# Stored data for newform 735.2.s.d, downloaded from the LMFDB on 18 April 2024.
{"label": "735.2.s.d", "space_label": "735.2.s", "level": 735, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13512035866247903, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1194586412317468197, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, -3, 1]], [13, [0, 1]], [17, [36, 6, 1]]], "qexp_display": "q+(2-\\zeta_{6})q^{2}+(-1-\\zeta_{6})q^{3}+(1-\\zeta_{6})q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "s", "char_is_real": false, "Nk2": 2940, "analytic_conductor": 5.869004548564108, "hecke_ring_index": 1, "level_radical": 105, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.188", "prec": 17}, "analytic_rank_proved": true, "char_values": [735, 6, [491, 442, 346], [3, 6, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [521, 656], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.965", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.312", "prec": 20}, {"__RealLiteral__": 0, "data": "1.360", "prec": 17}, {"__RealLiteral__": 0, "data": "90.556", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c6", "trace_display": [3, -3, 1, 0], "traces": [0, 2, 3, -3, 1, 1, -6, 0, 0, 3, 3, 6, -3, 0, 0, 0, 5, -6, 9, 6, 2, 0, 12, 6, 3, -1, 0, 0, 0, 0, -3, 6, 9, -6, 0, 0, 6, 2, 6, 0, -3, 12, 0, -16, 6, -3, 6, 12, 0, 0, 0, 18, 0, 0, -9, 0, 0, -12, -12, 12, -3, -12, 12, 0, -2, 0, -18, -8, 6, -12, 0, 0, -9, -12, 6, 3, 0, 0, 0, -8, -5, -9, 18, 0, 0, -12, -24, -12, -6, -6, 0, 0, 0, -6, 36, 6, -9, 0, 0, 0, 1, 6, 18, -6, 0, 0, 0, 18, -9, 2, 6, 0, 0, 0, -18, 6, -12, 0, 0, 0, 6, 1, -12, -18, 6, -2, 0, -8, -21, 24, 0, 12, -12, 0, 0, 9, -18, -36, -18, 0, 0, 0, 6, 0, -15, 12, -24, 0, 4, 12, 3, 8, 6, -36, 0, 0, 0, -24, -24, 0, 0, 0, 0, 16, 6, 6, 0, 24, 0, 26, -18, 18, -8, -18, 0, 0, 0, -36, -18, -18, 3, 0, 0, 24, 6, -2, -18, -36, 24, 0, 12, -18, 3, 14, 12, 0, 0, 0, 18, -18, -3, 24, 0, 0, 0, 6, -6, 18, 0, 24, 0, 8, 0, 6, 18, -8, 18, 0, 0, 12, 6, 0, -6, 0, 0, -6, -12, 24, -6, -12, 12, 0, 24, 12, 0, -12, -12, 0, 0, 0, 15, 0, 3, 27, 0, 0, -36, 0, -6, 0, -3, 24, 0, 24, -12, 18, -19, -6, 48, 0, 0, 36, 36, 42, 18, 0, 0, 0, 8, -18, 9, 42, -60, 0, -72, -6, -6, -14, 30, 0, 0, 0, -36, -30, 6, -6, 0, 0, 0, -19, 12, 12, -12, -12, 0, 24, -6, 18, 12, 0, 0, 0, 0, -18, 30, -12, -54, 0, 0, 12, 6, 0, 0, -36, -48, 0, -16, 48, 0, 24, -1, -36, 0, 0, 9, 0, 48, -6, 0, 0, 0, -28, 0, -6, 36, -16, 0, -28, 39, -12, -6, 12, 36, 0, 0, -6, -54, 30, 12, 0, 0, 0, 18, -6, -36, -6, -12, 0, -36, 6, -9, -7, -36, 0, 0, 0, 36, -18, 30, 18, 0, 0, -12, -14, -36, 3, -36, 0, 0, 8, 6, 12, -18, -12, 42, 0, 0, -24, 12, -12, 0, 0, 0, 0, -24, 8, 18, 24, -36, 0, -10, -48, 24, 0, -6, -18, 0, 0, 18, 0, 18, 36, 0, 0, 36, 0, 0, 30, 36, 24, 0, -20, 12, -36, 0, -6, 0, 0, 0, 0, -24, 18, 45, 0, 0, -24, -2, 12, 36, -30, -12, 0, 0, 18, -6, 6, -30, -24, 0, 0, -9, 36, -12, -24, 0, 0, 0, 38, -12, 54, 6, 36, 0, 40, 60, 6, 12, -24, 0, 0, 0, 24, 36, -48, 24, 0, 0, 0, -18, 0, 9, 0, 0, 0, 2, -12, 27, -4, -12, 0, 0, 0, -18, 72, 0, -18, 0, 0, 0, 20, -1, -36, 36, -24, 0, 