# Stored data for newform 735.2.a.k, downloaded from the LMFDB on 19 April 2024.
{"label": "735.2.a.k", "space_label": "735.2.a", "level": 735, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45035996307260127, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 2159282572225226074, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-5, 0, 1]], [13, [-20, 0, 1]]], "qexp_display": "q-\\beta q^{2}+q^{3}+3q^{4}+q^{5}-\\beta q^{6}-\\beta q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2940, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 5.869004548564108, "hecke_ring_index": 2, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, "analytic_rank_proved": true, "char_values": [735, 1, [491, 442, 346], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 7], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "1.919", "prec": 17}, {"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "9.202", "prec": 17}, {"__RealLiteral__": 0, "data": "0.597", "prec": 17}, {"__RealLiteral__": 0, "data": "61.845", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1], [7, -1]], "trace_display": [0, 2, 2, 0], "traces": [0, 2, 0, 2, 6, 2, 0, 0, 0, 2, 0, 4, 6, 0, 0, 2, -2, 4, 0, -4, 6, 0, -20, 8, 0, 2, 20, 2, 0, -4, 0, -12, 0, 4, 0, 0, 6, 4, -20, 0, 0, 4, 0, 0, 12, 2, 0, -8, -2, 0, 0, 4, 0, -16, 0, 4, 0, -4, 0, 0, 6, 4, -20, 0, -26, 0, -20, -8, 12, 8, 0, 20, 0, 16, 40, 2, -12, 0, 20, 8, -2, 2, 0, 16, 0, 4, -40, -4, -20, 4, 0, 0, 24, -12, 40, -4, 0, -8, 0, 4, 6, 28, 0, 0, 20, 0, -20, -8, 6, -4, -20, 4, 0, -8, -20, 8, -12, 0, -40, 0, 0, 26, 0, 4, -36, 2, 0, 8, 0, 0, 20, -8, 12, 0, 0, 2, 0, 16, 0, 12, 0, -8, 20, -40, -2, -4, -20, 0, 12, -12, 0, -32, -20, 4, 0, -12, 0, -8, -40, -16, 0, 0, 0, -16, 12, 4, -40, 16, 0, 14, 0, -4, 0, -12, 0, 0, -4, 0, 0, 4, 6, -20, 0, 4, 0, 4, -20, 8, -24, 0, -20, 28, -26, -28, 20, 0, 0, 40, -20, -28, 0, -8, 0, 0, 12, 4, 0, 8, 0, 32, 0, -16, -48, 20, 40, 0, 0, 0, 0, 16, 12, 0, 40, 8, 0, 2, -20, 16, -12, -12, 0, 0, 0, 8, 20, -8, 0, 8, 0, -12, -2, 20, -80, 2, 12, 0, 0, -40, -20, 16, 0, -16, 0, 16, 40, 4, -18, -20, -40, 0, 0, -4, 0, 32, -20, -16, 0, 4, -24, 12, 0, 12, -4, 0, 20, 4, 24, 20, 60, -12, 0, -4, 40, -24, 60, -4, 40, 0, 0, -26, 0, -8, 48, -28, 0, 0, 40, 4, 40, 0, 6, 0, 0, 28, 4, 4, 0, 48, 0, 0, -20, -16, 20, 8, -20, 0, 24, -16, -20, -8, -26, -8, 0, -8, 6, 0, 40, -4, 0, 0, -20, -16, 48, 4, 0, -8, 0, -12, 0, -8, 12, 16, -20, 0, -40, 8, -40, -16, -12, -12, 0, 0, 60, 20, -40, 20, 12, 0, -20, 28, 0, 10, -40, 26, 0, 16, 0, -24, -8, 4, 40, 0, -36, 12, -40, 2, 40, 0, 0, -40, -12, 8, 60, 16, 0, 0, 0, 0, -24, 4, 20, 16, 0, -8, 20, 8, 12, 0, 60, 0, -2, 20, 0, -40, 84, 2, 0, -72, 0, 12, 0, 16, 0, 0, 0, 16, -60, 12, 0, 24, 0, 44, 40, -8, -20, 4, 20, 0, -24, -40, -40, -28, -2, -24, 0, -4, -12, -16, -20, -12, -20, 0, 40, -16, 12, 4, -40, -12, 0, -28, 0, 8, -24, -32, 40, 0, -20, -4, 80, 4, 24, 28, 0, 24, 4, -12, 60, 0, 0, 0, 40, -8, -40, 80, -40, -4, 0, -16, 20, 0, 0, 80, -40, 0, 78, -8, 0, -24, 0, -16, 