# Stored data for newform 105.2.q.a, downloaded from the LMFDB on 19 April 2024.
{"label": "105.2.q.a", "space_label": "105.2.q", "level": 105, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1099545182313, "dim": 16, "is_polredabs": true, "trace_hash": 1528467184164063477, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-\\beta _{5}+\\beta _{6}-\\beta _{15})q^{2}+\\beta _{3}q^{3}+(1+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "q", "char_is_real": false, "Nk2": 420, "analytic_conductor": 0.838429221223444, "hecke_ring_index": 4, "level_radical": 105, "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": "0.515", "prec": 17}, "analytic_rank_proved": true, "char_values": [105, 6, [71, 22, 31], [6, 3, 4]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [3, 5, 7], "conrey_indexes": [4, 79], "field_disc": 27814731656356152999936, "field_disc_factorization": [[2, 24], [3, 8], [709, 4]], "field_poly": [1, -8, 32, -188, 734, -800, 584, -630, 291, 64, -40, 38, -14, -4, 2, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.679", "prec": 20}, {"__RealLiteral__": 0, "data": "5.002", "prec": 17}, {"__RealLiteral__": 0, "data": "1862.512", "prec": 27}, {"__RealLiteral__": 0, "data": "6224.672", "prec": 27}, {"__RealLiteral__": 0, "data": "455617.854", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 2, 0], "traces": [0, 16, 0, 0, 8, 2, -8, 0, 0, 8, -4, 0, 0, 0, -24, -4, 0, 0, 0, -24, -8, -4, 0, 0, -12, -4, -12, 0, 0, 24, -12, 16, 0, 0, 16, -10, 16, 0, 0, -4, 32, 16, 0, 0, 20, -2, -32, 0, 0, -40, -40, 4, 0, 0, -4, 8, 84, 0, 0, 4, 16, 16, 0, 0, 16, 30, 28, 0, 0, 40, 16, -56, 0, 0, 40, 8, -64, 0, 0, -16, 52, -8, 0, 0, 12, -64, -48, 0, 0, 16, -8, 8, 0, 0, -32, -22, 8, 0, 0, 0, -32, -52, 0, 0, -136, 42, 16, 0, 0, -16, 24, -96, 0, 0, -16, -8, -36, 0, 0, -20, -24, 16, 0, 0, 32, 44, -36, 0, 0, -16, 60, -36, 0, 0, 72, -2, 56, 0, 0, 144, -96, 40, 0, 0, 0, -32, 192, 0, 0, -12, -48, 8, 0, 0, 56, 76, 68, 0, 0, -40, 48, 80, 0, 0, 36, 12, -48, 0, 0, -32, 48, 24, 0, 0, 40, 24, -64, 0, 0, 8, -4, -64, 0, 0, 24, -10, -20, 0, 0, 4, 56, -64, 0, 0, 4, 44, -152, 0, 0, -24, -48, 12, 0, 0, -120, -28, -176, 0, 0, -72, 28, 144, 0, 0, -16, -42, -24, 0, 0, -24, -48, 116, 0, 0, -24, -8, 32, 0, 0, 0, -160, -72, 0, 0, 12, 4, -28, 0, 0, -88, -44, 48, 0, 0, -32, -104, 72, 0, 0, 12, -52, 32, 0, 0, 36, -24, -16, 0, 0, 64, 160, 12, 0, 0, 24, -32, 196, 0, 0, 132, 12, 64, 0, 0, -208, 100, 92, 0, 0, 32, 0, -8, 0, 0, -60, -2, 32, 0, 0, -16, 108, -4, 0, 0, 104, -32, -116, 0, 0, 132, 96, -48, 0, 0, 40, 16, 8, 0, 0, 64, -44, -100, 0, 0, -48, 28, -48, 0, 0, -40, 32, -64, 0, 0, 8, -68, 80, 0, 0, -28, -16, 88, 0, 0, 16, -156, -160, 0, 0, -48, -64, 16, 0, 0, 104, -48, 