# Stored data for newform 1800.2.d.l, downloaded from the LMFDB on 20 April 2024. {"label": "1800.2.d.l", "space_label": "1800.2.d", "level": 1800, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49539802093061896, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1556235168530221713, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4, 0, 8, 0, 1]], [11, [4, 0, 1]], [13, [-12, 0, 1]], [37, [2, 1]], [41, [-8, -4, 1]], [53, [52, -16, 1]]], "qexp_display": "q+(-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}-\\zeta_{12}^{3})q^{4}+\\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": 2, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": [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": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.036", "prec": 17}, {"__RealLiteral__": 0, "data": "3.570", "prec": 17}, {"__RealLiteral__": 0, "data": "1.649", "prec": 17}, {"__RealLiteral__": 0, "data": "64.325", "prec": 20}, {"__RealLiteral__": 0, "data": "52.697", "prec": 20}, {"__RealLiteral__": 0, "data": "1571.223", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 0, 0, 0], "traces": [0, 4, -2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 4, 0, 0, -8, 8, 0, 12, 0, 0, -8, 4, 0, 0, 8, 0, 28, 8, 0, 20, 0, 0, 12, 0, 0, -24, 32, 0, 0, -8, 0, 24, 0, 0, 0, -8, 0, 0, 0, 0, 36, 0, 0, 0, -8, 0, 0, 4, 0, -16, -8, 0, 32, 0, 0, -16, 12, 0, 0, -20, 0, -16, 8, 0, 0, 4, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -20, 24, 0, 28, -28, 0, 24, 0, 0, 0, -16, 0, 0, 0, 0, 40, -12, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 20, 0, 0, 0, 0, -8, 32, 0, 16, 0, 0, -40, -40, 0, 0, 32, 0, -20, 24, 0, -12, 0, 0, -4, 0, 0, 12, 8, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -8, 0, 0, 0, 20, 0, 0, 8, 0, 0, 44, 0, -24, 64, 0, -48, 0, 0, -16, 48, 0, 0, 44, 0, 0, 32, 0, 0, -24, 0, -4, 0, 0, 0, -44, 0, 0, 0, 0, 0, -32, 0, 36, 36, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -24, -80, 0, 24, -14, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, -8, -36, 0, -32, 0, 0, 0, 0, 0, 60, 0, 0, 0, -56, 0, -12, 0, 0, -8, -48, 0, 20, 0, 0, 8, -4, 0, 0, -56, 0, 4, 24, 0, 24, 0, 0, 20, 0, 0, 16, -8, 0, 0, 16, 0, -36, 0, 0, 0, -32, 0, -48, 0, 0, 4, -24, 0, 0, -56, 0, 0, 44, 0, 48, -48, 0, 0, 0, 0, -28, -48, 0, 0, 28, 0, -16, -32, 0, 0, 12, 0, -12, 0, 0, 0, 2, 0, 0, 0, 0, 0, -56, 0, -4, -28, 0, 0, 0, 0, -16, 0, 0, 0, -48, 0, -12, 48, 0, -36, 32, 0, -24, 0, 0, 0, -72, 0, 0, 0, 0, -8, -24, 0, -40, 0, 0, 0, 0, 0, -64, 0, 0, 0, -4, 0, 16, 0, 0, -72, -24, 0, -20, 0, 0, 32, 72, 0, 0, -24, 0, -48, 16, 0, -48, 0, 0, -24, 0, 0, 28, -8, 0, 0, 48, 0, -40, 0, 0, 0, 84, 0, -64, 0, 0, -40, 12, 0, 0, 72, 0, 0, 8, 0, -40, -56, 0, -80, 0, 0, 24, -20, 0, 0, -4, 0, 32, -24, 0, 0, 24, 0, -84, 0, 0, 0, 8, 0, 0, 0, 0, 0, -96, 0, 36, 68, 0, 0, 0, 0, 32, 0, 0, 0, 24, 0, 40, -32, 0, 0, 24, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -96, -24, 0, -16, 0, 0, 0, 0, 0, -60, 0, 0, 0, -32, 0, -60, 0, 0, 8, 64, 0, -4, 0, 0, -40, 8, 0, 0, 120, 0, 68, 24, 0, 36, 0, 0, -20, 0, 0, 72, -48, 0, 0, -72, 0, -28, 0, 0, 0, -56, 0, 48, 0, 0, 140, -8, 0, 0, -96, 0, 0, -4, 0, 16, 24, 0, -24, 0, 0, 40, -12, 0, 0, 28, 0, 16, -40, 0, 0, 0, 0, -8, 0, 0, 0, -10, 0, 0, 0, 0, 0, -32, 0, -44, 36, 0, 0, 0, 0, -16, 0, 0, 0, 24, 0, 48, 0, 0, 88, -28, 0, 72, 0, 0, 0, 80, 0, 0, 0, 0, -64, -92, 0, 