# Stored data for newform 600.2.b.g, downloaded from the LMFDB on 28 March 2024. {"label": "600.2.b.g", "space_label": "600.2.b", "level": 600, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021666517254744, "dim": 12, "is_polredabs": true, "nf_label": "12.0.537291533250985984.1", "trace_hash": 1289497245417023556, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [284, 0, 225, 0, 30, 0, 1]], [11, [200, 0, 112, 0, 19, 0, 1]], [23, [-9088, 0, 2136, 0, -104, 0, 1]], [43, [148, -29, -10, 1]]], "qexp_display": "q+\\beta _{8}q^{2}-\\beta _{5}q^{3}+(1+\\beta _{4})q^{4}+(-\\beta _{4}+\\cdots)q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "b", "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": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [600, 2, [151, 301, 401, 577], [1, 1, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [251], "field_disc": 537291533250985984, "field_disc_factorization": [[2, 22], [71, 6]], "field_poly": [64, 0, -80, 0, 56, 0, -30, 0, 14, 0, -5, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "9.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1124.979", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "204535.764", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -2, 0, 0], "traces": [0, 12, 0, -2, 10, 0, 7, 0, 0, -2, 0, 0, 3, 0, 0, 0, -6, 0, 5, -4, 0, 0, 2, 0, 5, 0, 0, -8, 20, 0, 0, 0, 0, -18, -2, 0, 19, 0, 0, 0, 0, 0, 14, 40, 0, 0, -16, 0, 27, -36, 0, -30, 4, 0, -30, 0, 0, -42, -52, 0, 0, 0, 0, 0, 10, 0, 7, 60, 0, 0, 0, 0, 39, -12, 0, 0, -38, 0, -54, 0, 0, -10, -58, 0, -34, 0, 0, 0, -34, 0, 0, -24, 0, 0, 28, 0, -31, 32, 0, 58, 0, 0, 17, 0, 0, 0, 56, 0, -32, 0, 0, 0, -52, 0, 11, 0, 0, 0, -4, 0, 0, 56, 0, 26, 88, 0, 66, 0, 0, 32, 0, 0, 15, 0, 0, 0, 2, 0, 84, 12, 0, 0, -12, 0, 35, 0, 0, -94, 108, 0, 0, 0, 0, -42, -52, 0, 50, 0, 0, 0, 0, 0, 47, 68, 0, 0, -62, 0, 106, -76, 0, -26, -24, 0, -82, 0, 0, -60, -70, 0, 0, 0, 0, 0, -40, 0, -52, 12, 0, 0, 0, 0, 63, -68, 0, 0, -58, 0, -49, 0, 0, -34, -84, 0, -55, 0, 0, 0, -124, 0, 0, 108, 0, 0, 54, 0, -50, 40, 0, 6, 0, 0, -38, 0, 0, 0, 46, 0, -65, 0, 0, 0, 12, 0, 70, 0, 0, 0, 148, 0, 0, 44, 0, -62, 36, 0, 45, 0, 0, 22, 0, 0, -58, 0, 0, 0, -14, 0, 100, -80, 0, 0, 12, 0, 37, 0, 0, 94, 66, 0, 0, 0, 0, -16, -18, 0, 108, 0, 0, 0, 0, 0, 66, -84, 0, 0, -124, 0, 107, 64, 0, -68, 82, 0, -43, 0, 0, 20, -164, 0, 0, 0, 0, 0, -110, 0, -7, 116, 0, 0, 0, 0, 78, 112, 0, 0, -76, 0, -152, 0, 0, -38, 24, 0, -89, 0, 0, 0, -102, 0, 0, -52, 0, 0, 92, 0, -82, 44, 0, 42, 0, 0, -15, 0, 0, 0, 56, 0, -146, 0, 0, 0, -138, 0, 34, 0, 0, 0, 54, 0, 0, -72, 0, 24, 88, 0, 82, 0, 0, -2, 0, 0, -36, 0, 0, 0, 212, 0, 188, 116, 0, 0, 152, 0, 69, 0, 0, -160, 100, 0, 0, 0, 0, 76, -136, 0, 69, 0, 0, 0, 0, 0, 7, 8, 0, 0, -64, 0, 83, 20, 0, 170, -76, 0, -124, 0, 0, 42, 26, 0, 0, 0, 0, 0, -144, 0, -150, -216, 0, 0, 0, 0, -56, 132, 0, 0, 4, 0, -97, 0, 0, 50, -84, 0, -70, 0, 0, 0, -172, 0, 0, 28, 0, 0, 44, 0, -31, -36, 0, -148, 0, 0, -82, 0, 0, 0, 120, 