# Stored data for newform 1710.2.d.e, downloaded from the LMFDB on 19 April 2024. {"label": "1710.2.d.e", "space_label": "1710.2.d", "level": 1710, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014604701468334, "dim": 6, "is_polredabs": true, "nf_label": "6.0.350464.1", "trace_hash": 1241477619053453506, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [256, 0, 256, 0, 32, 0, 1]], [11, [32, -16, -4, 1]], [13, [64, 0, 112, 0, 44, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-q^{4}-\\beta _{2}q^{5}+(-\\beta _{2}-\\beta _{5})q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "d", "char_is_real": true, "Nk2": 6840, "analytic_conductor": 13.654418745638946, "hecke_ring_index": 8, "level_radical": 570, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [1710, 2, [191, 1027, 1351], [2, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 19], "conrey_indexes": [1369], "field_disc": -350464, "field_disc_factorization": [[-1, 1], [2, 8], [37, 2]], "field_poly": [2, -4, 4, 2, 2, -2, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.472", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "163.147", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7169.610", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, -2, 0], "traces": [0, 6, 0, 0, -6, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 6, 0, 0, 6, 2, 0, 0, 0, 0, -2, -12, 0, 0, 20, 0, 28, 0, 0, -20, -32, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 12, 0, 0, -22, 8, 0, 0, 0, 0, 16, 0, 0, 0, 28, 0, 12, 0, 0, -6, -32, 0, 0, 0, 0, 8, 8, 0, 0, 4, 0, -6, 0, 0, -44, -2, 0, 0, 0, 0, 8, 20, 0, 0, 8, 0, -64, 0, 0, 4, -2, 0, 0, 0, 0, 2, 12, 0, 0, 12, 0, 28, 0, 0, -8, -24, 0, 0, 0, 0, 32, -20, 0, 0, 16, 0, 30, 0, 0, -28, -26, 0, 0, 0, 0, 12, -32, 0, 0, -16, 0, 20, 0, 0, -24, 32, 0, 0, 0, 0, 12, 16, 0, 0, 28, 0, 12, 0, 0, -48, -44, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -10, -20, 0, 0, 0, 0, -16, 8, 0, 0, 52, 0, 40, 0, 0, -12, -48, 0, 0, 0, 0, 0, 64, 0, 0, -12, 0, 22, 0, 0, 16, -8, 0, 0, 0, 0, 8, 64, 0, 0, 8, 0, 16, 0, 0, -8, -40, 0, 0, 0, 0, -16, -24, 0, 0, 0, 0, -20, 0, 0, 12, -12, 0, 0, 0, 0, 16, -28, 0, 0, -16, 0, 4, 0, 0, -12, -30, 0, 0, 0, 0, 48, -56, 0, 0, -64, 0, 6, 0, 0, -96, 32, 0, 0, 0, 0, -16, 0, 0, 0, 44, 0, 80, 0, 0, -44, -88, 0, 0, 0, 0, -8, -32, 0, 0, -8, 0, -64, 0, 0, -18, -24, 0, 0, 0, 0, -36, -4, 0, 0, 88, 0, -80, 0, 0, 6, -4, 0, 0, 0, 0, -40, 64, 0, 0, -44, 0, 44, 0, 0, 112, 2, 0, 0, 0, 0, 0, 44, 0, 0, 32, 0, 88, 0, 0, 16, 16, 0, 0, 0, 0, -8, 48, 0, 0, -20, 0, -4, 0, 0, 92, 48, 0, 0, 0, 0, -40, -8, 0, 0, 80, 0, 6, 0, 0, 64, 48, 0, 0, 0, 0, 60, -32, 0, 0, -64, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, -128, 44, 