32, 0, 0, -144, -48, -8, 0, 0, 4, 36, 392, 0, 0, -28, -32, 16, 0, 0, 176, 68, 76, 0, 0, 8, 136, 40, 0, 0, 12, -2, 48, 0, 0, 64, 32, 92, 0, 0, -16, 132, -352, 0, 0, -156, -64, -224, 0, 0, -128, 114, -20, 0, 0, 0, 0, -104, 0, 0, -84, -4, -128, 0, 0, 16, -80, 32, 0, 0, -64, 52, -112, 0, 0, 80, 68, -80, 0, 0, 112, -60, -120, 0, 0, -12, -44, 4, 0, 0, -140, -120, 160, 0, 0, -48, -152, -8, 0, 0, -60, 24, 16, 0, 0, 32, -20, 88, 0, 0, 0, -130, 104, 0, 0, -4, -56, 32, 0, 0, 184, -30, -24, 0, 0, -152, 8, 48, 0, 0, 56, 152, 116, 0, 0, -4, 32, -32, 0, 0, 192, 16, 4, 0, 0, -16, 124, -8, 0, 0, 24, 4, -32, 0, 0, 0, 156, -56, 0, 0, 36, -40, -148, 0, 0, 16, 120, -96, 0, 0, -72, 18, -12, 0, 0, 104, -24, -152, 0, 0, -32, 104, 336, 0, 0, 144, 120, 8, 0, 0, -100, 48, 132, 0, 0, 60, 32, 0, 0, 0, -104, -76, -184, 0, 0, -16, 32, -40, 0, 0, 272, -38, 24, 0, 0, 176, -56, 24, 0, 0, 8, 12, 32, 0, 0, 88, -72, 16, 0, 0, -16, 184, 8, 0, 0, -32, -160, 164, 0, 0, -20, -30, 136, 0, 0, 48, 28, 64, 0, 0, 56, 56, -336, 0, 0, 4, -20, 48, 0, 0, 0, 6, -44, 0, 0, -124, -144, -36, 0, 0, -300, 72, -120, 0, 0, -120, -44, 20, 0, 0, 32, -104, -80, 0, 0, -32, -4, -336, 0, 0, -152, 54, -176, 0, 0, -28, -120, 56, 0, 0, -284, -68, 8, 0, 0, -8, -160, 0, 0, 0, 88, -60, -16, 0, 0, -304, 4, -8, 0, 0, -160, -64, 80, 0, 0, 80, 28, 360, 0, 0, 108, -8, -72, 0, 0, 72, 24, 96, 0, 0, -32, 48, 312, 0, 0, 128, -4, -112, 0, 0, -144, 50, 96, 0, 0, 56, -40, 160, 0, 0, 88, 48, -192, 0, 0, 72, 140, 16, 0, 0, 152, -88, -152, 0, 0, 36, 104, 136, 0, 0, -88, 8, 0, 0, 0, -16, -44, -104, 0, 0, 232, 34, 240, 0, 0, 16, 156, 112, 0, 0, -28, -8, -44, 0, 0, 36, -40, -56, 0, 0, 240, -216, 24, 0, 0, -100, 48, 28, 0, 0, 112, -32, 152, 0, 0, 224, 28, 64, 0, 0, 48, -20, -80, 0, 0, -132, -72, -168, 0, 0, 48, -40, 32, 0, 0, -76, 296, 144, 0, 0, 8, -24, -48, 0, 0, 112, 56, -16, 0, 0, -152, 168, -8, 0, 0, -196, -4, -112, 0, 0, 136, -36, -16, 0, 0, -8, -32, -64, 0, 0, 100, -40, 88, 0, 0, 8, -32, 80, 0, 0, -176, -12, 4, 0, 0, 8, 44, -16, 0, 0, 104, -80, -64, 0, 0, 8, 32, -64, 0, 0, -240, -44, 32, 0, 0, -112, -8, -36, 0, 0, -8, 72, 100, 0, 0, -168, 4, 128, 0, 0, -160, -158, -56, 0, 0, 60, -80, 120, 0, 0, -108, 12, 208, 0, 0, -40, -256, 0, 0, 0, 104, -200, 88, 0, 0, 68, 32, 88, 0, 0, -240, 58, 44, 0, 0, -104, -192, -80, 0, 0, 76, 28, 16, 0, 0, -104, 4, -92, 0, 0, 92, -120, -84, 0, 0, 136, 72, -192, 0, 0, 136, 56, -68, 0, 0, 16, -80, -36, 0, 0, 16, 6, 208, 0, 0, -64, 20, -136, 0, 0, 8, 36, 24, 0, 0, 244, 64, 96, 0, 0, 16, 140, -116, 0, 0, -32, 8, -268, 0, 0, 328, 20, 24, 0, 0, -304, -40, -32, 0, 0, -88, 216, -440, 0, 0, 40, -24, -168, 0, 0, 64, 296, 28, 0, 0, -48, 160], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 