0, -182, 0, 0, 0, 4, 0, 174, 0, 0, 0, 228, 0, 0, -16, 0, -80, 56, 0, 15, 0, 0, 2, 0, 0, -91, 0, 0, 0, 112, 0, 51, -232, 0, 0, -14, 0, 94, 0, 0, 198, 168, 0, 0, 0, 0, 72, -8, 0, 68, 0, 0, 0, 0, 0, 94, -116, 0, 0, -120, 0, 95, 140, 0, -84, 140, 0, 23, 0, 0, -30, -112, 0, 0, 0, 0, 0, 58, 0, -132, 100, 0, 0, 0, 0, 68, -112, 0, 0, -114, 0, -164, 0, 0, 98, -16, 0, -118, 0, 0, 0, -172, 0, 0, -72, 0, 0, 228, 0, -121, -52, 0, 30, 0, 0, -86, 0, 0, 0, 84, 0, -159, 0, 0, 0, 60, 0, 40, 0, 0, 0, 232, 0, 0, -196, 0, 46, 28, 0, 86, 0, 0, 24, 0, 0, -93, 0, 0, 0, 12, 0, 174, 152, 0, 0, 132, 0, 154, 0, 0, -106, 72, 0, 0, 0, 0, 6, -32, 0, 48, 0, 0, 0, 0, 0, -35, -160, 0, 0, -42, 0, 133, 24, 0, 216, 174, 0, -54, 0, 0, 182, -184, 0, 0, 0, 0, 0, -250, 0, -98, -352, 0, 0, 0, 0, 66, 8, 0, 0, 34, 0, -67, 0, 0, -132, 112, 0, 15, 0, 0, 0, -96, 0, 0, 148, 0, 0, -46, 0, -134, -156, 0, -240, 0, 0, -76, 0, 0, 0, -128, 0, -110, 0, 0, 0, -114, 0, 146, 0, 0, 0, 124, 0, 0, -112, 0, -26, 24, 0, 40, 0, 0, -212, 0, 0, -118, 0, 0, 0, 168, 0, 85, 0, 0, 0, 200, 0, 12, 0, 0, 274, 38, 0, 0, 0, 0, -58, -240, 0, 72, 0, 0, 0, 0, 0, 4, -24, 0, 0, 4, 0, 91, -100, 0, -104, -6, 0, -60, 0, 0, 136, -136, 0, 0, 0, 0, 0, -138, 0, -50, 104, 0, 0, 0, 0, -99, 184, 0, 0, -120, 0, -186, 0, 0, 42, -18, 0, -21, 0, 0, 0, -68, 0, 0, -280, 0, 0, 60, 0, -71, 24, 0, 240, 0, 0, -67, 0, 0, 0, 296, 0, -140, 0, 0, 0, -148, 0, 153, 0, 0, 0, 2, 0, 0, 212, 0, 200, 74, 0, 146, 0, 0, -18, 0, 0, 10, 0, 0, 0, 138, 0, 154, 116, 0, 0, -156, 0, 102, 0, 0, -148, 232, 0, 0, 0, 0, 204, -112, 0, 3, 0, 0, 0, 0, 0, 7, 364, 0, 0, 130, 0, 118, 128, 0, 78, 128, 0, -62, 0, 0, -16, 30, 0, 0, 0, 0, 0, 90, 0, -94, -256, 0, 0, 0, 0, -65, -252, 0, 0, -184, 0, -8, 0, 0, 146, -128, 0, -146, 0, 0, 0, -164, 0, 0, 268, 0, 0, 28, 0, -38, -44, 0, -204, 0, 0, -120, 0, 0, 0, 160, 0, -98, 0, 0, 0, 228, 0, 8, 0, 0, 0, 224, 0, 0, -20, 0, -98, -14, 0, 16, 0, 0, 122, 0, 0, -43, 0, 0, 0, 20, 0, -71, 52, 0, 0, 76, 0, 167, 0, 0, 424, 28, 0, 0, 0, 0, 42, 160, 0, 35, 0, 0, 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, 3, 2, -1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 24, 6, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 6, "minimal_twist": "600.2.b.g", "char_is_minimal": true, "conrey_index": 251, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, -1, 0, -1, 0, 1, 0, 1, -1, 0], [0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1], [0, 1, 1, 0, 1, 0, 1, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1, 0, 0, 0, 0, -1, 0, 1, 1, 1, 0, 1], [-1, 1, 0, -1, -1, 0, 0, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 1, -2, 1, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 1, -1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, -2, 0, -1, 0, -1], [-1, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -1, 1, -2, 1, 0, 1, 1, -1, -1], [0, -1, 0, -1, -1, -1, 0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, -1, 1, 0, 2, 2, 1], [0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, -2, 