# Stored data for newform 1386.2.r.c, downloaded from the LMFDB on 17 January 2021.
{"level_primes": [2, 3, 7, 11], "is_polredabs": true, "sato_tate_group": "1.2.3.c6", "rm_discs": [], "conrey_indexes": [89, 1277], "cm_discs": [], "trace_hash": 378294884957750613, "level_radical": 462, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 7, "is_cm": false, "hecke_orbit": 3, "analytic_conductor": 11.06726572014946, "inner_twist_count": 2, "field_disc_factorization": [[2, 16], [3, 4]], "is_rm": false, "char_order": 6, "level_is_square": false, "weight_parity": 1, "label": "1386.2.r.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "1386.2.r.a", "field_poly_is_cyclotomic": true, "dim": 8, "trace_zratio": {"__RealLiteral__": 0, "data": "0.200", "prec": 17}, "traces": [0, 8, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 24, 16, 0, 8, 24, 0, -4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 16, 0, 12, -8, 0, 0, 16, 0, -32, 0, 0, 8, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, -4, 16, 0, 0, 24, 0, -8, -12, 0, -24, 4, 0, -20, 0, 0, -24, -12, 0, 0, 0, 0, 40, 8, 0, 12, 72, 0, -32, -24, 0, 4, -16, 0, 36, 0, 0, 0, 24, 0, 0, 8, 0, 4, -24, 0, 36, 0, 0, -32, -48, 0, -32, 8, 0, 0, 0, 0, 60, 36, 0, 0, 32, 0, 4, 8, 0, 12, 0, 0, -16, 0, 0, 12, 40, 0, -72, 0, 0, -24, -48, 0, 0, 20, 0, 8, 0, 0, -72, -48, 0, 24, -12, 0, 8, 8, 0, 0, 0, 0, -48, -24, 0, 0, 4, 0, 28, 8, 0, 24, 32, 0, 56, 72, 0, -16, -20, 0, -16, 0, 0, -24, -48, 0, 0, -12, 0, -8, -32, 0, 24, 0, 0, -32, -24, 0, 0, 4, 0, 0, 0, 0, -24, -12, 0, 0, -40, 0, 32, -36, 0, 0, -16, 0, -80, 48, 0, 12, -76, 0, -8, 0, 0, 0, -48, 0, 0, 0, 0, -32, 8, 0, 84, 16, 0, -8, 0, 0, 32, -16, 0, 8, 0, 0, -72, 0, 0, 0, 0, 0, 24, 12, 0, 72, -64, 0, 16, -72, 0, -4, 16, 0, -56, 0, 0, 0, -12, 0, 0, -72, 0, 24, 56, 0, 72, 8, 0, -64, 12, 0, -8, -8, 0, -4, 0, 0, 0, -72, 0, 0, 16, 0, -16, 0, 0, -24, -104, 0, 72, -12, 0, -20, 12, 0, -116, 0, 0, -24, 72, 0, 0, 0, 0, 32, 24, 0, 24, -96, 0, 80, 72, 0, 4, -8, 0, -4, 0, 0, -48, 48, 0, 0, -88, 0, -12, 36, 0, 0, -128, 0, -48, 0, 0, -16, 12, 0, 0, 0, 0, -12, -36, 0, 0, -64, 0, -4, 40, 0, 132, -32, 0, 32, -108, 0, 84, 4, 0, 24, 0, 0, 0, -24, 0, 0, 24, 0, 40, -4, 0, 0, 48, 0, 104, 24, 0, 56, 8, 0, -16, 0, 0, -48, 72, 0, 0, 52, 0, 24, -88, 0, 12, -48, 0, 8, 24, 0, 24, 24, 0, -8, 0, 0, -72, -24, 0, 0, -16, 0, 24, 0, 0, 24, -16, 0, -48, -48, 0, -16, -60, 0, 136, 0, 0, 12, -24, 0, 0, 32, 0, 32, 32, 0, -48, 16, 0, 0, -48, 0, 84, 20, 0, 0, 0, 0, 12, -24, 0, 0, 24, 0, -16, -28, 0, 60, 0, 0, -32, 36, 0, -36, -16, 0, -8, 0, 0, -24, -24, 0, 0, 40, 0, 52, -40, 0, 96, 16, 0, 8, 96, 0, -12, -8, 0, -88, 0, 0, -12, 72, 0, 0, 76, 0, -16, 0, 0, -24, 24, 0, -160, 24, 0, -8, 24, 0, -56, 0, 0, 24, 48, 0, 0, 16, 0, -12, -80, 0, 24, 80, 0, 8, 108, 0, -20, -44, 0, -48, 0, 0, -120, 36, 0, 0, -44, 0, 32, 8, 0, -24, -96, 0, 128, -48, 0, -4, 32, 0, 16, 0, 0, 0, -24, 0, 0, 4, 0, 48, 32, 0, -24, 144, 0, 16, -48, 0, 24, 0, 0, -80, 0, 0, -120, 48, 0, 0, -120, 0, -16, -24, 0, 12, 96, 0, -96, 36, 0, 12, 16, 0, -84, 0, 0, -12, -24, 0, 0, 4, 0, -8, -8, 0, -72, 16, 0, -8, 84, 0, 32, -32, 0, 0, 