35, 10, 1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 10, "minimal_twist": "105.2.q.a", "char_is_minimal": true, "conrey_index": 4, "id": null, "nf_label": 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, 0, 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, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, -1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 1, -1, 0, 0], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, -1, -1, 0, -2, -1, 0, 0, -2, 0], [-2, 0, 2, 0, 0, 0, 0, 1, 1, -2, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, -1, 1, -2, 0, 0, 0, 0, 1, -1, 0, 1, 1], [0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1], [-1, -2, -1, 0, 0, 0, 0, -3, -1, 0, -3, 0, 1, -1, -1, 0], [0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 2, 2, 0], [0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0], [0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 0, 0, 0, 0, 0, 4, 0, -1, 1, 0, 0, 0, 0, 0], [-1, -1, -1, -3, -2, 0, -3, 0, 0, 0, 0, 0, -1, 1, 0, 1], [-1, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 0, 0, 0, 1, 0], [1, 0, -1, -4, 1, 0, -4, 0, 0, 0, 0, 0, 0, -1, 0, 1], [2, 0, -2, 0, 0, 3, -5, 0, -2, 0, 0, 0, -2, -2, 2, 3], [0, 0, 0, 0, 0, 0, 0, -2, -1, 0, -2, 0, 0, 0, -1, 0], [3, 0, -3, 2, 0, 1, 0, -2, -1, 3, -1, 1, 0, 0, 0, 0], [0, 3, 2, 0, 0, 0, 0, 1, 2, 2, 3, 0, -2, 2, 2, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -4, -1, -2, -2, 0, 0, 0, 0, -2, 0, 1, -2, 1], [2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0], [0, 1, -1, 0, 2, 0, 1, 2, -1, 0, 1, -2, 1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0], [-1, 0, 1, 0, -1, -2, 1, 0, 1, 0, 0, 1, 0, 1, 0, -2], [1, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0], [-2, -1, 0, 2, 0, -1, -1, 2, 0, 2, 0, 1, 2, 0, 0, -1], [1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, 6, 0, -1, 0, 0, -1, 0, -1, 0, 0], [0, 0, 0, -1, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0], [-1, 0, 1, 0, 0, 0, 0, -1, 0, -1, -2, 0, 0, 0, 0, 0], [3, -1, -1, 0, 1, -1, 2, -3, -1, -3, -1, -1, 0, -1, 0, -1], [-1, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [1, 0, -1, 0, 3, 0, 3, 0, 0, 0, 0, -1, 2, -1, -1, 0], [-1, 0, 1, 2, -3, 0, 2, 0, 0, 0, 0, 0, -2, 1, 0, -2], [3, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 0, 1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-5, 0, 5, 0, 0, 0, 0, -1, 0, -5, 1, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 1, -1, 0], [-2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [-3, 0, 1, 0, 0, 0, 0, 2, 0, 1, 3, 0, 0, 0, 0, 0], [-4, 2, 4, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0, 2, 0, -1], [2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0], [0, 