 1, 0, -1, 0, 1, 0, 1], [2, -2, 4, 2, 0, 4, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, 1, 1, -1, 1, 0], [1, -2, 4, 4, -3, 0, 3, 1], [4, -2, 2, 0, -2, 2, 0, -4], [0, -2, -2, 0, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -1, 3, 2, -2, 0, 1, 0], [-1, 0, 0, -1, 0, -1, 0, -1], [0, 0, -2, -2, -4, -2, 2, -2], [0, 0, 2, 0, 0, 4, -2, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -6, -2, 3, 7, -2, 4], [-4, -1, -5, -2, 4, 0, 3, 2], [0, 0, -1, 0, 2, 4, 0, 2], [2, 0, 6, -2, -2, 0, -4, -4], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, -1, -3, -5, -1, -4], [-2, 2, -6, 0, 2, 0, 0, 2], [-3, 1, -2, -1, 2, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, -1, 1, 7, -2, -4], [0, 0, 2, 2, 1, 4, 1, -1], [-2, -4, 0, 2, -2, 0, 0, -2], [-4, -4, 0, 0, 2, 0, 6, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, -2, 0, 5, 1, 2], [4, 0, 6, 4, 0, -2, -2, -2], [-3, -2, 1, -1, 1, 0, 2, 0], [2, 2, 0, 2, 2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -4, 2, 0], [0, 2, 4, 2, 0, -1, 4, -2], [-4, 4, -2, -4, 4, 8, -2, 4], [0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}