# Stored data for newform 1800.2.k.q, downloaded from the LMFDB on 24 April 2024. {"label": "1800.2.k.q", "space_label": "1800.2.k", "level": 1800, "weight": 2, "hecke_orbit": 17, "hecke_orbit_code": 72058281266251528, "dim": 8, "is_polredabs": true, "nf_label": "8.0.214798336.3", "trace_hash": 1088107430107424807, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [1, -12, -6, 4, 1]], [11, [1600, 0, 1344, 0, 336, 0, 32, 0, 1]], [17, [-24, 104, -40, 0, 1]]], "qexp_display": "q+\\beta _{3}q^{2}+(-\\beta _{4}-\\beta _{5}+\\beta _{6})q^{4}+(-1+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "k", "char_is_real": true, "Nk2": 7200, "analytic_conductor": 14.373072363830468, "hecke_ring_index": 4, "level_radical": 30, "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": "0.518", "prec": 17}, "analytic_rank_proved": true, "char_values": [1800, 2, [1351, 901, 1001, 577], [2, 1, 2, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [901], "field_disc": 214798336, "field_disc_factorization": [[2, 12], [229, 2]], "field_poly": [16, -16, 0, -4, 9, -2, 0, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.561", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "228.395", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11993.635", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 0, 0, -8], "traces": [0, 8, -2, 0, 4, 0, 0, -8, 4, 0, 0, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, -12, 8, 0, 0, 2, 0, 4, 0, 0, 8, 28, 0, 12, 0, 0, 0, 30, 0, 0, 0, 0, 0, 12, 0, 20, 0, 0, 0, 0, 0, 20, 0, 0, 0, -8, 0, -12, 0, 0, 0, 30, 0, -32, 0, 0, 0, -28, 0, 0, 40, 0, 16, -8, 0, -20, 0, 0, -16, 0, 0, 24, 0, 0, 0, 18, 0, 8, 0, 0, 0, -36, 0, -4, 0, 0, 8, -48, 0, 0, 0, 0, -64, -20, 0, -32, 0, 0, 0, 0, 0, 16, -32, 0, 0, -20, 0, 12, -72, 0, 24, -14, 0, 28, 0, 0, 32, 40, 0, 0, 0, 0, 0, -6, 0, 16, -64, 0, 0, 0, 0, 16, -40, 0, 0, -44, 0, -24, 0, 0, -24, 32, 0, 44, 0, 0, 0, 76, 0, 0, 48, 0, 0, 60, 0, 4, -40, 0, 16, 0, 0, 12, 0, 0, 0, 24, 0, -32, 0, 0, 0, 18, 0, -8, 0, 0, 0, -72, 0, 0, -56, 0, 8, 70, 0, 8, 0, 0, 8, 0, 0, -40, 0, 0, 0, 44, 0, 40, 32, 0, 0, 12, 0, 32, 0, 0, -72, -42, 0, 0, 0, 0, 56, -44, 0, -32, 0, 0, 0, 0, 0, 48, 0, 0, 0, -88, 0, 76, 72, 0, 40, 2, 0, -4, 0, 0, -56, 64, 0, 0, 0, 0, 0, -60, 0, 16, -16, 0, 0, 0, 0, 8, 40, 0, 0, -54, 0, -76, 0, 0, 0, 16, 0, 20, 0, 0, 0, 48, 0, 0, -48, 0, 0, 52, 0, -4, 56, 0, 24, 0, 0, -96, 0, 0, 0, 88, 0, -12, 0, 0, 0, 18, 0, -32, 0, 0, 0, -76, 0, 0, 80, 0, 24, 114, 0, -72, 0, 0, -64, 0, 0, -84, 0, 0, 0, 58, 0, 40, -32, 0, 0, 16, 0, -48, 0, 0, -56, -76, 0, 0, 0, 0, -88, -88, 0, 76, 0, 0, 0, 0, 0, -8, 16, 0, 0, -88, 0, 60, -88, 0, -80, -14, 0, -60, 0, 0, 88, 120, 0, 0, 0, 0, 0, -64, 0, -32, 48, 0, 0, 0, 0, 68, -32, 0, 0, -106, 0, -60, 0, 0, 0, -8, 0, 20, 0, 0, 0, 118, 0, 0, 16, 0, 0, 12, 0, 68, -80, 0, -24, 0, 0, -16, 0, 0, 0, 52, 0, -84, 0, 0, 0, 2, 0, -40, 0, 0, 0, -92, 0, 0, -136, 