# Stored data for newform 600.2.k.a, downloaded from the LMFDB on 25 April 2024.
{"label": "600.2.k.a", "space_label": "600.2.k", "level": 600, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 687228322392, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 988616981234309864, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [2, 1]]], "qexp_display": "q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "k", "char_is_real": true, "Nk2": 2400, "analytic_conductor": 4.791024121276823, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [600, 2, [151, 301, 401, 577], [2, 1, 2, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [301], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.883", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.898", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "148.419", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 0, 0, -4], "traces": [0, 2, -2, 0, 0, 0, 2, -4, 4, -2, 0, 0, -4, 0, 4, 0, -8, 12, 2, 0, 0, 0, -8, 8, 4, 0, 0, 0, 0, 0, 0, 20, 8, 8, -12, 0, 0, 0, -8, 0, 0, 20, -4, 0, 16, 0, -8, 8, 0, -6, 0, 0, 0, 0, -2, 0, -8, 8, 12, 0, 0, 0, -20, 4, 0, 0, -8, 0, 0, 0, 0, -8, -4, -20, 8, 0, 16, 0, 0, -28, 0, 2, -20, 0, 8, 0, -8, -12, -16, 28, 0, 0, 0, 0, -8, 0, -8, 20, 6, 0, 0, 0, 12, 4, 0, 0, -20, 0, 4, 0, 0, -8, 16, -12, -8, 0, -24, 0, -16, -24, 0, -10, 16, 0, 0, 0, -4, 12, -16, 8, 0, 0, 0, 0, -24, 0, 24, 4, 8, 0, 0, 0, 8, 0, 8, 0, 20, 0, -16, 0, 0, -4, -16, -12, 16, 0, 0, 0, 28, 20, 0, -16, -2, 0, 0, 0, 0, -48, -8, 26, 0, 0, 16, 0, 12, 0, 0, 16, -28, 0, 0, 0, 0, -16, 16, 0, 20, 0, 0, 0, 0, -16, 16, 28, -20, 0, 0, 0, 8, -12, 0, 24, -28, 0, -24, 0, -4, -8, 0, -32, 0, 0, 40, 0, 8, 0, -4, -40, -8, 0, 0, 0, 8, -20, -16, 0, 12, 0, 0, 0, 0, -16, 24, 12, 0, 0, 32, 0, 24, 32, 0, -60, 10, 0, -32, 0, 20, 0, 40, 0, 0, 0, 0, 0, -12, 0, 32, 4, -8, 0, 0, 0, 0, 0, 16, 0, 16, 0, 48, 0, 0, -4, -48, 0, -4, 0, -16, 0, 8, -20, 0, -20, 8, 0, 0, 0, 0, -40, -8, 38, 0, 0, 0, 0, -6, 0, 16, -8, 12, 0, 0, 0, 4, 28, 0, 0, 12, 0, -32, 0, 0, 16, 0, -12, 40, 0, 0, 0, -20, 48, 0, -8, 16, 0, 0, 0, 40, 8, 40, -16, 0, 0, 0, 0, 48, 0, 0, -60, -26, 0, 0, 0, 8, 40, -16, 0, -20, 0, 0, 0, 0, 0, 32, 36, -16, 0, 0, 0, 0, 24, 0, 6, 40, 0, 0, 0, 16, 36, -32, -20, 0, 0, -40, 0, -48, 0, 16, 0, 4, 0, 0, 0, 16, -48, -16, 0, -28, 0, 0, 0, 0, 48, -12, 0, -20, 0, -16, 0, 12, -16, 0, 60, -24, 0, 56, 0, -24, 32, 24, -12, 0, 0, 0, 0, 8, 0, 0, -8, 32, 0, 0, 0, -24, -8, -40, 0, -8, 0, -16, 0, 0, -72, 0, -28, 40, 0, 16, 0, -20, 4, 0, 6, 0, 0, 0, 0, 20, -12, 0, -36, 0, 0, 0, 0, 0, 0, 16, -36, 8, 0, 0, 0, 16, 44, 0, 0, -12, 0, 0, 0, 0, -40, -32, -32, -28, 0, 0, 0, -32, 8, 0, 0, 60, 0, 0, 0, 2, 60, 32, -40, 0, 0, -40, 0, 0, 0, -80, 16, 0, 0, 0, 0, -24, 24, 8, 0, -32, 0, 0, 0, 0, 40, -32, -8, -4, 0, 0, 0, -16, 20, 0, -12, -12, 0, 0, 0, 0, 120, -32, -14, 0, 0, -32, 0, 