# Stored data for newform 5733.2.a.bu, downloaded from the LMFDB on 29 March 2024. {"label": "5733.2.a.bu", "space_label": "5733.2.a", "level": 5733, "weight": 2, "hecke_orbit": 47, "hecke_orbit_code": 207165582892602981, "dim": 6, "is_polredabs": true, "nf_label": "6.6.4507648.1", "trace_hash": 2214835180205047833, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-2, -4, 14, 0, -8, 0, 1]], [5, [31, -26, -31, 24, 5, -6, 1]], [11, [-562, 692, 186, -156, -38, 4, 1]], [17, [-5294, 6792, -2792, 324, 56, -16, 1]], [19, [-73, 6, 83, -16, -17, 2, 1]], [31, [-44249, 10046, 4181, -508, -115, 6, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(1-\\beta _{1}-\\beta _{3}+\\beta _{4})q^{4}+(1+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 22932, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 45.77823547880004, "hecke_ring_index": 1, "level_radical": 273, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [5733, 1, [2549, 1522, 5293], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [3, 7, 13], "conrey_indexes": [1], "field_disc": 4507648, "field_disc_factorization": [[2, 11], [31, 1], [71, 1]], "field_poly": [-1, -6, 7, 8, -5, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.108", "prec": 17}, {"__RealLiteral__": 0, "data": "5.559", "prec": 17}, {"__RealLiteral__": 0, "data": "2.177", "prec": 17}, {"__RealLiteral__": 0, "data": "81.350", "prec": 20}, {"__RealLiteral__": 0, "data": "63.735", "prec": 20}, {"__RealLiteral__": 0, "data": "1796.535", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, 1], [13, 1]], "trace_display": [0, 0, 6, 0], "traces": [0, 6, 0, 0, 4, 6, 0, 0, 0, 0, -4, -4, 0, -6, 0, 0, 0, 16, 0, -2, 16, 0, -12, 6, 0, -4, 0, 0, 0, 6, 0, -6, 20, 0, 0, 0, 0, 0, 8, 0, -4, -8, 0, 2, 4, 0, 8, 30, 0, 0, -8, 0, -4, 14, 0, 8, 0, 0, -8, 24, 0, 0, 28, 0, -20, -6, 0, 16, 28, 0, 0, -8, 0, 6, 12, 0, 16, 0, 0, -22, -28, 0, 40, 50, 0, -8, 16, 0, -44, 26, 0, 0, -20, 0, 32, 6, 0, 14, 0, 0, -8, -4, 0, -16, 0, 0, 56, 8, 0, 8, -20, 0, 0, 30, 0, 2, 44, 0, 4, 0, 0, 26, -20, 0, 44, -6, 0, -28, -16, 0, 4, 32, 0, 0, 4, 0, 52, -4, 0, 20, 0, 0, -28, 4, 0, 38, -16, 0, 4, 0, 0, 28, -4, 0, 0, 46, 0, -4, -52, 0, 40, 0, 0, -20, 4, 0, -4, 42, 0, 6, -36, 0, 68, 0, 0, 0, -28, 0, 16, 38, 0, 56, 0, 0, 20, 4, 0, -56, 48, 0, 16, 36, 0, -20, -48, 0, 0, -8, 0, -20, -28, 0, -8, 0, 0, -24, -44, 0, 0, 36, 0, 10, 20, 0, -96, 34, 0, 0, 32, 0, -4, -16, 0, 10, 0, 0, -20, 56, 0, 40, 24, 0, 16, -18, 0, 14, 68, 0, 0, -28, 0, 6, -64, 0, -24, 0, 0, 2, 36, 0, 24, 84, 0, -88, 32, 0, -24, -8, 0, 0, -16, 0, -56, -14, 0, 18, 0, 0, 16, -4, 0, 44, 40, 0, -8, 20, 0, -14, 