0, 0, 10, 0, 1, 0, 0, 3, 0, 0, 5, 0, 0, 2, 0], [0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [3, 1, -2, -2, 3, 0, -2, 0, 0, 0, 0, 0, 2, -3, 0, 2], [5, -2, -3, 0, 0, 0, 0, 0, -1, -2, -2, 0, 1, -1, -1, 0], [0, 0, 0, -3, -1, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, -1], [-3, 0, 3, 0, -7, -1, -4, 0, 3, 0, 0, 7, -4, 3, 4, -1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, -1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 0, 0, 2, 0], [4, -3, -2, 0, 0, 0, 0, -5, -2, 5, -3, 0, 2, -2, -2, 0], [-2, 0, 2, 3, -2, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, -1], [-1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, -1], [0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0], [2, -1, 0, 0, 1, -4, 0, -3, 0, -2, -1, -1, 2, 0, -2, -4], [1, 0, -1, 0, 0, 0, 0, 3, -1, 1, -1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -4, 0, 0, -2, 0], [3, 0, -3, 0, 4, 0, 8, 0, -3, 0, 0, -4, 1, -3, -1, 0], [3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0], [0, 0, 3, 8, 2, 3, 2, -1, -1, -1, -1, -1, 0, 0, 0, -1], [0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0], [1, 0, -1, 0, 2, 0, 2, 0, -1, 0, 0, -2, 1, -1, -1, 0], [0, 0, 0, -4, 0, -4, 0, 0, 1, 0, 0, 3, 0, 0, 2, 0], [6, 0, -6, 0, 0, 0, 0, 3, 1, 6, 3, 0, 0, 0, 1, 0], [1, -1, -1, 0, 1, 3, -1, -1, -1, -1, -1, -1, 0, -1, 0, 3], [-3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 3, 0, 1, 0, 0, 4, 0, 0, 3, 1], [-2, 0, 2, -3, -3, 0, -3, 0, 0, 0, 0, 0, -1, 2, 0, 2], [-3, 3, 4, 0, 0, 0, 0, 2, 4, -1, 3, 0, -4, 4, 4, 0], [-2, 0, 2, -8, 0, -4, 0, 8, 2, -2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -3, 0, 3, -1, -4, 0, -3, 0, 0, -3, 0, -3, 0, -1], [2, 0, -2, -1, 2, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -1], [3, 2, -1, 0, 0, 0, 0, 1, 1, 3, 3, 0, 0, 0, 1, 0], [-4, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 4], [-5, -3, -3, 0, 0, 0, 0, 5, -3, 2, -3, 0, 3, -3, -3, 0], [0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, -3, 0, 0, -1, 0], [0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, -2, 0], [-3, -3, 1, 0, 0, 0, 0, -1, 1, -6, -3, 0, -1, 1, 1, 0], [0, 2, 1, -2, -1, 0, -2, 0, 0, 0, 0, 0, -2, 1, 0, 0], [2, -2, -5, 0, 0, 0, 0, 0, -2, -1, -1, 0, 0, 0, -2, 0], [-3, 0, 3, -12, -4, 0, -12, 0, 0, 0, 0, 0, -1, 3, 0, 0], [0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, -2, 2, 0, -2, 0], [-2, 0, 2, 0, 0, 0, 0, -4, 0, -2, -2, 0, 0, 0, 0, 0], [2, 0, -2, -1, 0, -1, 0, -5, 1, 2, -1, -1, 0, 0, 1, 0], [0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1], [3, 0, -3, 3, 2, 4, -7, 0, 0, 0, 0, 2, -1, -3, 2, 1], [-1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [-6, 1, 4, 0, -4, 2, -8, 3, 4, 1, 1, 4, -4, 4, 4, 2]]}