# Stored data for newform 1800.2.d.q, downloaded from the LMFDB on 24 April 2024. {"label": "1800.2.d.q", "space_label": "1800.2.d", "level": 1800, "weight": 2, "hecke_orbit": 17, "hecke_orbit_code": 72057800229914376, "dim": 6, "is_polredabs": true, "nf_label": "6.0.399424.1", "trace_hash": 1789819750356315567, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [256, 0, 320, 0, 36, 0, 1]], [11, [4096, 0, 1088, 0, 64, 0, 1]], [13, [-16, -28, 0, 1]], [37, [-256, -60, 4, 1]], [41, [232, -36, -10, 1]], [53, [-2, 1]]], "qexp_display": "q-\\beta _{2}q^{2}-\\beta _{1}q^{4}+(-\\beta _{1}-\\beta _{2}+\\beta _{4}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 40, "char_orbit_label": "d", "char_is_real": true, "Nk2": 7200, "analytic_conductor": 14.373072363830468, "hecke_ring_index": 8, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [1800, 2, [1351, 901, 1001, 577], [2, 1, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [1549], "field_disc": -399424, "field_disc_factorization": [[-1, 1], [2, 6], [79, 2]], "field_poly": [8, -8, 6, -6, 3, -2, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "5.637", "prec": 17}, {"__RealLiteral__": 0, "data": "1.041", "prec": 17}, {"__RealLiteral__": 0, "data": "160.748", "prec": 24}, {"__RealLiteral__": 0, "data": "91.397", "prec": 20}, {"__RealLiteral__": 0, "data": "6354.310", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 6, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, -16, 0, 10, 0, 0, 0, 0, 0, -12, 0, 0, 0, -28, 0, -20, 0, 0, -12, -10, 0, -12, 0, 0, -8, 20, 0, 0, 20, 0, 8, -4, 0, -20, 0, 0, -30, 0, 0, 12, 12, 0, 0, -4, 0, 4, 0, 0, 0, -28, 0, -22, 0, 0, -24, 0, 0, 0, 8, 0, 0, 12, 0, 12, -32, 0, -36, 0, 0, 16, 32, 0, 0, 16, 0, 60, -28, 0, 0, -12, 0, -4, 0, 0, 0, -56, 0, 0, 0, 0, 0, -28, 0, 0, 40, 0, 0, 0, 0, -28, 0, 0, 0, -8, 0, -4, -24, 0, -62, 24, 0, 8, 0, 0, 0, -42, 0, 0, 0, 0, 64, 0, 0, -32, 0, 0, 0, 0, 0, -40, 0, 0, 0, 12, 0, -68, 0, 0, 28, -12, 0, 32, 0, 0, 56, 28, 0, 0, -64, 0, 40, 60, 0, 16, 0, 0, 34, 0, 0, 56, 28, 0, 0, 12, 0, 16, 0, 0, 0, 40, 0, 12, 0, 0, 64, 4, 0, 0, 48, 0, 0, 28, 0, 14, 84, 0, 76, 0, 0, 4, -8, 0, 0, -32, 0, 44, 48, 0, 0, 4, 0, -72, 0, 0, 0, -32, 0, 0, 0, 0, 0, -60, 0, -44, 0, 0, 0, 0, 0, -16, 0, 0, 0, -20, 0, -56, 64, 0, 28, 32, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, -48, -48, 0, 2, 0, 0, 0, 0, 0, 44, 0, 0, 0, 40, 0, -8, 0, 0, 124, 24, 0, 12, 0, 0, -16, 52, 0, 0, 28, 0, -120, 80, 0, 8, 0, 0, -34, 0, 0, -24, 12, 0, 0, 20, 0, 4, 0, 0, 0, -44, 0, -4, 0, 0, -88, 96, 0, 0, -48, 0, 0, 44, 0, -24, -68, 0, 16, 0, 0, -40, 48, 0, 0, -16, 0, -4, 0, 0, 0, 64, 0, -12, 0, 0, 0, -24, 0, 0, 0, 0, 0, 8, 0, -24, -32, 0, 0, 0, 0, -4, 0, 0, 0, 44, 0, -36, -8, 0, 34, -64, 0, 72, 0, 0, 0, 4, 0, 0, 0, 0, -56, -80, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, -8, 