52, 0, 0, -48, 0, -56, -88, 0, 12, 0, 0, 42, -12, 0, -8, 2, 0, 36, -28, 0, -88, -6, 0, 0, -48, 0, 8, 56, 0, -34, 0, 0, 52, 48, 0, -32, 20, 0, 16, -32, 0, 12, -4, 0, 0, -24, 0, 4, -28, 0, 8, 0, 0, 44, 32, 0, 16, 20, 0, 6, 0, 0, 84, -24, 0, 0, 80, 0, -148, 16, 0, 38, 0, 0, 52, 36, 0, -64, 76, 0, -32, -84, 0, -76, 24, 0, 0, 6, 0, 84, 4, 0, 44, 0, 0, -60, -52, 0, -4, -6, 0, 28, -4, 0, -16, 68, 0, 0, -40, 0, 4, 0, 0, 20, 0, 0, -12, 54, 0, 50, 52, 0, -52, -4, 0, 6, -36, 0, 0, 60, 0, 18, 36, 0, -64, 0, 0, 86, -20, 0, -80, 80, 0, -28, 28, 0, 28, -76, 0, 0, 80, 0, -12, -76, 0, 4, 0, 0, -20, -46, 0, 48, -40, 0, 0, 42, 0, 82, 76, 0, 0, 20, 0, 24, 80, 0, -56, 0, 0, -32, 100, 0, -12, -32, 0, 72, -24, 0, 88, 68, 0, 0, 32, 0, 8, -60, 0, 0, 0, 0, 20, -50, 0, 0, -60, 0, 52, 46, 0, 12, -12, 0, 0, 68, 0, 0, -8, 0, -36, 0, 0, -12, -116, 0, 12, 56, 0, -4, 112, 0, -24, 22, 0, 0, -104, 0, 104, -52, 0, 60, 0, 0, 4, 16, 0, 40, -96, 0, -44, -52, 0, -28, 104, 0, 0, 8, 0, 84, -56, 0, 120, 0, 0, 8, 0, 0, 28, -8, 0, -14, 36, 0, 52, 30, 0, 0, -68, 0, -60, 60, 0, -2, 0, 0, 104, 84, 0, 110, -92, 0, 0, -38, 0, -14, -4, 0, 0, 12, 0, 76, 124, 0, 32, 0, 0, -48, -108, 0, -40, 86, 0, 30, -20, 0, 28, -46, 0, 0, -56, 0, -8, 58, 0, 20, 0, 0, -52, -2, 0, -16, 0, 0, 12, -30, 0, 8, -84, 0, 0, -12, 0, 84, -48, 0, 48, 0, 0, -66, -80, 0, -140, -64, 0, 20, -48, 0, 16, -72, 0, 0, -108, 0, 0, -26, 0, -32, 0, 0, 52, 4, 0, 60, 8, 0, 112, 12, 0, 32, 32, 0, 0, 18, 0, 30, 112, 0, 12, 0, 0, -18, 16, 0, -20, -80, 0, -10, -164, 0, 4, -68, 0, 0, 100, 0, 0, -24, 0, 92, 0, 0, -24, -14, 0, 14, -28, 0, -76, -24, 0, 12, 24, 0, 0, 90, 0, 64, 8, 0, -172, 0, 0, -28, -64, 0, 60, 26, 0, -8, -60, 0, -8, 0, 0, 0, -36, 0, -44, 20, 0, -4, 0, 0, -16, 80, 0, -38, -72, 0, -36, 108, 0, 4, -12, 0, 0, 8, 0, -28, 56, 0, -56, 0, 0, -18, 80, 0, 8, -4, 0, -42, 36, 0, -24, -62, 0, 0, 0, 0, -104, -24, 0, -2, 0, 0, -112, 4, 0, 60, -92, 0, -12, 20, 0, -104, -36, 0, 0, -124, 0, -74, 28, 0, -92, 0, 0, 0, -56, 0, -132, 68, 0, 72, 16, 0, 68, 188, 0, 0, -28, 0, -20, 98, 0, -56, 0, 0, -136, 8, 0, -6, -32, 0, -36, 56, 0, 48, -16, 0, 0, -28, 0, 40, -8, 0, 20, 0, 0, 66, 4, 0, 88, 36, 0, -72, -32, 0, 40, 6, 0, 0, 60, 0, -124, -60, 0, -94, 0, 0, 28, -8, 0, -28, 24, 0, 112, -104, 0, -60, 12, 0, 0, 96, 0, -16, -60, 0, 84, 0, 0, -40, 56, 0, 24, -72, 0, 64, -28, 0, 40, -32, 0, 0, 12, 0, 36, 86, 0, -58, 0, 0, 28, 74, 0, 4, 20, 0, -12, -12, 0, -62, -48, 0, 0, -14, 0, -96, 116, 0, 20, 0, 0, -60, -4, 0, -160, 8, 0, 4, 64, 0, 28, -146, 0, 0, -4, 0, -28, -28, 0, -112, 0, 0, 92, 54, 0, -52, 20, 0, -4, 56, 0, -6, 4, 0, 0, -26, 0, 40, -4, 0, -84, 0, 