0, -40, 98, 0, -12, 0, 0, -88, 0, 0, 4, 0, 0, 0, 70, 0, 64, -48, 0, 0, 8, 0, -32, 0, 0, 80, -74, 0, 0, 0, 0, 96, -64, 0, -80, 0, 0, 0, 0, 0, 112, 144, 0, 0, -44, 0, 56, 80, 0, 0, -98, 0, 28, 0, 0, -72, 100, 0, 0, 0, 0, 0, -150, 0, 16, 48, 0, 0, 0, 0, 48, -72, 0, 0, -24, 0, -48, 0, 0, -32, 40, 0, 32, 0, 0, 0, 48, 0, 0, 0, 0, 0, 4, 0, -16, 136, 0, 72, 0, 0, 76, 0, 0, 0, 144, 0, 20, 0, 0, 0, 36, 0, 8, 0, 0, 0, -88, 0, 0, 104, 0, 16, 34, 0, -56, 0, 0, 40, 0, 0, -60, 0, 0, 0, 26, 0, 40, 48, 0, 0, -92, 0, -40, 0, 0, 56, -134, 0, 0, 0, 0, 48, -80, 0, -60, 0, 0, 0, 0, 0, -48, -16, 0, 0, -32, 0, 92, -112, 0, 24, -98, 0, 140, 0, 0, 112, 148, 0, 0, 0, 0, 0, -26, 0, 96, -96, 0, 0, 0, 0, -92, 80, 0, 0, -38, 0, -132, 0, 0, 8, 32, 0, 8, 0, 0, 0, 96, 0, 0, 112, 0, 0, 100, 0, 60, -160, 0, 128, 0, 0, -84, 0, 0, 0, 16, 0, 4, 0, 0, 0, 24, 0, 16, 0, 0, 0, -140, 0, 0, -120, 0, 112, -26, 0, -56, 0, 0, -8, 0, 0, -20, 0, 0, 0, 142, 0, 32, 144, 0, 0, -100, 0, -100, 0, 0, -96, -120, 0, 0, 0, 0, -16, -24, 0, 44, 0, 0, 0, 0, 0, -96, -96, 0, 0, 32, 0, -16, 152, 0, -48, -84, 0, 4, 0, 0, -8, 104, 0, 0, 0, 0, 0, -46, 0, -40, 64, 0, 0, 0, 0, 0, -80, 0, 0, -22, 0, 80, 0, 0, -32, 48, 0, 92, 0, 0, 0, 62, 0, 0, -96, 0, 0, 20, 0, 192, 256, 0, 24, 0, 0, -20, 0, 0, 0, 44, 0, -112, 0, 0, 0, 80, 0, -176, 0, 0, 0, -112, 0, 0, -16, 0, -88, 78, 0, -4, 0, 0, 112, 0, 0, 112, 0, 0, 0, -22, 0, -8, -64, 0, 0, -116, 0, 16, 0, 0, -24, -178, 0, 0, 0, 0, -72, 32, 0, -76, 0, 0, 0, 0, 0, 48, 112, 0, 0, -108, 0, -8, 24, 0, -56, -8, 0, 36, 0, 0, 72, 32, 0, 0, 0, 0, 0, 42, 0, 216, 208, 0, 0, 0, 0, 20, 128, 0, 0, 34, 0, -84, 0, 0, 216, 68, 0, 76, 0, 0, 0, 134, 0, 0, -208, 0, 0, 44, 0, -96, -144, 0, -208, 0, 0, 116, 0, 0, 0, 0, 0, -128, 0, 0, 0, 88, 0, -32, 0, 0, 0, -44, 0, 0, -80, 0, -160, 60, 0, 20, 0, 0, -72, 0, 0, -24, 0, 0, 0, 12, 0, -8, -64, 0, 0, -68, 0, 20, 0, 0, 88, -50, 0, 0, 0, 0, -48, -176, 0, -60, 0, 0, 0, 0, 0, 8, 0, 0, 0, -44, 0, 60, 128, 0, 64, -40, 0, 52, 0, 0, -112, 4, 0, 0, 0, 0, 0, 38, 0, 24, 0, 0, 0, 0, 0, -104, -144, 0, 0, -152, 0, -68, 0, 0, -200, 84, 0, -64, 0, 0, 0, 106, 0, 0, 112, 0, 0, 40, 0, 72, 280, 0, -104, 0, 0, -112, 0, 0, 0, -24, 0, 68, 0, 0, 0, -20, 0, -16, 0, 0, 0, -120, 0, 0, 176, 0, 72, -88, 0, -56, 0, 0, 184, 0, 0, 4, 0, 0, 0, 70, 0, 40, 80, 0, 0, -12, 0, -180, 0, 0, 136, -58, 0, 0, 0, 0, 24, -68, 0, -8, 0, 0, 0, 0, 0, -128, -208, 0, 0, 100, 0, -64, -176, 0, 160, 18, 0, -96, 0, 0, 72, -8, 0, 0, 0, 0, 0, -104, 0, -72, -112, 0, 0, 0, 0, 116, 240, 0, 0, -44, 0, 52, 0, 0, 48, 56, 0, -84, 0, 0, 0, 22, 0, 0, 32, 0, 0, 28, 0, 20, -336, 0, 120, 0, 0, -108, 0, 0, 0, 104, 0, -100, 0, 0, 0, -26, 0, -88, 0, 0, 0, -4, 0, 0, -56, 0, 24, 34, 0, 44, 0, 0, -104, 0, 0, 108, 0, 0, 0, 40, 0, 32, 32, 0, 0, 0, 0, 72, 0, 0, 0, 10, 0, 0, 0, 0, 16, 32, 0, 0, 0, 0, 0, 0, 0, 216, -112, 0, 0, -76, 0, 80, 72, 0, -16, -30, 0, 156, 0, 0, -112, 48, 0, 0, 0, 0, 0, -84, 