12, 36, -39, -4, 30, 36, 0, 0, -18, -18, -6, 24, 0, 0, 0, 0, -6, 36, 30, 24, 0, 84, -36, 30, -11, 0, 72, 0, 0, 18, 18, -24, 18, 0, 0, 0, 34, 42, -36, -54, 4, 0, 16, -36, -36, -6, -24, 0, 0, 0, 6, 30, 48, 18, 0, 0, 72, 24, 0, -36, 12, -60, 0, -12, -48, -18, 4, 0, 36, 0, 0, -3, -60, -57, -42, 0, 0, 0, 0, 12, 0, -18, 0, 0, 24, 36, -24, -10, -6, 0, 0, 0, 18, 0, 42, 3, 0, 0, -48, -8, -1, -18, -30, 36, 0, -24, 0, -18, 34, -42, 0, 0, 0, 18, -30, 6, -18, 0, 0, 0, -1, -36, -36, -24, -24, 0, -80, 24, -12, 48, -4, 0, 0, 0, -18, -21, -48, -54, 0, 0, 0, 36, -12, -27, 72, 0, 0, 32, -72, -6, -12, 30, 0, 0, 0, -6, 84, -84, 0, 0, 0, 0, -24, 12, -30, -24, -48, 0, -28, -42, 9, 13, 6, 0, 0, 0, -72, 36, 30, 18, 0, 0, 24, -40, 0, -18, 54, -36, 0, 60, -30, -36, -36, 12, -24, 0, 0, 0, 12, -6, 36, 0, 0, 0, -22, -6, 24, 18, 24, 0, 0, -18, -18, 6, 0, -30, 0, 0, 0, -36, 12, -3, 0, 0, -54, -12, 48, 12, 0, -36, 0, 36, -48, 54, 4, 2, 0, 0, 0, 18, 12, -42, 0, 0, 0, 6, -16, -60, -36, 0, 16, 0, -4, 12, -36, -6, 42, 24, 0, 0, -18, -36, 0, 57, 0, 0, 0, -14, 6, -72, -6, -24, 0, -24, 36, 0, -12, 36, -72, 0, 0, -36, 42, -24, -42, 0, 0, -36, 0, 24, 0, -18, 36, 0, -144, -9, 18, -48, -24, 0, 0, 0, 54, 18, -96, -27, 0, 0, -84, 12, -16, 90, -48, 0, 0, 12, 36, 108, -44, -6, 12, 0, 0, 18, -60, 0, 42, 0, 0, 0, 12, 12, 18, 36, -48, 0, -38, -30, 24, 4, 13, 0, 0, 0, 30, -18, 12, -6, 0, 0, 0, 18, -30, 0, -66, -16, 0, 36, 30, 27, 18, -12, 0, 0, 0, -36, 0, 6, -36, 0, 0, 24, -38, -30, 18, -30, 60, 0, 32, 0, -36, 18, 36, 12, 0, 0, -54, -30, 72, -36, 0, 0, 0, -24, 24, -3, 0, 72, 0, 24, 36, -24, 32, -24, 36, 0, 0, -30, 0, 114, 12, 0, 0, 108, -16, -6, -42, 54, 0, 0, -4, 60, -18, 36, -30, 0, 0, 0, 0, -72, -36, 0, 0, 0, 72, 12, -18, 72, 36, 120, 0, -96, -54, 24, 0, 6, -96, 0, 0, 0, -18, -18, -72, 0, 0, 0, -19, 0, 54, 0, 28, 0, 40, -3, 36, -12, -60, 0, 0, 0, 0, -60, -12, -48, 0, 0, 12, 42, 60, 18, 24, 144, 0, 0, -48, -18, -16, 18, 0, 0, 0, 0, 0, 60, 18, 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, 21, 7, 1, 6, 0]], "char_orbit_index": 19, "prim_orbit_index": 7, "minimal_twist": "105.2.b.a", "char_is_minimal": false, "conrey_index": 521, "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], [2, -1], [-1, -1], [1, -1], [0, 1], [-3, 0], [0, 0], [-1, 2], [0, 3], [1, 1], [2, 2], [-2, 1], [0, 0], [0, 0], [1, -2], [0, 5], [-6, 6], [3, 3], [4, -2], [1, 0], [0, 0], [6, 0], [4, -2], [3, -3], [-1, 1], [0, 0], [3, -6], [0, 0], [4, -8], [0, -3], [2, 2], [3, 3], [0, -6], [-6, 12], [0, 0], [3, 0], [0, 2], [6, -6], [0, 0], [-2, 1], [6, 0], [0, 0], [-8, 0], [4, -2], [-3, 3], [6, -6], [0, 12], [5, -10], [0, 0], [-1, 2], [12, -6], [0, 0], [0, 0], [0, -9], [-2, 4], [0, 0], [-6, 0], [0, -12], [12, -12], [-1, -1], [-8, 4], [6, 0], [0, 0], [-1, 0], [0, 0], [-6, -6], [-8, 8], [0, 6], [-6, 0], [0, 0], [-2, 4], [-6, 3], [-4, -4], [2, 2], [2, -1], [2, -4], [0, 0], [0, 0], [0, -8], [-5, 5], [-9, 9], [12, -6], [0, 0], [0, 0], [-6, 0], [-16, 8], [-12, 12], [-6, 6], [0, -6], [-3, 6], [0, 0], [2, -4], [0, -6], [12, 12], [2, 2], [0, -9], [-4, 8], [0, 0], [-6, 12], [0, 1]]}