0, 0, -48, -26, 0, 56, 0, 0, 8, -44, 0, 0, 28, 0, 112, -8, 0, -16, 0, 0, 36, 0, 0, -36, -48, 0, 0, 4, 0, 8, 0, 0, 0, -12, 0, -12, 0, 0, 64, -16, 0, 0, 8, 0, 0, 72, 0, -40, 80, 0, -4, 0, 0, 0, -32, 0, 0, 24, 0, -60, -108, 0, 0, -96, 0, 56, 0, 0, 0, -64, 0, 0, 0, 0, 0, -32, 0, -20, -112, 0, 0, 0, 0, 28, 0, 0, 0, 16, 0, -16, -88, 0, -48, -24, 0, 86, 0, 0, 0, -120, 0, 0, 0, 0, 24, -24, 0, 24, 0, 0, 0, 0, 0, 68, 0, 0, 0, -8, 0, -4, 0, 0, -24, 30, 0, 12, 0, 0, -208, -56, 0, 0, -60, 0, -8, 44, 0, -28, 0, 0, 58, 0, 0, -56, -64, 0, 0, 24, 0, 52, 0, 0, 0, 68, 0, -104, 0, 0, 24, -48, 0, 0, -16, 0, 0, 100, 0, -4, -92, 0, -64, 0, 0, -24, -64, 0, 0, 0, 0, -48, 92, 0, 0, -72, 0, -16, 0, 0, 0, 136, 0, 0, 0, 0, 0, -48, 0, 112, 56, 0, 0, 0, 0, 28, 0, 0, 0, -8, 0, 24, 88, 0, -20, 16, 0, -32, 0, 0, 0, 84, 0, 0, 0, 0, -24, -96, 0, 64, 0, 0, 0, 0, 0, 64, 0, 0, 0, 4, 0, 60, 0, 0, -100, 64, 0, -8, 0, 0, 224, 40, 0, 0, 44, 0, 8, 56, 0, 0, 0, 0, -96, 0, 0, -40, 28, 0, 0, -52, 0, 104, 0, 0, 0, -44, 0, -16, 0, 0, 16, 20, 0, 0, 256, 0, 0, 44, 0, 142, 44, 0, 40, 0, 0, 32, -160, 0, 0, 48, 0, -72, 0, 0, 0, 140, 0, -24, 0, 0, 0, 104, 0, 0, 0, 0, 0, -116, 0, -76, -8, 0, 0, 0, 0, 44, 0, 0, 0, -4, 0, 40, 88, 0, -136, -24, 0, 24, 0, 0, 0, 136, 0, 0, 0, 0, -64, -56, 0, -84, 0, 0, 0, 0, 0, -32, 0, 0, 0, 12, 0, 176, 0, 0, 84, 20, 0, 16, 0, 0, -128, -60, 0, 0, -28, 0, -144, 16, 0, -12, 0, 0, -12, 0, 0, -24, 12, 0, 0, 48, 0, -12, 0, 0, 0, 0, 0, 38, 0, 0, -56, 4, 0, 0, -280, 0, 0, -4, 0, -16, -60, 0, 176, 0, 0, 40, 48, 0, 0, 32, 0, -16, 92, 0, 0, -56, 0, -168, 0, 0, 0, 112, 0, 0, 0, 0, 0, -100, 0, 0, 120, 0, 0, 0, 0, 124, 0, 0, 0, -168, 0, 4, -56, 0, 150, -96, 0, -84, 0, 0, 0, 20, 0, 0, 0, 0, 56, -64, 0, -112, 0, 0, 0, 0, 0, -40, 0, 0, 0, -28, 0, 112, 0, 0, 0, -8, 0, 24, 0, 0, -24, -12, 0, 0, 20, 0, 40, 112, 0, 88, 0, 0, -104, 0, 0, -52, 16, 0, 0, 116, 0, -112, 0, 0, 0, 136, 0, -16, 0, 0, 88, -24, 0, 0, -32, 0, 0, -60, 0, -24, 176, 0, -172, 0, 0, -92, 160, 0, 0, -56, 0, 24, -76, 0, 0, 64, 0, -96, 0, 0, 0, 64, 0, 0, 0, 0, 0, -52, 0, 160, 24, 0, 0, 0, 0, -32, 0, 0, 0, -32, 0, 72, -72, 0, -50, 168, 0, 140, 0, 0, 0, 94, 0, 0, 0, 0, 96, 16, 0, -24, 0, 0, 0, 0, 0, -36, 0, 0, 0, -56, 0, -56, 0, 0, -60, 24, 0, 96, 0, 0, -24, -28, 0, 0, -128, 0, 112, 92, 0, 12, 0, 0, 124, 0, 0, 168, -76, 0, 0, -36, 0, -188, 0, 0, 0, -48, 0, -38, 0, 0, -112, 48, 0, 0, -64, 0, 0, 72, 0, 56, -128, 0, -164, 0, 0, 0, -8, 0, 0, 48, 0, -52, -108, 0, 0, 52, 0, 24, 0, 0, 0, -24, 0, 0, 0, 0, 0, -24, 0, -200, -112, 0, 0, 0, 0, -40, 0, 0, 0, 104, 0, 76, -64, 0, -16, -48, 0, -48, 0, 0, 0, 88, 0, 0, 0, 0, 80, 64, 0, -128, 0, 0, 0, 0, 0, 16, 0, 0, 0, 56, 0, 12, 0, 0, 16, 20, 0, -24, 0, 0, 240, -144, 0, 0, 16, 0, -24, 140, 0, -88, 0, 0, -4, 0, 0, -40, 128, 0, 0, 16, 0, -40, 0, 0, 0, -12, 0, -8, 0, 