0, 0, 48, 24, 0, 0, -68, 0, -24, 16, 0, -48, 56, 0, 24, -24, 0, 32, -4, 0, 0, 0, 0, 0, 24, 0, 0, -16, 0, -8, 96, 0, 24, 96, 0, 56, 48, 0, -104, -8, 0, 92, 0, 0, -204, 48, 0, 0, 64, 0, 56, 16, 0, -48, 16, 0, -128, -24, 0, 28, 80, 0, 80, 0, 0, 12, 96, 0, 0, 0, 0, 16, -24, 0, 216, -40, 0, -176, 0, 0, -48, 64, 0, 64, 0, 0, -144, 0, 0, 0, 56, 0, -12, 4, 0, -24, 80, 0, 24, -48, 0, -4, 80, 0, -72, 0, 0, -36, -48, 0, 0, -36, 0, -28, 0, 0, -24, -112, 0, -16, -36, 0, -8, 32, 0, -36, 0, 0, 24, -96, 0, 0, -8, 0, 88, 0, 0, 24, 88, 0, 48, 48, 0, -16, 20, 0, -100, 0, 0, 72, 24, 0, 0, 16, 0, 0, 80, 0, 24, 8, 0, 0, 120, 0, -8, -48, 0, 0, 0, 0, 48, 48, 0, 0, 96, 0, -12, -12, 0, -24, 64, 0, 112, -12, 0, -16, -24, 0, 72, 0, 0, 0, 72, 0, 0, -8, 0, 12, -48, 0, 120, -48, 0, 64, 36, 0, 64, 36, 0, -4, 0, 0, 84, 120, 0, 0, 120, 0, 0, -8, 0, 24, -64, 0, -56, 72, 0, -40, 56, 0, 0, 0, 0, 132, 24, 0, 0, 116, 0, -12, 112, 0, 12, -152, 0, 0, -144, 0, 112, -16, 0, 32, 0, 0, -24, -24, 0, 0, -104, 0, 64, -48, 0, 0, -64, 0, -32, -48, 0, 0, -4, 0, 48, 0, 0, 12, 24, 0, 0, 0, 0, 0, -56, 0, -192, 16, 0, -64, 72, 0, -48, -8, 0, 48, 0, 0, 24, -144, 0, 0, 120, 0, 88, 8, 0, 48, -96, 0, -112, -72, 0, -4, -80, 0, -16, 0, 0, -24, 72, 0, 0, -32, 0, -32, -24, 0, 120, -32, 0, -32, 48, 0, 24, -32, 0, -32, 0, 0, -60, 12, 0, 0, -40, 0, -44, 48, 0, -72, 56, 0, -96, 0, 0, 8, -56, 0, 120, 0, 0, 0, 72, 0, 0, 0, 0, 36, 24, 0, -24, 184, 0, 48, -204, 0, 28, -12, 0, -4, 0, 0, 168, -48, 0, 0, 24, 0, -16, -32, 0, 180, 304, 0, 240, 72, 0, 8, 96, 0, -140, 0, 0, -24, -108, 0, 0, 44, 0, 4, -60, 0, -12, 32, 0, -144, 24, 0, -128, 0, 0, 56, 0, 0, 48, 12, 0, 0, 144, 0, -16, -24, 0, 0, 16, 0, 32, -12, 0, 28, -92, 0, -76, 0, 0, 108, -144, 0, 0, -48, 0, 0, -4, 0, -72, 80, 0, 48, -264, 0, 168, -56, 0, 0, 0, 0, -60, -120, 0, 0, -116, 0, -32, 4, 0, -12, 120, 0, -160, -48, 0, -32, -48, 0, 120, 0, 0, -192, -240, 0, 0, -20, 0, 8, -104, 0, 0, -16, 0, -48, -96, 0, -136, 72, 0, 16, 0, 0, 288, -60, 0, 0, 16, 0, -24, 112, 0, 0, -72, 0, -64, -72, 0, -48, 32, 0, 8, 0, 0, 0, 192, 0, 0, -64, 0, -48, 28, 0, -24, 24, 0, -32, 24, 0, -184, 0, 0, 24, 0, 0, 72, 48, 0, 0, -104, 0, -20, -52, 0, -144, 256, 0, 24, -48, 0, 36, -104, 0, 0, 0, 0, 48, -144, 0, 0, 132, 0, 20, -96, 0, -96, 24, 0, 144, 24, 0, 72, 32, 0, -40, 0, 0, 24, 24, 0, 0, -120, 0, -36, 56, 0, -24, -256, 0, 152, 72, 0, -36, -20, 0, 60, 0, 0, 0, -408, 0, 0, 0, 0, -16, -96, 0, 48, 56, 0, 64, -72, 0, 32, -24, 0, 112, 0, 0, 48, 156, 0, 0, 8, 0, 32, -48, 0, 180, -208, 0, -96, 36, 0, 40, 8, 0, 80, 0, 0, -144, -36, 0, 0, 0, 0, -4, 48, 0, -180, -16, 0, 16, 36, 0, -12, 48, 0, 16, 0, 0, 120, 120, 0, 0, -224, 0, -48, 16, 0, -48, -96, 0, -16, 48, 0, -8, 24, 0, 40, 0, 0, -12, -120, 0, 0, -68, 0, 44, -4, 0, 48, 8, 0, -24, -144, 0, -16, -36, 0, -136, 0, 0, -144, 48, 0, 0, 108, 0, 24, -64, 0, 0, -192, 0, 168, 24, 0, -24, -88, 0, -40, 0, 0, 24, 228, 0, 0, 16, 0, 16, 108, 0, -48, 24, 0, 32, 120, 0, -124, -48, 0, 0, 0, 0, 72, 24, 0, 0, 64, 0, 72, -4, 0, -12, 56, 0, 48, -36, 0, 40, -24, 0, -176, 0, 0, -120, -72, 0, 0, -80, 0, -16, 36, 0, 72, -384, 0, -8, 24, 0, 60, -40, 0, -16, 0, 