# Stored data for newform 600.2.r.c, downloaded from the LMFDB on 20 April 2024.
{"label": "600.2.r.c", "space_label": "600.2.r", "level": 600, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9008367519400536, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1649846017244853795, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4, 8, 8, -4, 1]], [17, [196, -56, 8, 4, 1]]], "qexp_display": "q+(\\zeta_{8}-\\zeta_{8}^{3})q^{3}+(1+\\zeta_{8}-\\zeta_{8}^{2}-\\zeta_{8}^{3})q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 15, "char_orbit_label": "r", "char_is_real": false, "Nk2": 2400, "analytic_conductor": 4.791024121276823, "hecke_ring_index": 2, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.254", "prec": 17}, "analytic_rank_proved": true, "char_values": [600, 4, [151, 301, 401, 577], [4, 4, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [257, 593], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "3.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.132", "prec": 17}, {"__RealLiteral__": 0, "data": "60.070", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1469.836", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 4], "traces": [0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 4, 0, -12, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 12, 0, -20, 0, 0, 0, -4, 0, 0, 0, -20, 0, 0, 0, 12, 0, 12, 0, 0, 0, -8, 0, -16, 0, 24, 0, -12, 0, 0, 0, -12, 0, 4, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, -28, 0, 4, 0, 0, 0, 32, 0, 40, 0, -40, 0, 32, 0, 0, 0, -4, 0, 32, 0, 0, 0, 28, 0, 0, 0, 44, 0, 0, 0, 4, 0, -4, 0, 0, 0, -36, 0, 24, 0, -4, 0, 0, 0, 0, 0, -28, 0, 4, 0, 0, 0, 8, 0, 0, 0, 28, 0, 0, 0, -12, 0, 24, 0, 0, 0, 4, 0, -8, 0, -32, 0, 28, 0, 0, 0, 12, 0, -12, 0, 0, 0, -4, 0, 0, 0, -20, 0, 0, 0, 32, 0, -20, 0, 0, 0, 0, 0, -48, 0, 24, 0, -32, 0, 0, 0, -40, 0, -28, 0, 0, 0, -36, 0, 0, 0, -36, 0, 0, 0, -28, 0, 24, 0, 0, 0, 4, 0, -48, 0, 16, 0, 8, 0, 0, 0, 32, 0, 28, 0, 0, 0, 28, 0, 0, 0, -20, 0, 0, 0, 8, 0, -36, 0, 0, 0, 8, 0, 64, 0, -24, 0, 0, 0, 0, 0, 24, 0, -28, 0, 0, 0, 8, 0, 0, 0, -4, 0, 0, 0, -8, 0, -12, 0, 0, 0, 32, 0, 24, 0, 64, 0, -48, 0, 0, 0, 44, 0, 0, 0, 0, 0, -4, 0, 0, 0, 32, 0, 0, 0, 4, 0, 44, 0, 0, 0, -40, 0, 56, 0, 8, 0, -16, 0, 0, 0, -12, 0, 20, 0, 0, 0, -36, 0, 0, 0, -4, 0, 0, 0, 36, 0, -40, 0, 0, 0, -16, 0, -24, 0, -16, 0, -20, 0, 0, 0, -4, 0, -44, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, -4, 0, 28, 0, 0, 0, 16, 0, -96, 0, 28, 0, 64, 0, 0, 0, 36, 0, 64, 0, 0, 0, -36, 0, 0, 0, -56, 0, 0, 0, 36, 0, -44, 0, 0, 0, 12, 0, -72, 0, -8, 0, 24, 0, 0, 0, -20, 0, 8, 0, 0, 0, -64, 0, 0, 0, 8, 0, 0, 0, 44, 0, -16, 0, 0, 0, 24, 0, 16, 0, 56, 0, -4, 0, 0, 0, -8, 0, -40, 0, 0, 0, 60, 0, 0, 0, 8, 0, 0, 0, -64, 0, -28, 0, 0, 0, -64, 0, 40, 0, -64, 0, -32, 0, 0, 0, -4, 0, -36, 0, 0, 0, 92, 0, 0, 0, -20, 0, 0, 0, -60, 0, -24, 0, 0, 0, 12, 0, 0, 0, -88, 0, 40, 0, 0, 0, 4, 0, 4, 0, 0, 0, 72, 0, 0, 0, 56, 0, 0, 0, -44, 0, 52, 0, 0, 0, 20, 0, -8, 0, 56, 0, -40, 0, 0, 0, -56, 0, 52, 0, 0, 0, -68, 0, 0, 0, 64, 0, 0, 0, -16, 0, 64, 0, 0, 0, 0, 0, 72, 0, -72, 0, -64, 0, 0, 0, -12, 0, 24, 0, 0, 0, -8, 0, 0, 0, 28, 0, 0, 0, 88, 0, 68, 0, 0, 0, -60, 0, 136, 0, 48, 0, 