0, -32, -168, 0, 0, 32, 0, 0, 60, 0, -190, -64, 0, -96, 0, 0, -48, -120, 0, 0, -24, 0, -96, 16, 0, 0, -44, 0, 72, 0, 0, 0, -64, 0, 0, 0, 0, 0, 132, 0, 4, -40, 0, 0, 0, 0, -16, 0, 0, 0, 56, 0, 152, -64, 0, 100, 48, 0, -128, 0, 0, 0, -72, 0, 0, 0, 0, -128, -16, 0, 44, 0, 0, 0, 0, 0, -8, 0, 0, 0, 28, 0, 72, 0, 0, 108, -224, 0, -12, 0, 0, 16, 68, 0, 0, 72, 0, -160, -224, 0, 112, 0, 0, -36, 0, 0, 40, -80, 0, 0, -12, 0, 16, 0, 0, 0, -4, 0, -104, 0, 0, -80, -260, 0, 0, -104, 0, 0, 92, 0, -72, -100, 0, 4, 0, 0, 136, 0, 0, 0, 128, 0, 24, 20, 0, 0, 16, 0, 140, 0, 0, 0, 112, 0, 0, 0, 0, 0, -56, 0, -8, -136, 0, 0, 0, 0, -156, 0, 0, 0, 136, 0, 76, 104, 0, 12, 56, 0, 28, 0, 0, 0, -32, 0, 0, 0, 0, -80, -16, 0, 140, 0, 0, 0, 0, 0, -64, 0, 0, 0, 36, 0, 24, 0, 0, -184, -58, 0, -104, 0, 0, -16, 96, 0, 0, 12, 0, 16, -64, 0, 16, 0, 0, 50, 0, 0, 104, -100, 0, 0, -136, 0, -56, 0, 0, 0, 100, 0, -52, 0, 0, -48, 120, 0, 0, 288, 0, 0, -40, 0, 56, 64, 0, 124, 0, 0, -68, 96, 0, 0, 104, 0, 188, -28, 0, 0, -80, 0, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, -132, 0, 64, 96, 0, 0, 0, 0, -4, 0, 0, 0, -80, 0, -24, -184, 0, 192, -200, 0, 142, 0, 0, 0, 120, 0, 0, 0, 0, 272, -96, 0, 136, 0, 0, 0, 0, 0, -16, 0, 0, 0, 4, 0, -52, 0, 0, 76, -44, 0, 48, 0, 0, -192, -92, 0, 0, -4, 0, 296, -40, 0, -92, 0, 0, 92, 0, 0, -84, -92, 0, 0, -144, 0, -64, 0, 0, 0, -140, 0, 76, 0, 0, 160, 16, 0, 0, -104, 0, 0, -44, 0, -84, -240, 0, 284, 0, 0, 192, -64, 0, 0, -112, 0, -48, -48, 0, 0, -28, 0, 40, 0, 0, 0, -168, 0, 0, 0, 0, 0, 160, 0, 56, 224, 0, 0, 0, 0, -80, 0, 0, 0, -72, 0, -40, 264, 0, -56, 176, 0, -16, 0, 0, 0, 58, 0, 0, 0, 0, -128, -192, 0, -28, 0, 0, 0, 0, 0, -200, 0, 0, 0, -16, 0, -116, 0, 0, -224, -120, 0, 0, 0, 0, 160, -160, 0, 0, 36, 0, -176, -68, 0, 120, 0, 0, 108, 0, 0, 144, 20, 0, 0, -32, 0, -200, 0, 0, 0, -76, 0, -8, 0, 0, -40, -24, 0, 0, 88, 0, 0, -80, 0, -36, 132, 0, 16, 0, 0, 148, -24, 0, 0, 8, 0, -44, 296, 0, 0, -16, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 84, 0, 60, 56, 0, 0, 0, 0, -40, 0, 0, 0, 12, 0, 24, 48, 0, 98, 0, 0, 40, 0, 0, 0, 4, 0, 0, 0, 0, -296, 240, 0, -20, 0, 0, 0, 0, 0, -104, 0, 0, 0, -132, 0, -192, 0, 0, -32, 240, 0, 28, 0, 0, 24, 84, 0, 0, 252, 0, -8, 80, 0, 84, 0, 0, -160, 0, 0, -40, 180, 0, 0, 144, 0, 64, 0, 0, 0, 112, 0, -56, 0, 0, 152, -104, 0, 0, -248, 0, 0, -20, 0, 64, 320, 0, -116, 0, 0, -208, 304, 0, 0, -240, 0, -48, -32, 0, 0, 72, 0, -12, 0, 0, 0, -136, 0, 0, 0, 0, 0, -4, 0, -8, -96, 0, 0, 0, 0, 164, 0, 0, 0, 12, 0, 8, 120, 0, 28, -24, 0, 88, 0, 0, 0, -200, 0, 0, 0, 0, -56, 144, 0, 56, 0, 0, 0, 0, 0, 208, 0, 0, 0, 112, 0, -136, 0, 0, -92, -40, 0, 80, 0, 0, -240, 52, 0, 0, 48, 0, -112, -24, 0, -192, 0, 0, 30, 0, 0, 60, -48, 0, 0, -16, 0, 80, 0, 0, 0, -148, 0, 160, 0, 0, -216, 64, 0, 0, 144, 0, 0, 220, 0, 80, 156, 0, -28, 0, 0, 