0, 80, -12, 0, 236, -36, 0, -92, 44, 0, -132, 16, 0, 0, 144, 0, -104, 76, 0, -76, 0, 0, 124, 62, 0, -56, 0, 0, -16, 26, 0, -68, -16, 0, 0, -188, 0, 32, -200, 0, -44, 0, 0, 68, -4, 0, 12, 42, 0, -84, -12, 0, -64, -16, 0, 0, 156, 0, -64, -80, 0, 20, 0, 0, 24, -36, 0, 22, -132, 0, -36, 50, 0, 48, -296, 0, 0, -100, 0, 128, 28, 0, 20, 0, 0, 44, 80, 0, -168, 44, 0, -32, 16, 0, 72, -102, 0, 0, -124, 0, -12, -24, 0, 116, 0, 0, -40, 132, 0, -164, -172, 0, -16, 48, 0, -4, 32, 0, 0, -50, 0, -94, -12, 0, -32, 0, 0, -52, -168, 0, 56, 4, 0, -28, 124, 0, -124, 106, 0, 0, 20, 0, 0, -20, 0, 8, 0, 0, -88, 64, 0, -24, -60, 0, 76, 62, 0, -26, -16, 0, 0, 68, 0, -66, -64, 0, -52, 0, 0, -120, -80, 0, 8, -28, 0, 0, -12, 0, -44, -4, 0, 0, -16, 0, 44, 36, 0, -12, 0, 0, -4, -18, 0, 8, -96, 0, 88, -26, 0, -60, -44, 0, 0, -72, 0, -66, -80, 0, -8, 0, 0, -90, -136, 0, -44, -80, 0, 12, 92, 0, 100, -42, 0, 0, -20, 0, 140, -54, 0, -88, 0, 0, 16, 12, 0, -12, 20, 0, -24, 80, 0, 56, -180, 0, 0, 58, 0, 76, -12, 0, -120, 0, 0, 38, -36, 0, -12, -34, 0, 46, -60, 0, -32, 100, 0, 0, 128, 0, -76, -12, 0, 76, 0, 0, -120, -6, 0, -102, -160, 0, -12, -96, 0, 44, -4, 0, 0, 50, 0, -88, 108, 0, -20, 0, 0, 72, -112, 0, 36, -6, 0, -14, -136, 0, -176, -60, 0, 0, -52, 0, 92, 72, 0, 44, 0, 0, 44, 80, 0, 54, -24, 0, -160, -14, 0, -68, -88, 0, 0, 144, 0, -32, 80, 0, 64, 0, 0, -66, -264, 0, 8, 8, 0, -12, 64, 0, 84, 136, 0, 0, -56, 0, 8, 4, 0, 94, 0, 0, -16, -94, 0, -170, -180, 0, -44, -12, 0, -50, -44, 0, 0, 36, 0, 214, 96, 0, -52, 0, 0, 16, 40, 0, 208, -128, 0, -32, 16, 0, -32, -148, 0, 0, 0, 0, 12, 52, 0, -92, 0, 0, -28, -136, 0, 62, -276, 0, -56, 100, 0, -58, 32, 0, 0, -68, 0, -52, 28, 0, -56, 0, 0, 10, -120, 0, -68, -2, 0, 86, -68, 0, 104, -8, 0, 0, 196, 0, 160, -260, 0, 72, 0, 0, 76, 160, 0, -52, -96, 0, 112, -148, 0, 80, -20, 0, 0, -60, 0, -8, -124, 0, -20, 0, 0, 116, -40, 0, -40, 140, 0, 94, 20, 0, -32, 28, 0, 0, -168, 0, -76, 14, 0, 80, 0, 0, -36, 58, 0, -4, 24, 0, -8, -116, 0, 104, 8, 0, 0, -50, 0, 44, 20, 0, 152, 0, 0, -14, -188, 0, 164, -30, 0, 0, 52, 0, -112, -44, 0, 0, -92, 0, -104, -88, 0, -116, 0, 0, -32, 46, 0, -160, -132, 0, 16, 132, 0, -2, -192, 0, 0, 86, 0, -14, 0, 0, 80, 0, 0, 232, -44, 0, -120, -180, 0, 60, -28, 0, -72, -48, 0, 0, 56, 0, 100, 52, 0, 136, 0, 0, -92, 4, 0, -120, 8, 0, -4, -38, 0, 38, 60, 0, 0, -104, 0, 4, -184, 0, -48, 0, 0, 64, -44, 0, -144, 54, 0, 76, -84, 0, 28, -52, 0, 0, 356, 0, -20, -44, 0, -70, 0, 0, 72, 62, 0, -26, 212, 0, 28, -38, 0, 64, -52, 0, 0, -122, 0, 52, 20, 0, -164, 0, 0, -128, -16, 0, 180, 64, 0, -72, 228, 0, 96, -4, 0, 0, -52, 0, -200, 68, 