0, 132, -84, 0, 0, 52, 0, -32, -16, 0, 96, 32, 0, 64, -12, 0, 16, 96, 0, 156, 0, 0, 96, 168, 0, 0, -72, 0, -84, 144, 0, -168, 8, 0, 16, -24, 0, -24, -36, 0, -12, 0, 0, -96, -84, 0, 0, -24, 0, -88, 32, 0, 0, -144, 0, -288, -24, 0, -24, 8, 0, 12, 0, 0, 0, -12, 0, 0, -12, 0, -36, 40, 0, 24, -80, 0, 80, 168, 0, -24, 4, 0, 8, 0, 0, 264, 24, 0, 0, -144, 0, -32, 24, 0, -120, -160, 0, -32, -48, 0, 52, -116, 0, -132, 0, 0, 72, -72, 0, 0, -40, 0, -56, 8, 0, -48, 16, 0, 0, 60, 0, -136, -72, 0, -20, 0, 0, -132, -120, 0, 0, -120, 0, 36, -32, 0, -48, -32, 0, 80, 72, 0, 104, 144, 0, 56, 0, 0, 0, 120, 0, 0, 44, 0, -144, 8, 0, 0, 0, 0, 48, 312, 0, 72, 88, 0, -96, 0, 0, 252, -156, 0, 0, -24, 0, -104, -24, 0, -72, 0, 0, 32, -72, 0, 4, -24, 0, -24, 0, 0, -24, 168, 0, 0, -48, 0, -24, -144, 0, -312, 48, 0, -8, -120, 0, -92, 88, 0, 32, 0, 0, 0, -12, 0, 0, 120, 0, -108, 8, 0, -72, 80, 0, -40, -24, 0, -36, -24, 0, -40, 0, 0, -36, -24, 0, 0, -20, 0, -16, -8, 0, -24, -72, 0, 48, -24, 0, -56, 0, 0, -52, 0, 0, -72, 24, 0, 0, 56, 0, -52, -8, 0, 48, -232, 0, -16, 24, 0, -24, 24, 0, -40, 0, 0, 0, 216, 0, 0, 0, 0, 16, 48, 0, -48, -120, 0, -16, -144, 0, -32, -16, 0, 44, 0, 0, 96, 48, 0, 0, 80, 0, -104, -16, 0, 12, 368, 0, 80, -24, 0, -16, -48, 0, 144, 0, 0, 36, -36, 0, 0, 40, 0, 40, -40, 0, -216, 48, 0, 64, 276, 0, 48, -32, 0, 40, 0, 0, 288, 120, 0, 0, 192, 0, 24, 8, 0, 24, -240, 0, 168, 132, 0, 0, 56, 0, -20, 0, 0, -12, 48, 0, 0, 48, 0, -84, 24, 0, -180, 40, 0, -96, -96, 0, 16, 36, 0, 0, 0, 0, -144, -24, 0, 0, -4, 0, 48, 112, 0, 12, 144, 0, -144, -24, 0, 8, 24, 0, 96, 0, 0, 60, 204, 0, 0, 72, 0, -56, -76, 0, 96, 72, 0, -32, 96, 0, -12, 28, 0, -96, 0, 0, 0, -120, 0, 0, -176, 0, -8, 0, 0, -24, 40, 0, 376, -48, 0, -16, 8, 0, 184, 0, 0, 0, 0, 0, 0, 120, 0, 36, -60, 0, -120, -32, 0, -32, -24, 0, 96, -40, 0, 32, 0, 0, -84, 60, 0, 0, -140, 0, 0, 24, 0, -24, -96, 0, 176, -24, 0, 88, 88, 0, 12, 0, 0, -48, 96, 0, 0, 8, 0, 28, 72, 0, 192, 296, 0, 104, 36, 0, -52, 40, 0, 40, 0, 0, -312, 120, 0, 0, 16, 0, -112, 8, 0, 180, -48, 0, 48, -96, 0, 4, -48, 0, 112, 0, 0, 288, -180, 0, 0, 24, 0, 12, 16, 0, 24, -16, 0, 32, -60, 0, 240, -16, 0, 16, 0, 0, 132, -48, 0, 0, 144, 0, 16, -64, 0, -12, 80, 0, -192, 72, 0, -36, -28, 0, 80, 0, 0, -12, 48, 0, 0, 32, 0, 32, -4, 0, -24, 112, 0, -32, -84, 0, -8, 0], "hecke_ring_index_factorization": [], "nf_label": "8.0.5308416.1", "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "has_non_self_twist": 1, "char_values": [1386, 6, [155, 199, 1135], [3, 5, 6]], "Nk2": 5544, "field_poly_root_of_unity": 24, "analytic_rank": 0, "char_orbit_label": "r", "weight": 2, "trace_display": [0, 0, 8, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-\\zeta_{24}^{2}q^{2}+\\zeta_{24}^{4}q^{4}+(2+\\zeta_{24}-2\\zeta_{24}^{4}+\\cdots)q^{5}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 5308416, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[5, [1, -16, 236, -304, 271, -128, 44, -8, 1]]], "space_label": "1386.2.r", "level": 1386, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 21, 7, 1, 6, 0]], "char_degree": 2, "char_conductor": 21, "char_orbit_index": 