0, 0, -124, 0, 24, 0, 0, 40, -20, 0, 0, 0, 0, -2, -96, 0, 0, -12, 0, -48, 0, 0, 52, 32, 0, 0, 0, 0, -24, -12, 0, 0, 0, 0, -32, 0, 0, -28, 80, 0, 0, 0, 0, 28, -16, 0, 0, -80, 0, 8, 0, 0, 20, 24, 0, 0, 0, 0, -48, 64, 0, 0, -56, 0, -48, 0, 0, 40, 0, 0, 0, 0, 0, -32, -68, 0, 0, 20, 0, -36, 0, 0, 32, 44, 0, 0, 0, 0, -2, -16, 0, 0, 48, 0, -88, 0, 0, -30, 72, 0, 0, 0, 0, 48, 80, 0, 0, -12, 0, 28, 0, 0, 40, 26, 0, 0, 0, 0, -84, 64, 0, 0, 4, 0, 96, 0, 0, -20, 8, 0, 0, 0, 0, -12, -96, 0, 0, 32, 0, 28, 0, 0, 50, 44, 0, 0, 0, 0, 48, 16, 0, 0, -200, 0, -188, 0, 0, -20, 144, 0, 0, 0, 0, 48, 20, 0, 0, -28, 0, 24, 0, 0, -40, -32, 0, 0, 0, 0, -32, 28, 0, 0, -88, 0, -40, 0, 0, 64, 0, 0, 0, 0, 0, -12, -48, 0, 0, -16, 0, 12, 0, 0, 28, -8, 0, 0, 0, 0, 80, -28, 0, 0, 0, 0, 100, 0, 0, -12, -42, 0, 0, 0, 0, 0, 40, 0, 0, -136, 0, 48, 0, 0, 40, 44, 0, 0, 0, 0, 22, 24, 0, 0, 136, 0, 8, 0, 0, -36, 56, 0, 0, 0, 0, 0, 80, 0, 0, -64, 0, -20, 0, 0, 0, 52, 0, 0, 0, 0, -8, 0, 0, 0, 52, 0, -128, 0, 0, 0, -32, 0, 0, 0, 0, -48, 16, 0, 0, -60, 0, 10, 0, 0, 144, 20, 0, 0, 0, 0, 72, 96, 0, 0, 24, 0, -104, 0, 0, -16, -8, 0, 0, 0, 0, 16, 20, 0, 0, -8, 0, -20, 0, 0, 124, 48, 0, 0, 0, 0, -176, -52, 0, 0, -96, 0, 16, 0, 0, -40, -92, 0, 0, 0, 0, 32, 136, 0, 0, -104, 0, 12, 0, 0, 8, 48, 0, 0, 0, 0, -36, -4, 0, 0, 96, 0, -140, 0, 0, -88, -60, 0, 0, 0, 0, 0, -116, 0, 0, -64, 0, -104, 0, 0, 108, 48, 0, 0, 0, 0, -20, 12, 0, 0, 0, 0, -160, 0, 0, -22, 8, 0, 0, 0, 0, -40, -64, 0, 0, -4, 0, -16, 0, 0, 104, 8, 0, 0, 0, 0, 0, -136, 0, 0, 100, 0, 72, 0, 0, 32, -104, 0, 0, 0, 0, -8, -204, 0, 0, -64, 0, -16, 0, 0, -104, 80, 0, 0, 0, 0, -16, -8, 0, 0, -24, 0, -22, 0, 0, -16, -2, 0, 0, 0, 0, 44, 88, 0, 0, 0, 0, 8, 0, 0, 120, 40, 0, 0, 0, 0, 80, 28, 0, 0, -48, 0, 0, 0, 0, 12, 32, 0, 0, 0, 0, 16, -44, 0, 0, 24, 0, 120, 0, 0, 112, 16, 0, 0, 0, 0, -28, 0, 0, 0, 104, 0, 200, 0, 0, 20, 112, 0, 0, 0, 0, 112, -8, 0, 0, -32, 0, -12, 0, 0, -72, 12, 0, 0, 0, 0, -128, 64, 0, 0, 44, 0, -22, 0, 0, -24, -48, 0, 0, 0, 0, -16, -68, 0, 0, 28, 0, 16, 0, 0, 128, 8, 0, 0, 0, 0, 40, 16, 0, 0, 144, 0, 94, 0, 0, -4, 72, 0, 0, 0, 0, 60, -100, 0, 0, 0, 0, 12, 0, 0, -112, 30, 0, 0, 0, 0, 80, -104, 0, 0, 40, 0, -148, 0, 0, 96, 16, 0, 0, 0, 0, -48, -352, 0, 0, 56, 0, -28, 0, 0, -116, -24, 0, 0, 0, 0, -192, 64, 0, 0, -52, 0, -200, 0, 0, -6, 48, 0, 0, 0, 0, -48, -32, 0, 0, 128, 0, 96, 0, 0, 84, -32, 0, 0, 0, 0, 16, -24, 0, 0, 244, 0, -8, 0, 0, -24, 48, 0, 0, 0, 0, 16, 148, 0, 0, 0, 0, 64, 0, 0, 60, 40, 0, 0, 0, 0, -96, -44, 0, 0, -48, 0, -40, 0, 0, -80, -160, 0, 0, 0, 0, 72, -220, 0, 0, -120, 0, 44, 0, 0, 16, 88, 0, 0, 0, 0, 40, -80, 0, 0, 164, 0, -96, 0, 0, -40, 8, 0, 0, 0, 0, 8, 28, 0, 0, 32, 0, -8, 0, 0, -44, -84, 