0, -128, 0, 0, -44, -48, 0, -24, -40, 0, 4, 32, 0, 110, -104, 0, 0, 6, 0, 64, 136, 0, -140, 0, 0, 128, 144, 0, -88, 88, 0, -116, 112, 0, 140, 130, 0, 0, -52, 0, 16, -12, 0, 28, 0, 0, -44, -24, 0, 50, -96, 0, 100, -104, 0, 202, 16, 0, 0, 50, 0, -154, -24, 0, -28, 0, 0, -8, -36, 0, -72, -174, 0, 58, -16, 0, -4, 110, 0, 0, 116, 0, -4, 6, 0, -104, 0, 0, -36, 72, 0, 80, -48, 0, 184, -32, 0, -148, 12, 0, 0, -8, 0, 104, -148, 0, -196, 0, 0, -24, -28, 0, 124, -34, 0, -112, 4, 0, 128, 72, 0, 0, -288, 0, 24, -12, 0, -44, 0, 0, 128, 184, 0, -4, -4, 0, 36, 62, 0, -116, -40, 0, 0, -20, 0, 68, -20, 0, 184, 0, 0, -18, 4, 0, -144, 128, 0, 152, -80, 0, -52, 56, 0, 0, 236, 0, 156, -24, 0, -160, 0, 0, 56, 4, 0, 136, 84, 0, -76, -56, 0, 8, -124, 0, 0, 108, 0, -152, 208, 0, 172, 0, 0, -72, 188, 0, -320, -60, 0, -20, -140, 0, -28, 20, 0, 0, 120, 0, -104, -58, 0, 44, 0, 0, 12, -60, 0, 8, -20, 0, -112, 0, 0, -96, 56, 0, 0, 220, 0, 28, -100, 0, -80, 0, 0, -30, 32, 0, 28, -128, 0, 68, 68, 0, 188, -52, 0, 0, -84, 0, -116, -4, 0, 2, 0, 0, -8, -16, 0, 140, 188, 0, -64, 74, 0, -18, 84, 0, 0, -256, 0, 84, -48, 0, 28, 0, 0, -38, -72, 0, 104, 168, 0, 144, -356, 0, 44, -28, 0, 0, 16, 0, -72, 190, 0, 140, 0, 0, -40, 208, 0, 150, 28, 0, 4, 68, 0, 28, -16, 0, 0, -52, 0, 28, 112, 0, -4, 0, 0, 44, 180, 0, -72, -90, 0, -218, -172, 0, 52, 0, 0, 0, 48, 0, -116, -8, 0, 16, 0, 0, -24, 52, 0, 140, -16, 0, -100, -52, 0, -52, -68, 0, 0, 92, 0, -28, 76, 0, -232, 0, 0, -36, -48, 0, 196, 112, 0, 136, 4, 0, -120, 76, 0, 0, -204, 0, 108, 98, 0, 82, 0, 0, 88, -180, 0, -176, -44, 0, -144, -84, 0, 142, 88, 0, 0, -166, 0, -204, 132, 0, -12, 0, 0, 2, 224, 0, 52, -46, 0, 104, 52, 0, -36, -70, 0, 0, 0, 0, -72, -84, 0, -40, 0, 0, 124, -28, 0, 176, 40, 0, 32, 4, 0, 4, 96, 0, 0, -38, 0, 82, 56, 0, -96, 0, 0, 86, 52, 0, -112, 180, 0, -200, -16, 0, -224, -76, 0, 0, -52, 0, 52, 8, 0, 52, 0, 0, -300, 40, 0, -36, 112, 0, -40, 36, 0, 54, 112, 0, 0, -160, 0, -172, -140, 0, 24, 0, 0, 84, -96, 0, -40, -30, 0, 108, -144, 0, 48, -76, 0, 0, 348, 0, -56, 8, 0, 42, 0, 0, -28, 22, 0, 20, -52, 0, -36, 200, 0, -20, 160, 0, 0, -18, 0, -28, -4, 0, 76, 0, 0, 216, -32, 0, 116, -148, 0, 160, 144, 0, -20, 2, 0, 0, -168, 0, 124, 96, 0, 48, 0, 0, 4, 84, 0, 140, 268, 0, 152, -164, 0, 64, -96, 0, 0, -42, 0, 52, 60, 0, -184, 0, 0, 76, -20, 0, -176, 116, 0, -50, 88, 0, -64, -24, 0, 0, -116, 0, -80, 84, 0, -6, 0, 0, 92, -176, 0, 2, 48, 0, 100, 176, 0, 188, 36, 0, 0, 80, 0, 118, -144, 0, 124, 0, 0, 8, 172, 0, 80, 36, 0, -104, -80, 0, 204, -90, 0, 0, -96, 0, -68, -162, 0, 64, 0, 0, -48, 82, 0, -16, 180, 0, 48, 0, 0, -40, 144, 0, 0, -196, 