40, 0, 0, 0, -36, 0, -68, 0, 0, 0, -24, 0, 0, 0, -20, 0, 0, 0, -68, 0, 28, 0, 0, 0, 40, 0, -32, 0, 8, 0, 68, 0, 0, 0, 36, 0, -8, 0, 0, 0, -4, 0, 0, 0, 60, 0, 0, 0, 68, 0, 72, 0, 0, 0, 64, 0, 40, 0, -32, 0, 96, 0, 0, 0, -60, 0, 96, 0, 0, 0, -4, 0, 0, 0, -20, 0, 0, 0, 0, 0, -84, 0, 0, 0, 60, 0, -48, 0, -8, 0, -56, 0, 0, 0, -8, 0, 20, 0, 0, 0, 60, 0, 0, 0, 28, 0, 0, 0, 36, 0, -28, 0, 0, 0, -80, 0, -24, 0, -112, 0, 8, 0, 0, 0, -64, 0, 20, 0, 0, 0, 8, 0, 0, 0, -48, 0, 0, 0, -32, 0, -32, 0, 0, 0, 0, 0, -64, 0, 40, 0, 32, 0, 0, 0, 68, 0, -92, 0, 0, 0, -36, 0, 0, 0, -56, 0, 0, 0, -40, 0, -76, 0, 0, 0, 52, 0, 72, 0, 64, 0, -72, 0, 0, 0, 44, 0, -24, 0, 0, 0, -16, 0, 0, 0, 16, 0, 0, 0, -52, 0, -20, 0, 0, 0, -56, 0, -64, 0, -80, 0, -32, 0, 0, 0, 116, 0, 68, 0, 0, 0, 40, 0, 0, 0, -4, 0, 0, 0, 40, 0, -72, 0, 0, 0, -128, 0, -152, 0, 112, 0, -32, 0, 0, 0, -24, 0, -40, 0, 0, 0, 28, 0, 0, 0, -20, 0, 0, 0, -60, 0, 68, 0, 0, 0, -32, 0, -96, 0, 28, 0, 0, 0, 0, 0, 60, 0, -28, 0, 0, 0, -4, 0, 0, 0, -100, 0, 0, 0, 64, 0, 20, 0, 0, 0, 4, 0, 48, 0, 184, 0, -4, 0, 0, 0, -52, 0, -12, 0, 0, 0, -132, 0, 0, 0, -20, 0, 0, 0, 64, 0, -56, 0, 0, 0, 112, 0, 128, 0, -24, 0, 0, 0, 0, 0, -108, 0, -64, 0, 0, 0, -56, 0, 0, 0, 40, 0, 0, 0, 68, 0, 104, 0, 0, 0, 12, 0, -88, 0, 72, 0, -56, 0, 0, 0, 124, 0, 28, 0, 0, 0, -32, 0, 0, 0, 44, 0, 0, 0, 28, 0, 28, 0, 0, 0, 80, 0, 88, 0, 4, 0, 28, 0, 0, 0, 68, 0, 88, 0, 0, 0, 40, 0, 0, 0, -36, 0, 0, 0, 0, 0, -12, 0, 0, 0, -64, 0, 8, 0, -128, 0, -32, 0, 0, 0, 44, 0, -76, 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, 15, 5, 1, 4, 0]], "char_orbit_index": 18, "prim_orbit_index": 5, "minimal_twist": "120.2.r.b", "char_is_minimal": true, "conrey_index": 257, "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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 1, -1, -1], [0, 0, 0, 0], [1, 0, -2, 0], [0, 0, 0, 0], [0, 2, 2, 0], [0, 0, 0, 0], [-1, 1, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 1, 2, -2], [0, 0, 0, 0], [0, 2, 2, 0], [0, 0, 0, 0], [1, 3, -2, 0], [0, 0, 0, 0], [-3, -3, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5, 0, 1], [0, 0, 0, 0], [-2, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [-2, -4, -2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3, 3, -2, -2], [0, 0, 0, 0], [-5, 3, 1, 3], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [-1, 1, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 5, 1, -1], [0, 0, 0, 0], [0, -1, -4, 0], [0, 0, 0, 0], [3, -5, -3, -1], [0, 0, 0, 0], [3, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, -4, -2, -2], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 4], [0, 0, 0, 0], [-3, 5, -3, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, -3, 5, 5], [0, 0, 0, 0], [1, -5, 4, 2], [0, 0, 0, 0], [0, -2, 6, 0], [0, 0, 0, 0], [-1, 1, 4, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, -2, 0, 0], [0, 0, 0, 0], [0, -2, -2, 0], [0, 0, 0, 0], [-7, 0, -4, 0], [0, 0, 0, 0], [1, 1, 3, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, -2, -4, 2], [0, 0, 0, 0], [10, 0, 0, -4], [0, 0, 0, 0], [-10, 0, 0, 6], [0, 0, 0, 0], [8, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, -1, 0, 0], [0, 0, 0, 0], [8, 2, 2, 4], [0, 0, 0, 0]]}