# Stored data for newform 5733.2.a.br, downloaded from the LMFDB on 25 April 2024.
{"label": "5733.2.a.br", "space_label": "5733.2.a", "level": 5733, "weight": 2, "hecke_orbit": 44, "hecke_orbit_code": 193654784010491493, "dim": 6, "is_polredabs": true, "nf_label": "6.6.4507648.1", "trace_hash": 788084478434442333, "analytic_rank": 1, "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.559", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "81.350", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__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]]}