0, 20, 12, -8, -40, 4, 12, 0, -40, 8, 6, 16, 40, -64, 0, 28, -80, 14, 24, 12, 0, 0, 0, -4, 40, 0, 0, -96, 0, -12, 20, 4, 0, 0, -24, 0, 40, -24, -4, -14, -20, 0, 0, 0, 0, -8, 0, 4, 80, 0, 6, 12, 20, -20, 0, -4, 0, -24, 48, 4, -20, 8, 0, 0, -40, 4, 36, 32, -20, -80, 0, 8, 40, 8, -24, -8, 0, 0, 20, -44, -20, -8, -120, 28, 0, 8, -26, 24, 0, -28, -12, 0, 20, 8, -20, 0, -40, 8, 0, 64, -40, 40, -4, -12, -20, 0, -36, -28, 80, -20, 0, -60, 0, -8, -96, 26, 0, -24, 60, 0, 0, 80, 12, 4, 40, 4, 0, 24, 0, -52, -36, 8, 80, 0, 0, 2, -60, 32, -24, 8, 0, 8, -40, -16, -100, 8, -48, 0, 40, 20, 0, -20, 40, 48, 0, 0, -40, -32, 0, 80, 20, 0, -48, -72, 0, -8, -4, 16, 0, -20, 12, 36, -40, 0, -40, 0, 40, -16, 48, 8, 0, 8, 0, -36, 80, 2, 42, -60, -20, 0, 0, 16, 80, 32, -12, 16, 0, -12, 0, -40, 0, -44, -36, 0, 0, 12, 0, 8, -80, 8, 0, -68, 20, -88, -52, -8, 80, 0, 0, -20, 20, 8, 0, -48, 0, -40, 12, -12, -20, -40, -2, 0, 80, 20, -60, -4, -80, 24, 0, 2, -20, 0, 12, -48, -40, 0, 0, -16, 0, 24, 12, -40, 0, 16, -20, -12, 0, 16, 24, 0, 0, -24, 8, -16, -40, -32, 0, 28, 80, 16, -20, 20, 40, 0, 84, 4, 0, -80, -18, 52, 0, -20, -84, 68, -40, -12, 20, 0, 40, -8, 0, 0, 0, -4, 0, -8, 0, -80, 120, 32, -40, 0, -20, 0, -60, -16, -84, 20, 0, -16, 0, 4, 0, 72, -24, 0, -120, 12, 0, 60, 0, -84, 0, 12, 40, -16, -4, 80, 80, 0, 12, -4, 20, 72, 0, 4, 0, 8, 24, 44, -40, 20, 0, 0, 60, 16, 96, -12, -80, -56, 0, -50, 0, -4, -48, 14, 40, 0, 16, -24, 0, 16, 60, 0, 0, -4, 40, -20, 40, -92, 0, 0, 20, 8, 0, -12, 20, -26, 0, 96, 0, 0, 0, -8, -80, 0, 48, -60, -20, -28, -4, 20, 0, -40, 0, 0, 0, 8, 40, 0, 0, 4, 24, -64, 40, 4, 0, 0, 0, 24, 6, -32, -40, 0, -20, -20, 0, 72, 48, 28, 0, 12, 4, 112, -40, 4, -36, 0, 0, -88, 0, 48, 80, 40, 0, 4, -40, 0, 0, 68, -20, 0, 24, -16, -40, 8, 20, 96, 0, 8, -24, 60, -20, 16, 0, 0, -80, 0, 24, -40, -20, -16, 0, -40, -20, 28, -36, -8, -80, 0, -26, 50, 40, -8, 60, -28, 0, 16, -80, -8, 20, -64, 6, 0, 40, 0, -4, 88, 40, 8, 0, -4, 140, -8, 0, 40, 0, 0, -120, 0, -20, -8, 60, -16, 0, -28, 48, -16, 80, 4, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "105.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, -1], [1, 0], [3, 0], [1, 0], [0, -1], [0, 0], [0, -1], [1, 0], [0, -1], [2, 2], [3, 0], [0, -2], [0, 0], [1, 0], [-1, 0], [2, 0], [0, -1], [-2, 2], [3, 0], [0, 0], [-10, -2], [4, 0], [0, -1], [1, 0], [10, 0], [1, 0], [0, 0], [-2, 0], [0, -1], [-6, 2], [0, 3], [2, 2], [0, -2], [0, 0], [3, 0], [2, -4], [-10, 2], [0, -2], [0, -1], [2, 0], [0, 0], [0, 4], [6, 6], [1, 0], [0, -4], [-4, -4], [-1, 0], [0, 0], [0, -1], [2, 0], [0, -6], [-8, 2], [0, -1], [2, 2], [0, 0], [-2, 2], [0, 2], [0, 4], [3, 0], [2, 0], [-10, 6], [0, 0], [-13, 0], [0, -2], [-10, -2], [-4, 0], [6, 0], [4, 0], [0, 0], [10, -2], [0, -1], [8, 2], [20, -2], [1, 0], [-6, 6], [0, 0], [10, 0], [4, 4], [-1, 0], [1, 0], [0, -2], [8, 4], [0, 0], [2, 0], [-20, 0], [-2, 0], [-10, -2], [2, 0], [0, -1], [0, 0], [12, 0], [-6, 2], [20, 4], [-2, 2], [0, 3], [-4, -2], [0, 0], [2, 2], [3, 0]]}