0, 1, 1, 1, 0], [-1, -1, -1, 0, -1, 0, 1, 0, 2, 0, 0, 1], [3, -3, 0, -1, 0, -1, 0, 1, 0, 2, -2, 0], [0, 0, 0, 0, 0, 0, 1, 0, -3, -2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, 1, -2, 1, 0, -1, 0, -1, 1, 0], [0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 1, -2], [-1, 1, 1, 0, 1, 0, 0, 1, -1, 0, 0, 0], [-2, 1, 0, 1, -1, 1, 0, -1, 0, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, -1, -1, -2, 2, -2, 1, -1, 0, 1], [0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, -1, -1, -1, 1], [1, 0, -1, 1, 0, 0, 1, 0, -2, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 1, 1, 1, 3, 0, 0, 1], [2, 3, -2, -1, 1, 1, -2, 3, -1, 0, 0, -2], [3, -3, 0, 0, -3, -2, 0, 2, 0, 0, 0, 0], [0, 0, -2, 0, 0, 2, -2, 2, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 1, -1, -3, 0, 3, 0, 1, -1, 0], [0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, -2], [4, 0, 0, 0, 1, -1, 2, 1, 1, 2, -1, 1], [-4, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 2, 0, -1, -1, 2, -2, 0, 0, 0, 2], [-1, -4, 0, 0, -3, -2, 0, 2, 0, -1, 1, 0], [0, 0, 2, 0, 0, 0, -1, 0, 1, -2, -2, 1], [-4, 1, 0, 1, 1, 2, 0, 0, -1, -2, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 4, -2, 4, -1, -1, -1, -1], [-4, -1, -1, 0, -1, 1, -2, 0, -1, 0, 0, -2], [-6, 3, 0, -1, -1, 3, 0, -3, 0, -1, 1, 0], [0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 0, -1, 1, -2, 0, 2, 0, 3, -3, 0], [0, 0, 4, 0, 0, -3, 2, -3, 1, 0, 0, 3], [1, -2, 0, 1, 2, -1, 0, -1, 4, 3, 1, 0], [2, -2, 0, -2, -2, -4, 0, 4, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 1, -1, 0, -1, -1, 2, -1, -1], [5, 1, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 2, -2, 2, 1, 1, 2], [0, 2, 2, 0, -2, -2, 1, -2, 3, -2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, -1, 1, -2, -2, -2, 1], [2, 3, -1, 1, 0, 2, -2, -2, 2, -1, 2, 0], [0, 4, 0, 0, 4, 1, 0, -1, 0, 0, 0, 0], [0, 0, 4, 0, 0, -2, 0, -2, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -1, 0, 1, 0, 3, 0, -3, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, -3, -2, -2, -1], [-4, 3, 4, -1, -1, -2, 2, 0, -1, -1, -1, 1], [4, -4, 0, 0, 4, -2, 0, 2, 0, 4, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -3, 3, 0, -3, -1, 1, -2, -2, 0, 0, 1], [-6, 1, 0, 1, 3, 1, 0, -1, 0, -2, 2, 0], [0, 0, -6, 0, 0, 3, -4, 3, 2, 0, 0, -4], [-1, -2, 0, -2, 1, -4, -2, 0, 2, 3, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 3, 3, 2, 2, 3], [2, -4, -1, 0, 4, 1, -1, 3, -4, 2, -2, 1], [-2, -4, 0, 0, 0, -2, 0, 2, 0, 1, -1, 0], [0, 0, -2, 0, 0, 3, 0, 3, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 5, 0, 0, 5, 2, 0, -2, 0, 0, 0, 0], [0, 0, 2, 0, 0, 2, 2, 2, -2, 2, 2, 2], [-3, 1, 0, 1, -1, 2, 1, -2, -3, -5, 1, -1], [4, 6, 0, -2, 2, -2, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 3, 2, 1, 2, 0, 0, 0, 1, -1, 0, -1], [3, 4, 0, 0, 4, 3, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -4, -3, -3, 0], [5, 1, -2, 0, 1, 2, 0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}