0, 112, -32, 0, 0, 0, 0, 52, -88, 0, 0, 104, 0, 60, 0, 0, -128, -128, 0, 96, 0, 0, 0, 102, 0, 0, 48, 0, 0, 104, 0, -144, 296, 0, -80, 0, 0, 180, 0, 0, 0, 76, 0, -144, 0, 0, 0, -38, 0, 192, 0, 0, 0, -24, 0, 0, 104, 0, 40, -128, 0, 48, 0, 0, 216, 0, 0, -184, 0, 0, 0, 128, 0, 48, 16, 0, 0, 4, 0, 136, 0, 0, -88, -24, 0, 0, 0, 0, 200, 24, 0, -116, 0, 0, 0, 0, 0, 32, 144, 0, 0, 40, 0, 40, 16, 0, -80, 104, 0, 72, 0, 0, 88, 0, 0, 0, 0, 0, 0, -80, 0, -136, 32, 0, 0, 0, 0, -68, 208, 0, 0, -44, 0, -4, 0, 0, 72, -104, 0, -20, 0, 0, 0, -26, 0, 0, -96, 0, 0, 132, 0, 40, -264, 0, 40, 0, 0, -180, 0, 0, 0, -36, 0, 176, 0, 0, 0, -32, 0, 48, 0, 0, 0, 144, 0, 0, 24, 0, 120, 64, 0, 64, 0, 0, -56, 0, 0, -92, 0, 0, 0, 16, 0, 192, -272, 0, 0, -12, 0, -24, 0, 0, 184, 146, 0, 0, 0, 0, -96, 64, 0, 140, 0, 0, 0, 0, 0, -128, 160, 0, 0, -164, 0, -84, -32, 0, -96, 100, 0, -64, 0, 0, -136, -12, 0, 0, 0, 0, 0, 70, 0, -80, -96, 0, 0, 0, 0, 212, -264, 0, 0, -8, 0, 36, 0, 0, -24, -24, 0, -60, 0, 0, 0, -120, 0, 0, -80, 0, 0, 60, 0, 64, 160, 0, -16, 0, 0, -76, 0, 0, 0, -72, 0, -64, 0, 0, 0, -12, 0, -56, 0, 0, 0, 36, 0, 0, 200, 0, -96, 30, 0, -36, 0, 0, 112, 0, 0, 168, 0, 0, 0, -74, 0, 56, 16, 0, 0, 88, 0, 68, 0, 0, 0, 58, 0, 0, 0, 0, -88, -132, 0, 128, 0, 0, 0, 0, 0, 216, -80, 0, 0, 44, 0, -104, -336, 0, 56, 16, 0, -176, 0, 0, -8, 80, 0, 0, 0, 0, 0, -14, 0, 136, -96, 0, 0, 0, 0, 48, 240, 0, 0, -178, 0, 44, 0, 0, 336, 88, 0, -72, 0, 0, 0, -56, 0, 0, 128, 0, 0, -124, 0, -136, -416, 0, -168, 0, 0, 108, 0, 0, 0, 64, 0, -24, 0, 0, 0, 34, 0, 152, 0, 0, 0, 16, 0, 0, -296, 0, 128, 54, 0, 12, 0, 0, -112, 0, 0, -76, 0, 0, 0, -106, 0, -80, 208, 0, 0, 216, 0, -128, 0, 0, -176, -96, 0, 0, 0, 0, -72, 120, 0, -192, 0, 0, 0, 0, 0, -64, -272, 0, 0, -44, 0, 156, 224, 0, -72, 126, 0, 88, 0, 0, -232, -104, 0, 0, 0, 0, 0, -94, 0, -240, -16, 0, 0, 0, 0, -144, -136, 0, 0, 94, 0, -20, 0, 0, -176, -152, 0, -232, 0, 0, 0, -112, 0, 0, 144, 0, 0, -140, 0, -216, 280, 0, -152, 0, 0, -76, 0, 0, 0, -4, 0, -40, 0, 0, 0, -2, 0, 56, 0, 0, 0, 164, 0, 0, 208, 0, -80, 82, 0, -68, 0, 0, 8, 0, 0, -120, 0, 0, 0, -106, 0, -96, -64, 0, 0, 48, 0, -124, 0, 0, -40, 212, 0, 0, 0, 0, -40, 128, 0, 116, 0, 0, 0, 0, 0, -112, 240, 0, 0, 48, 0, -92, -64, 0, -72, 16, 0, -24, 0, 0, -16, -160, 0, 0, 0, 0, 0, 56, 0, 56, 320, 0, 0, 0, 0, 140, 56, 0, 0, 88, 0, 120, 0, 0, -80, -20, 0, 40, 0, 0, 0, -70, 0, 0, -336, 0, 0, 28, 0, 48, -328, 0, -144, 0, 0, -48, 0, 0, 0, -184, 0, 76, 0, 0, 0, 24, 0, -40, 0, 0, 0, -44, 0, 0, -144, 0, -424, -174, 0, 212, 0, 0, -352, 0, 0, 228, 0, 0, 0, -24, 0, -56, -176, 0, 0, 12, 0, 4, 0, 0, 16, 60, 0, 0, 0, 0, 288, 72, 0, -72, 0, 0, 0, 0, 0, 120, -48, 0, 0, 96, 0, -156, 248, 0, -32, 48, 0, -104, 0, 0, -240, -4, 0, 0, 0, 0, 0, 164, 0, 72, -96, 0, 0, 0, 0, -12, -168, 0, 0, -8, 0, -124, 0, 0, -72, 36, 0, 220, 0, 0, 0, -48, 0, 0, 144, 0, 0, -40, 0, -88, 280, 0, 96, 0, 0, 240, 0, 0, 