0, -72, -108, 0, 80, 0, 0, -154, 80, 0, 96, 190, 0, -116, -152, 0, -28, -8, 0, 0, -224, 0, 16, 50, 0, 88, 0, 0, 84, -136, 0, 88, 28, 0, 116, 34, 0, 36, 176, 0, 0, 64, 0, 6, 28, 0, 192, 0, 0, 32, -196, 0, 124, 44, 0, -24, 164, 0, -16, 184, 0, 0, 112, 0, -28, -60, 0, 56, 0, 0, 76, -38, 0, -268, 132, 0, -184, -44, 0, 88, 104, 0, 0, 64, 0, 172, 220, 0, -148, 0, 0, 156, -32, 0, -60, -238, 0, -56, -84, 0, -64, -64, 0, 0, -28, 0, 196, -28, 0, -240, 0, 0, -16, 40, 0, 146, -12, 0, -248, -58, 0, -108, 96, 0, 0, 104, 0, 24, -44, 0, 72, 0, 0, 60, 32, 0, -20, -120, 0, 74, 268, 0, -72, 14, 0, 0, 8, 0, 128, -4, 0, 114, 0, 0, -252, -18, 0, -72, -164, 0, -60, 24, 0, -12, 196, 0, 0, 68, 0, 60, -68, 0, 196, 0, 0, 56, 24, 0, -148, 76, 0, -44, 44, 0, -124, -56, 0, 0, -48, 0, -4, -54, 0, 146, 0, 0, -184, -168, 0, 36, 28, 0, -40, -44, 0, -8, -64, 0, 0, 56, 0, 36, 16, 0, -16, 0, 0, -142, 80, 0, 80, 202, 0, 60, 28, 0, -84, -36, 0, 0, -44, 0, -72, -56, 0, 202, 0, 0, 136, -112, 0, 56, 96, 0, -32, -208, 0, -164, -32, 0, 0, -68, 0, 20, -24, 0, 152, 0, 0, -16, 8, 0, 208, -148, 0, -102, 48, 0, 36, 36, 0, 0, 108, 0, 236, -8, 0, 88, 0, 0, -140, 16, 0, 56, -68, 0, -68, -116, 0, -66, -60, 0, 0, -138, 0, 60, -100, 0, -44, 0, 0, -62, 28, 0, -200, 8, 0, 92, 116, 0, -180, 148, 0, 0, 196, 0, 12, 66, 0, -8, 0, 0, 148, -112, 0, 138, 36, 0, 56, 196, 0, 20, -148, 0, 0, 220, 0, 148, 200, 0, 64, 0, 0, -14, 28, 0, 108, 144, 0, 36, 64, 0, -56, 32, 0, 0, 156, 0, -72, -68, 0, -96, 0, 0, 24, 22, 0, 40, 104, 0, 8, -272, 0, 24, -20, 0, 0, -4, 0, 52, 68, 0, -12, 0, 0, 16, -100, 0, -72, -24, 0, 52, 116, 0, -44, 48, 0, 0, 152, 0, 128, 88, 0, 158, 0, 0, -164, 14, 0, 24, 68, 0, -100, -52, 0, 192, -72, 0, 0, 72, 0, -116, 44, 0, -24, 0, 0, -124, 20, 0, -292, 60, 0, -44, 168, 0, 148, -190, 0, 0, -164, 0, 96, 140, 0, 216, 0, 0, 0, -72, 0, -168, -116, 0, 40, -64, 0, -150, 228, 0, 0, -36, 0, 168, 36, 0, 152, 0, 0, -12, -40, 0, -16, 168, 0, -210, 188, 0, 68, 26, 0, 0, -224, 0, -60, 32, 0, -10, 0, 0, -168, 128, 0, -154, 204, 0, -28, 118, 0, 22, -20, 0, 0, 234, 0, -140, 48, 0, 24, 0, 0, -152, -48, 0, -68, 108, 0, 324, -212, 0, -72, -18, 0, 0, -28, 0, 96, -46, 0, -8, 0, 0, 136, -162, 0, 92, 188, 0, 164, -34, 0, 44, 124, 0, 0, 112, 0, -158, 24, 0, -144, 0, 0, -48, 268, 0, 100, -50, 0, 148, -48, 0, 4, 74, 0, 0, -124, 0, -136, 80, 0, 36, 0, 0, -132, -144, 0, 124, -32, 0, 12, -98, 0, 48, 156, 0, 0, -18, 0, -82, -80, 0, 72, 0, 0, -76, 200, 0, 140, -42, 0, 82, -40, 0, 4, 92, 0, 0, 40, 0, -388, -292, 0, -160, 0, 0, -88, 16, 0, 82, -68, 0, 24, -212, 0, -32, 128, 0, 0, 196, 0, 112, 28, 0, 192, 0, 0, -144, 20, 0, 40, 