# Stored data for newform 572.2.f.c, downloaded from the LMFDB on 25 April 2024.
{"label": "572.2.f.c", "space_label": "572.2.f", "level": 572, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007542885679676, "dim": 8, "is_polredabs": true, "trace_hash": 1648248574513872711, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [15, -3, -10, 1, 1]]], "qexp_display": "q-\\beta _{2}q^{3}+(\\beta _{1}+\\beta _{5}+\\beta _{6}-\\beta _{7})q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 13, "char_orbit_label": "f", "char_is_real": true, "Nk2": 2288, "analytic_conductor": 4.567442995617238, "hecke_ring_index": 1, "level_radical": 286, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [572, 2, [287, 365, 353], [2, 2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 11, 13], "conrey_indexes": [441], "field_disc": 832094244864, "field_disc_factorization": [[2, 12], [3, 2], [4751, 2]], "field_poly": [225, 0, 309, 0, 136, 0, 21, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "7.173", "prec": 17}, {"__RealLiteral__": 0, "data": "1.517", "prec": 17}, {"__RealLiteral__": 0, "data": "272.301", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "17390.109", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -2, 0, 0], "traces": [0, 8, 0, -2, 0, 0, 0, 0, 0, 18, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 10, 0, -52, 0, -32, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, -20, 0, 0, 0, 0, 0, 2, 0, 40, 0, 38, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 36, 0, 0, 0, -52, 0, 0, 0, 0, 0, 10, 0, -10, 0, 40, 0, 32, 0, 0, 0, 0, 0, 56, 0, 0, 0, 22, 0, 0, 0, -12, 0, 0, 0, 0, 0, -48, 0, 18, 0, -76, 0, -28, 0, 0, 0, 0, 0, 58, 0, 0, 0, -88, 0, 0, 0, -8, 0, 0, 0, 0, 0, -32, 0, 60, 0, -56, 0, 80, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, 64, 0, -92, 0, 2, 0, -54, 0, 0, 0, 0, 0, 8, 0, 0, 0, 28, 0, 0, 0, 56, 0, 0, 0, 0, 0, 60, 0, 38, 0, 64, 0, -76, 0, 0, 0, 0, 0, -66, 0, 0, 0, -28, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, -28, 0, 2, 0, -16, 0, 0, 0, 0, 0, 52, 0, 0, 0, -12, 0, 0, 0, -78, 0, 0, 0, 0, 0, 44, 0, 52, 0, 16, 0, -60, 0, 0, 0, 0, 0, -148, 0, 0, 0, -62, 0, 0, 0, -86, 0, 0, 0, 0, 0, -42, 0, 60, 0, 64, 0, 32, 0, 0, 0, 0, 0, -14, 0, 0, 0, -8, 0, 0, 0, 80, 0, 0, 0, 0, 0, -92, 0, 48, 0, 6, 0, 48, 0, 0, 0, 0, 0, 148, 0, 0, 0, 32, 0, 0, 0, 12, 0, 0, 0, 0, 0, -40, 0, -38, 0, -18, 0, 172, 0, 0, 0, 0, 0, -32, 0, 0, 0, 88, 0, 0, 0, 48, 0, 0, 0, 0, 0, -52, 0, -80, 0, 94, 0, 48, 0, 0, 0, 0, 0, 100, 0, 0, 0, 80, 0, 0, 0, -20, 0, 0, 0, 0, 0, -62, 0, 2, 0, -68, 0, 18, 0, 0, 0, 0, 0, -84, 0, 0, 0, -84, 0, 0, 0, 64, 0, 0, 0, 0, 0, 28, 0, -6, 0, -96, 0, -136, 0, 0, 0, 0, 0, -178, 0, 0, 0, 36, 0, 0, 0, -12, 0, 0, 0, 0, 0, 44, 0, 104, 0, -60, 0, 34, 0, 0, 0, 0, 0, 40, 0, 0, 0, -22, 0, 0, 0, -82, 0, 0, 0, 0, 0, -12, 0, -180, 0, 30, 0, -124, 0, 0, 0, 0, 0, -2, 0, 0, 0, -40, 0, 0, 0, -192, 0, 0, 0, 0, 0, -28, 0, 84, 0, -60, 0, -128, 0, 0, 0, 0, 0, 158, 0, 0, 0, -8, 0, 0, 0, 92, 0, 0, 0, 0, 0, 188, 0, 72, 0, 84, 0, 136, 0, 0, 0, 0, 0, 160, 0, 0, 0, 6, 0, 0, 0, 64, 0, 0, 0, 0, 0, -28, 0, -224, 0, 58, 0, -48, 0, 0, 0, 0, 0, -22, 0, 0, 0, 90, 0, 0, 0, -84, 0, 0, 0, 0, 0, 42, 0, -28, 0, 48, 0, -8, 0, 0, 0, 0, 0, 204, 0, 0, 0, -68, 0, 0, 0, -28, 0, 0, 0, 0, 0, 156, 0, 56, 0, -30, 0, -98, 0, 0, 0, 0, 0, -102, 0, 0, 0, 28, 0, 0, 0, -24, 0, 0, 0, 0, 0, 112, 0, 126, 0, 10, 0, 