0, -160, 0, 132, 0, 0, 0, 70, 0, 144, 0, 0, 0, 76, 0, 0, -88, 0, -48, 120, 0, -20, 0, 0, 216, 0], "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, 8, 2, 1, 2, 0]], "char_orbit_index": 11, "prim_orbit_index": 2, "minimal_twist": "600.2.k.d", "char_is_minimal": true, "conrey_index": 901, "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, 0, 0], [1, 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, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, 0, 0, 1, 0], [1, 0, 1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, -1, 1, -1, 0], [0, 1, -1, -2, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 2, 1, -1, 1, -2], [0, 1, 0, 0, 1, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -3, -1, -1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -3, 0, -1, -1, 1, 0], [1, -2, 0, 3, 3, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -4, 1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 3, 2, 0, 2, 0, 0], [0, 1, 4, 2, -1, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, -2, -2, -1, 0], [4, 2, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 1, 2, -1, 1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, -2, 0, 2, -2], [6, -1, -3, 0, 0, 3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 2, -3, -2, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -3, 3, -1, -2, 2], [2, 0, 0, -2, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 3, -3, 0, -1, -1, 1, 0], [0, 0, 0, 0, 4, 2, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -6, -2, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -4, 0, -3, 1, -1, 0], [0, 3, 2, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -5, 0, 2, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -1, -2, 1, -1, 1, 4], [-4, 2, 2, 0, 2, -4, 4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -5, 2, -3, 1, 1, -2], [4, -3, 3, 4, -2, -1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 4, 4, -2, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 2, -1, 1, 1, -3, 4, -2], [-4, 2, -4, -2, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, -2, 0, 3, -1, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -2, 6, 4, -2, -2], [0, 0, -4, -2, -2, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -3, -7, 6, -2, 0, 2, -4], [-4, -1, -4, -2, 1, -4, 2, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, 6, 4, 0, -2, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 1, 0, -1, -3, -1, 0], [2, -2, 2, 2, -4, 2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 7, 2, 2, 1, -1, -4], [0, 0, 0, 0, 0, 0, 0, 0], [2, -4, -2, 4, 2, 2, 0, -2], [0, -2, 0, 0, 6, 4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -5, -1, 1, -3, 2, -2], [-2, 0, 4, 2, -6, 0, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -2, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 6, 4, 0, -2, -4], [-4, -4, 4, 2, 2, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}