28, 0, -48, 0, -20, 0, 0, 0, 4, -40, 48, 0, 0, 0, 0, 0, 0, 48, 16, 56, -32, 0, -16, 0, 20, 0, 0, 48, 20, 0, -16, 0, -8, -4, -16, 4, 0, 0, 0, 0, 40, 0, 0, 4, -38, 0, 0, 0, 20, -80, -40, 0, -4, 0, 12, 0, 0, 20, 0, -44, 8, 0, -24, 0, 0, 24, 0, -28, 16, 0, 0, 0, -28, -4, 32, 24, 0, 0, 0, 0, 56, 0, 32, 12, 4, 0, 0, 0, -16, -56, 0, 0, 12, 0, -80, 0, 0, -36, -56, 24, 36, 0, 0, 0, -48, 8, 0, 28, 8, 0, 0, 0, -48, -24, 4, -64, 0, 0, -80, 0, -8, 0, -80, 20, 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 64, 16, 4, 60, 0, 0, 0, -12, -40, 0, 0, -80, 0, -16, 0, -40, -8, 0, 0, 0, 0, 40, 0, 32, 0, -24, 120, -16, 0, 0, 0, 0, 32, -64, 0, -36, 0, 0, 0, 0, 28, 56, 80, -24, 0, 0, 0, -24, -72, 0, -8, -6, 0, -80, 0, -10, 28, 0, -2, 0, 0, 0, 0, -36, 0, 32, -96, 20, 0, 0, 0, 40, 96, 40, 0, 40, 0, 96, 0, 0, 52, -32, 24, 0, 0, -8, 0, 72, 32, 0, 20, 12, 0, 0, 0, 48, 0, 0, -12, 0, 0, 0, 0, 8, 0, 40, 16, -20, 0, 0, 0, -48, 12, 24, 0, 0, 0, 40, 0, 0, 24, 16, 0, 40, 0, 0, 0, 16, 48, 0, -28, -60, 0, 0, 0, 0, 20, -56, 20, 0, 0, 48, 0, -32, 0, 0, -32, 12, 0, 0, 0, 4, -84, 8, 0, 32, 0, 0, 0, 0, 32, 0, -36, 8, 0, 0, 0, 8, 8, 0, -14, -40, 0, 48, 0, 8, 20, 0, 8, 0, 0, 16, 0, -32, 0, 16, -12, 0, 0, 0, 0, 72, -48, 8, 0, 28, 0, 0, 0, 0, 0, -16, -20, -32, 0, 40, 0, -4, 4, 0, -12, -6, 0, 0, 0, 32, -32, -16, -24, 0, 0, 0, 0, 12, 0, 32, 0, 36, 0, 0, 0, -80, -16, -24, 0, -4, 0, 0, 0, 0, -96, -32, 0, 36, 0, -16, 0, -12, -52, 0, -56, 68, 0, 0, 0, -44, -4, -48, 92, 0, 0, 0, 0, -16, 0, 0, -44, 48, 0, 0, 0, 40, 80, 0, 0, 32, 0, 56, 0, 0, -36, -48, 52, 20, 0, 0, 0, -8, -8, 0, 138, 0, 0, 0, 0, -16, -92, -20, 48, 0, 0, -4, 0, -60, 0, 0, 44, 40, 0, 0, 0, 80, 64, 40, 0, 72, 0, 0, 0, 0, 4, 80, 8, -16, 0, 0, 0, 40, 8, 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, 8, 2, 1, 2, 0]], "char_orbit_index": 11, "prim_orbit_index": 2, "minimal_twist": "120.2.k.a", "char_is_minimal": true, "conrey_index": 301, "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], [1, 0], [-1, 1], [0, -1], [0, -2], [0, 0], [1, 1], [-2, 0], [2, 2], [-1, 0], [0, 0], [0, 4], [-2, 0], [0, 0], [2, -2], [0, 0], [-4, 0], [6, 0], [1, -1], [0, 4], [0, 0], [0, 2], [-4, -4], [4, 0], [2, -2], [0, 0], [0, 0], [0, 1], [0, 4], [0, -6], [0, 0], [10, 0], [4, -4], [4, 0], [-6, 6], [0, 0], [0, 2], [0, -4], [-4, -4], [0, 0], [0, 0], [10, 0], [-2, -2], [0, 4], [8, 0], [0, 0], [-4, 4], [4, 0], [0, 4], [-3, 0], [0, 0], [0, -6], [0, 0], [0, 10], [-1, -1], [0, 0], [-4, -4], [4, 0], [6, 6], [0, 8], [0, 0], [0, -8], [-10, 10], [2, 0], [0, 8], [0, 0], [-4, 4], [0, 12], [0, -12], [0, -4], [0, 0], [-4, 0], [-2, -2], [-10, 0], [4, 4], [0, 0], [8, 0], [0, -8], [0, 0], [-14, 0], [0, 0], [1, 0], [-10, 10], [0, 0], [4, 0], [0, 0], [-4, -4], [-6, 0], [-8, 8], [14, 0], [0, 0], [0, 0], [0, -8], [0, -10], [-4, 4], [0, 0], [-4, -4], [10, 0], [3, -3], [0, -4], [0, 0]]}