56, 0, 0, 0, 0, 0, -56, 0, 0, 0, -44, 0, 0, 0, 388, 0, 0, 0, 0, 0, -6, 0, -144, 0, 136, 0, -78, 0, 0, 0, 0, 0, -100, 0, 0, 0, 96, 0, 0, 0, 94, 0, 0, 0, 0, 0, -58, 0, 20, 0, -340, 0, 36, 0, 0, 0, 0, 0, -116, 0, 0, 0, 12, 0, 0, 0, -188, 0, 0, 0, 0, 0, 52, 0, -92, 0, -128, 0, 88, 0, 0, 0, 0, 0, -92, 0, 0, 0, -16, 0, 0, 0, -56, 0, 0, 0, 0, 0, -184, 0, -88, 0, -164, 0, 200, 0, 0, 0, 0, 0, 140, 0, 0, 0, -56, 0, 0, 0, -156, 0, 0, 0, 0, 0, -52, 0, 102, 0, 222, 0, 40, 0, 0, 0, 0, 0, 16, 0, 0, 0, -10, 0, 0, 0, -208, 0, 0, 0, 0, 0, -78, 0, 44, 0, 72, 0, 90, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -160, 0, 164, 0, 40, 0, 76, 0, 0, 0, 0, 0, 236, 0, 0, 0, -52, 0, 0, 0, -284, 0, 0, 0, 0, 0, -42, 0, -44, 0, -76, 0, -76, 0, 0, 0, 0, 0, -144, 0, 0, 0, -12, 0, 0, 0, -142, 0, 0, 0, 0, 0, 214, 0, 152, 0, 64, 0, 44, 0, 0, 0, 0, 0, 56, 0, 0, 0, -148, 0, 0, 0, 228, 0, 0, 0, 0, 0, -200, 0, -4, 0, 86, 0, -14, 0, 0, 0, 0, 0, 138, 0, 0, 0, 116, 0, 0, 0, 312, 0, 0, 0, 0, 0, 30, 0, 38, 0, 204, 0, -88, 0, 0, 0, 0, 0, -148, 0, 0, 0, 144, 0, 0, 0, 176, 0, 0, 0, 0, 0, -2, 0, -108, 0, 162, 0, -26, 0, 0, 0, 0, 0, -92, 0, 0, 0, 28, 0, 0, 0, -4, 0, 0, 0, 0, 0, 94, 0, 72, 0, -60, 0, -16, 0, 0, 0, 0, 0, -536, 0, 0, 0, -30, 0, 0, 0, 136, 0, 0, 0, 0, 0, 72, 0, -132, 0, 32, 0, -264, 0, 0, 0, 0, 0, 74, 0, 0, 0, 88, 0, 0, 0, 24, 0, 0, 0, 0, 0, 196, 0, 4, 0, -208, 0, -38, 0, 0, 0, 0, 0, 20, 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, 13, 2, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 2, "minimal_twist": "572.2.f.c", "char_is_minimal": true, "conrey_index": 441, "id": null, "nf_label": 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, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -2, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -5, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, -1, -1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 2, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -6, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 2, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, -1, 3, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 2, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -10, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -2, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 9, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -2, -1, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -2, 2, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 5, -3, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [5, -2, 2, 1, 7, 0, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, -2, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -4, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 6, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, -3, 0, 3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -2, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 3, 1, 0, -3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, -1, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -10, -1, -1, -4], [0, 0, 0, 0, 0, 0, 0, 0], [8, 0, -2, 4, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, -4, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 1, 0, -2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 0, -2, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -8, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0]]}