18, "hecke_ring_generator_nbound": 5, "hecke_orbit_code": 9008367519401322, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.632", "prec": 17}, {"__RealLiteral__": 0, "data": "0.342", "prec": 17}, {"__RealLiteral__": 0, "data": "246.778", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14165.122", "prec": 30}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [2, 1, 0, 0, -2, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, -1, 0, 1, 2, 1], [0, 0, -1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, -1, 0, -2], [0, 0, 0, -2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, -2, -2, 0, -1, 0, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, -2, 2, -4, 0, 4], [2, 1, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [2, 1, -2, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -4, -1, -4, -1, 0], [0, -2, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 3, 0, 0], [3, 2, 0, -2, -6, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -3, -2, -1, 2, 3, 0], [0, 0, 1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, 2, 4, 2, 1, 0], [3, 6, 3, 0, -2, -4, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 4, 1, -6, -3, 2, -2, 2], [0, 4, -2, -2, -2, -2, -2, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, -1, 0, 0, 0, 0], [2, 4, -2, 4, 0, -4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -5, 4, -5, 0, -1, -2, 6], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, -1, 2, -1, -2, 0], [0, -3, 0, -2, 0, 5, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 5, 0], [-1, 0, 0, 0, 2, 4, 1, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 2, 0, -2, 0, -1], [8, 1, 4, 2, -4, -2, -4, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 1], [0, 0, 0, 1, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, -3, -2, 1, 0, 6, 0], [0, 1, -2, 0, 4, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, 6, 0, 7, 0, -7], [3, 0, -2, 0, 0, 2, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [-1, -4, -3, -2, -1, 2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, -2, -6, -2, 3, 0], [1, 0, 2, 2, -1, -2, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -3, -6, -1, 0, 2, 4], [-6, -3, 0, 3, 12, -1, 2, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -3, 6, -2, 2, 2, -6, 3], [-2, 2, -3, -4, 1, 4, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 0, -4, 4, -2, 2, 2], [0, 0, 0, -3, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [10, 1, 2, 0, -10, -1, -4, -1], [0, 0, 0, 1, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, -4, 1, -4, 0, 4], [9, -6, -4, -6, 0, 0, 2, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -9, -12, -9, 0, 6, 6, 3], [-2, 6, 4, 5, -2, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-4, -8, 2, 3, 4, 5, -4, 5], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -1, 0, -1, 0, -4, 0], [-2, 0, 0, 0, 4, 1, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 3, 0, -3, 0, -5], [4, 2, 4, 8, -2, -8, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, 0, 4, 8, 0, 1, -4], [5, 0, 0, 0, -8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 1, 0, -1, -4, -2, -4]]}