36, 312, 0, 0, 40, 0, 44, 140, 0, 0, 96, 0, -112, 0, 0, 0, 48, 0, 0, 0, 0, 0, 48, 0, -44, 40, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -152, -16, 0, 88, 88, 0, -88, 0, 0, 0, -52, 0, 0, 0, 0, 120, 104, 0, -274, 0, 0, 0, 0, 0, -156, 0, 0, 0, 120, 0, 76, 0, 0, 44, 8, 0, -60, 0, 0, 128, 232, 0, 0, -16, 0, 176, 44, 0, 180, 0, 0, 0, 0, 0, 32, 252, 0, 0, -40, 0, 80, 0, 0, 0, 76, 0, 168, 0, 0, 296, 16, 0, 0, -192, 0, 0, -196, 0, 12, -60, 0, -116, 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, 40, 6, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 6, "minimal_twist": "120.2.k.b", "char_is_minimal": false, "conrey_index": 1549, "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], [1, 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], [0, -1, -1, 0, 1, 0], [-1, 0, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 2], [0, 0, 0, 0, 0, 0], [0, -1, 3, -1, 1, 0], [-3, -2, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0], [2, 0, 1, 1, 1, 0], [0, -1, -1, -1, 1, -2], [0, 0, 0, 0, 0, 0], [0, 1, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, -2, 0, -2, -1, -1], [0, -1, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 0, 2, 2, 1, -1], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [-2, -1, 3, -1, 1, 0], [-1, 0, -1, -1, 2, -1], [0, 0, 0, 0, 0, 0], [-2, 0, 0, 2, 0, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 3, -1, 1, 1, 0], [4, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, -2, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0], [0, -2, -2, 0, -2, 0], [-1, 2, 0, 4, -3, 1], [0, 0, 0, 0, 0, 0], [-4, -2, 0, 0, 0, 0], [0, 1, 1, -1, -1, 4], [0, 0, 0, 0, 0, 0], [-5, -2, 6, -2, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 6, -2, 0, 2], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 2, 4, 0, 3, -1], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, -1], [0, 0, 0, 1, 0, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, -4], [-4, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, -2, 3, -1, 1, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0], [0, -2, 2, -2, 2, -4], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -4, 4, -2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0], [2, -2, 4, -4, 2, 2], [0, 0, 0, 0, 0, 0], [2, 0, -2, -2, 0, 2], [-8, -4, -4, 0, -4, 0], [0, 0, 0, 0, 0, 0], [-6, 1, -3, 1, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, -6, 4, -2, -2], [4, -2, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, -4, 4, -2, -2], [0, 0, 0, 0, 0, 0], [11, 2, 0, 0, 1, -3], [-6, -2, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0], [0, 4, 4, -2, -4, 4], [-2, 0, 2, 2, 0, -2], [0, 0, 0, 0, 0, 0], [-2, -2, 0, -4, -2, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, 2, 3, -2, 4], [-8, 4, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}