0, 0, 0, 0, 96, 8, 0, 0, -160, 0, -208, 0, 0, 64, -36, 0, 0, 0, 0, -52, -128, 0, 0, -32, 0, 18, 0, 0, 12, 24, 0, 0, 0, 0, 232, 112, 0, 0, -32, 0, 216, 0, 0, -112, -96, 0, 0, 0, 0, 36, -28, 0, 0, 4, 0, 100, 0, 0, -48, 144, 0, 0, 0, 0, -56, -88, 0, 0, 128, 0, 20, 0, 0, 80, 84, 0, 0, 0, 0, -128, 160, 0, 0, 0, 0, -6, 0, 0, -24, 4, 0, 0, 0, 0, 178, 4, 0, 0, 140, 0, -4, 0, 0, -172, -32, 0, 0, 0, 0, 40, 128, 0, 0, -64, 0, 32, 0, 0, -60, -80, 0, 0, 0, 0, -16, 44, 0, 0, 160, 0, 120, 0, 0, -44, 176, 0, 0, 0, 0, 32, -80, 0, 0, 140, 0, -112, 0, 0, -264, -2, 0, 0, 0, 0, 96, -132, 0, 0, 28, 0, -120, 0, 0, 180, -128, 0, 0, 0, 0, 0, -12, 0, 0, -44, 0, -56, 0, 0, -96, 24, 0, 0, 0, 0, -32, -32, 0, 0, 168, 0, 124, 0, 0, -88, -144, 0, 0, 0, 0, 8, 144, 0, 0, 88, 0, -16, 0, 0, 144, -16, 0, 0, 0, 0, 20, -44, 0, 0, 8, 0, 144, 0, 0, -76, -112, 0, 0, 0, 0, 8, -80, 0, 0, -48, 0, -56, 0, 0, -122, -28, 0, 0, 0, 0, 80, 20, 0, 0, 160, 0, 40, 0, 0, 4, 120, 0, 0, 0, 0, -64, 80, 0, 0, -16, 0, -92, 0, 0, -4, -48, 0, 0, 0, 0, 88, 4, 0, 0, 48, 0, 160, 0, 0, -48, -216, 0, 0, 0, 0, 40, -244, 0, 0, 8, 0, 136, 0, 0, -84, 16, 0, 0, 0, 0, 48, -80, 0, 0, -192, 0, -128, 0, 0, -6, -170, 0, 0, 0, 0, 64, 144, 0, 0, -184, 0, -64, 0, 0, -152, -48, 0, 0, 0, 0, 192, 60, 0, 0, -104, 0, 180, 0, 0, -96, 28, 0, 0, 0, 0, -60, 232, 0, 0, 32, 0, 16, 0, 0, -20, -8, 0, 0, 0, 0, -24, 64, 0, 0, 40, 0, -44, 0, 0, 4, -96, 0, 0, 0, 0, 72, -128, 0, 0, 148, 0, 0, 0, 0, -124, -2, 0, 0, 0, 0, -4, 144, 0, 0, 64, 0, 328, 0, 0, -72, 16, 0, 0, 0, 0, 128, 0, 0, 0, -44, 0, -140, 0, 0, -232, -32, 0, 0, 0, 0, 40, 124, 0, 0, 16, 0, 16, 0, 0, -24, -128, 0, 0, 0, 0, -12, -44, 0, 0, 16, 0, -40, 0, 0, 96, 20, 0, 0, 0, 0, -192, -24, 0, 0, 192, 0, -232, 0, 0, -76, -32, 0, 0, 0, 0, 2, -252, 0, 0, 96, 0, 192, 0, 0, -84, -112, 0, 0, 0, 0, 8, 12, 0, 0, 144, 0, -52, 0, 0, 48, 128, 0, 0, 0, 0, 36, 464, 0, 0, 20, 0, -52, 0, 0, 0, -32, 0, 0, 0, 0, -96, -152, 0, 0, 72, 0, -16, 0, 0, 104, -120, 0, 0, 0, 0, 24, -240, 0, 0, 12, 0, 148, 0, 0, 164, 48, 0, 0, 0, 0, 128, 0, 0, 0, -128, 0, -182, 0, 0, 32, 56, 0, 0, 0, 0, 176, 8, 0, 0, -256, 0, 28, 0, 0, -96, -80, 0, 0, 0, 0, 64, 100, 0, 0, -132, 0, 56, 0, 0, -100, 64, 0, 0, 0, 0, -28, -380, 0, 0, 16, 0, -200, 0, 0, -64, -68, 0, 0, 0, 0, -8, 80, 0, 0, -152, 0, 168, 0, 0, -8, -100, 0, 0, 0, 0, -120, 160, 0, 0, -84, 0, -20, 0, 0, 24, -24, 0, 0, 0, 0, 56, 68, 0, 0, 40, 0, 352, 0, 0, -8, 168, 0, 0, 0, 0, 48, 56, 0, 0, -64, 0, 4, 0, 0, 72, 56, 0, 0, 0, 0, 88, 56, 0, 0, 192, 0, 196, 0, 0, 48, -2, 0, 0, 0, 0, 8, 88, 0, 0, 128, 0, -40, 0, 0, 48, 0, 0, 0, 0, 0, -96, 112, 0, 0, 200, 0, -136, 0, 0, 48, 80, 0, 0, 0, 0, 32, -64, 0, 0, 68, 0, 80, 0, 0, 42, -28, 0, 0, 0, 0, -144, -20, 0, 