28, 0, -10, -112, 0, 68, 112, 0, 0, -216, 0, 144, -10, 0, 48, 0, 0, 396, 4, 0, 100, 84, 0, -144, 212, 0, -124, 444, 0, 0, 72, 0, -68, 16, 0, 184, 0, 0, -14, -36, 0, 20, 184, 0, 132, -8, 0, -56, -70, 0, 0, 8, 0, -64, -56, 0, -156, 0, 0, 60, -54, 0, -148, 72, 0, 204, 58, 0, 70, -116, 0, 0, -168, 0, -126, -348, 0, -264, 0, 0, -40, 32, 0, 60, 32, 0, 8, 84, 0, 76, -40, 0, 0, -24, 0, -124, -20, 0, 106, 0, 0, -156, 224, 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": "637.2.a.m", "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, -1, 0, -1, 1, 0], [1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-1, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, -1, -1, 0], [3, -2, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 1, 1], [3, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 1, -1, 4, -2, -2], [0, 1, 0, 1, -1, -2], [0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, 1, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, -2, 2, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 2, 0, 3, -1], [4, -1, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [1, -3, 3, -3, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, 2, -2, 1, 2], [1, -1, 0, 1, 0, -2], [0, 0, 0, 0, 0, 0], [0, -3, -1, 0, -1, -1], [0, -3, 2, 2, 0, 1], [0, 0, 0, 0, 0, 0], [1, -4, 0, 0, 2, -2], [0, 4, -3, -2, -1, 2], [0, 0, 0, 0, 0, 0], [2, 1, 1, -3, 2, 3], [6, 0, 3, -3, 1, 3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 3, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, -1, 0], [2, 1, 4, -1, 1, 0], [0, 0, 0, 0, 0, 0], [1, 3, 0, -3, 0, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 0, 3, 0, 0, -2], [5, -1, 1, -3, 2, 2], [0, 0, 0, 0, 0, 0], [-2, 3, -1, 2, 1, -3], [5, 0, 3, -5, 3, 1], [0, 0, 0, 0, 0, 0], [-4, 2, 2, 4, 0, 0], [-1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [4, -1, 1, 1, 1, 3], [6, -5, 3, -4, 5, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, -1, -4, 5, -5, -3], [0, 0, 0, 0, 0, 0], [2, 2, 1, -1, 1, 5], [1, -1, -1, 4, 0, -4], [0, 0, 0, 0, 0, 0], [3, 0, 1, -3, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, -2, -3, 3, 3, 0], [-4, -1, 2, -2, 0, 1], [0, 0, 0, 0, 0, 0], [8, -3, -1, -3, 1, 1], [7, 2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0], [0, -6, -4, -2, 1, -2], [4, -2, 5, -8, 2, 2], [0, 0, 0, 0, 0, 0], [-8, 2, -1, 3, -1, 0], [4, -1, 1, -1, 3, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, -3, 1, 4, 0, -2], [0, 0, 0, 0, 0, 0], [5, -5, 4, 3, 0, -6], [1, 2, 2, -2, 0, 2], [0, 0, 0, 0, 0, 0], [4, -3, -3, 5, 1, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 2, -3, 3, -3, 0]]}