0, -376, 0, 56, 0, 0, 36, 112, 0, 0, 0, 0, -16, 160, 0, 0, 72, 0, -32, 0, 0, -200, -44, 0, 0, 0, 0, -240, -64, 0, 0, -160, 0, 56, 0, 0, 152, -112, 0, 0, 0, 0, 2, 156, 0, 0, 16, 0, 4, 0, 0, 48, 48, 0, 0, 0, 0, 32, -48, 0, 0, 12, 0, -248, 0, 0, 88, 0, 0, 0, 0, 0, -156, 4, 0, 0, -24, 0, 30, 0, 0, 240, -72, 0, 0, 0, 0, 84, -128, 0, 0, 196, 0, 396, 0, 0, -164, -40, 0, 0, 0, 0, -48, -264, 0, 0, -80, 0, -128, 0, 0, -64, 16, 0, 0, 0, 0, 4, 12, 0, 0, 28, 0, -432, 0, 0, -28, -120, 0, 0, 0, 0, -112, 288, 0, 0, 20, 0, -40, 0, 0, 0, -26], "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, 5, 2, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "570.2.d.d", "char_is_minimal": true, "conrey_index": 1369, "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [2, 0, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [0, 2, -1, 0, 0, -1], [0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 4, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, -1, 1, -1, -1], [0, -2, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [-1, -2, 1, -2, 0, -1], [-2, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [4, 0, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [4, 0, 1, 1, 1, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, -1], [-6, -2, 1, -2, 0, -1], [0, 0, 0, 0, 0, 0], [0, -2, -1, -2, 2, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [0, -4, -1, -1, 1, -1], [-2, 0, 1, -1, -1, -1], [0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 1, 0], [0, -2, 1, -2, 2, 1], [0, 0, 0, 0, 0, 0], [-5, 0, 2, -2, -2, -2], [2, -1, 0, -1, 1, 2], [0, 0, 0, 0, 0, 0], [0, -2, 1, 0, 0, 1], [0, -6, 0, -2, 2, 0], [0, 0, 0, 0, 0, 0], [2, 4, -1, -1, -1, -3], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 4, -1, 1, -1, -1], [4, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0], [0, 4, -1, -1, 1, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-6, -2, 1, -2, -2, -1], [0, 0, 0, 0, 0, 0], [0, 4, 0, 2, -2, 0], [0, -4, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0], [2, -6, 0, -1, 1, 2], [0, 0, 2, -2, -2, -2], [0, 0, 0, 0, 0, 0], [0, -4, 2, -2, 2, 2], [2, 0, -2, -1, -1, 2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 8, -4, 0, 0, -4], [0, 0, 0, 0, 0, 0], [-8, 0, 1, 1, 1, -1], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, -2, 0, -3, 3, 0], [0, 0, 0, 0, 0, 0], [2, 4, 0, -1, -3, 2], [4, 0, -1, -1, -1, 1], [0, 0, 0, 0, 0, 0], [0, -2, 1, -1, 1, 1], [0, 0, 2, -1, -1, -2], [0, 0, 0, 0, 0, 0], [-12, 0, 2, -4, -4, -2], [0, 2, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0], [2, 0, -2, 1, 1, 2], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 3, -3, 3, 3], [0, -5, 2, -2, 2, 2], [0, 0, 0, 0, 0, 0], [1, 2, -1, 2, 0, 1]]}