16, 0, 0, 0, 0, 0, -32, 0, 0, 0, 12, 0, -48, 0, 0, -24, -64, 0, 36, 0, 0, 48, -48, 0, 0, 40, 0, -108, 24, 0, 72, 0, 0, 32, 0, 0, -36, -48, 0, 0, 16, 0, 52, 0, 0, 0, -28, 0, -24, 0, 0, -144, -60, 0, 0, 16, 0, 0, 60, 0, 0, -112, 0, 56, 0, 0, -32, 36, 0, 0, -40, 0, 56, 48, 0, 0, 0, 0, 44, 0, 0, 0, 56, 0, 0, 0, 0, 0, 64, 0, -36, -64, 0, 0, 0, 0, -16, 0, 0, 0, -48, 0, 0, 48, 0, 32, 114, 0, 64, 0, 0, 0, 48, 0, 0, 0, 0, 168, 12, 0, 64, 0, 0, 0, 0, 0, -32, 0, 0, 0, 100, 0, 48, 0, 0, 8, 24, 0, 48, 0, 0, -104, 108, 0, 0, -88, 0, -8, 120, 0, -60, 0, 0, -24, 0, 0, 16, -48, 0, 0, -32, 0, 44, 0, 0, 0, 24, 0, 24, 0, 0, 4, -24, 0, 0, 24, 0, 0, 68, 0, -96, -48, 0, 24, 0, 0, 60, -32, 0, 0, 0, 0, -32, 40, 0, 0, 48, 0, -8, 0, 0, 0, 72, 0, 0, 0, 0, 0, -56, 0, -8, -44, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 52, 16, 0, -76, -20, 0, 24, 0, 0, 0, 64, 0, 0, 0, 0, 128, 32, 0, 8, 0, 0, 0, 0, 0, -24, 0, 0, 0, -44, 0, 16, 0, 0, 24, 80, 0, 88, 0, 0, 104, -32, 0, 0, -24, 0, -20, 48, 0, 100, 0, 0, 48, 0, 0, -44, 104, 0, 0, -64, 0, -48, 0, 0, 0, -16, 0, -48, 0, 0, 68, 132, 0, 0, 72, 0, 0, 84, 0, 16, 72, 0, 128, 0, 0, 32, -48, 0, 0, -20, 0, 96, -56, 0, 0, -48, 0, -4, 0, 0, 0, -36, 0, 0, 0, 0, 0, 48, 0, 16, -36, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 64, 56, 0, -60, -24, 0, -72, 0, 0, 0, -56, 0, 0, 0, 0, -40, -36, 0, 96, 0, 0, 0, 0, 0, 44, 0, 0, 0, 48, 0, 48, 0, 0, 152, -64, 0, 8, 0, 0, 80, -68, 0, 0, 48, 0, 48, -72, 0, -12, 0, 0, 104, 0, 0, 72, 0, 0, 0, 120, 0, -24, 0, 0, 0, 8, 0, 0, 0, 0, -96, -8, 0, 0, -168, 0, 0, 32, 0, -8, 96, 0, -16, 0, 0, -12, -120, 0, 0, -52, 0, -48, 56, 0, 0, 12, 0, -48, 0, 0, 0, -26, 0, 0, 0, 0, 0, -80, 0, 48, -32, 0, 0, 0, 0, 72, 0, 0, 0, -8, 0, 36, -24, 0, 16, -64, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, -176, -76, 0, 16, 0, 0, 0, 0, 0, 144, 0, 0, 0, -32, 0, 0, 0, 0, -32, -32, 0, -84, 0, 0, -168, 96, 0, 0, -16, 0, 132, -24, 0, -60, 0, 0, 8, 0, 0, -60, -56, 0, 0, -16, 0, 8, 0, 0, 0, 44, 0, 0, 0, 0, 16, 32, 0, 0, 184, 0, 0, -140, 0, 0, 96, 0, 64, 0, 0, -12, -36, 0, 0, 56, 0, -48, 96, 0, 0, 96, 0, -36, 0, 0, 0, 16, 0, 0, 0, 0, 0, -16, 0, -116, 156, 0, 0, 0, 0, -48, 0, 0, 0, 72, 0, -120, 80, 0, 56, -56, 0, 40, 0, 0, 0, 16, 0, 0, 0, 0, 32, -100, 0, -128, 0, 0, 0, 0, 0, 48, 0, 0, 0, -4, 0, 180, 0, 0, 8, -16, 0, -36, 0, 0, -112, -28, 0, 0, -48, 0, -48, 120, 0, -8, 0, 0, -56, 0, 0, -72, 72, 0, 0, 80, 0, -24, 0, 0, 0, -48, 0, 64, 0, 0, -64, -24, 0, 0, 32, 0, 0, 12, 0, 96, -72, 0, -80, 0, 0, -56, 156, 0, 0, 12, 0, -64, -72, 0, 0, -96, 0, 36, 0, 0, 0, 8, 0, 0, 0, 0, 0, 40, 0, 108, -92, 0, 0, 0, 0, -32, 0, 0, 0, -72, 0, -60, -192, 0, -136, 4, 0, -56, 0, 0, 0, 24, 0, 0, 0, 0, -32, 48, 0, 120, 0, 0, 0, 0, 0, 40, 0, 0, 0, 20, 0, 24, 0, 0, -40, 8, 0, 92, 0, 0, 88, -40, 0, 0, -120, 0, 48, -16, 0, -108, 0, 0, -132, 0, 0, 16, 0, 0, 0, 32, 0, 72, 0, 0, 0, 36, 0, -16, 0, 0, 16, -60, 0, 0, -24, 0, 0, 0, 0, 112, 120, 0, 80, 0, 0, -28, 152, 0, 0, -8, 0, -32, -24, 0, 0, -24, 0, 80, 0, 0, 0, 56, 0, 0, 0, 0, 0, 16, 0, -88, -180, 0, 0, 0, 0, 96, 0, 0, 0, -48, 0, -72, 0, 0, -48, -4, 0, -192, 0, 0, 0, -128, 0, 0, 0, 0, -64, 76, 0, -48, 0, 0, 0, 0, 0, 72, 0, 0, 0, -108, 0, -60, 0, 0, 136, 32, 0, 48, 0, 0, 120, -84, 0, 0, 40, 0, 44, 8, 0, -60, 0, 0, -104, 0, 0, -192, 0, 0, 0, 0, 0, 4, 0, 0, 0, 80, 0, -64, 0, 0, 16, 96, 0, 0, -40, 0, 0, 76, 0, 48, -16, 0, -72, 0, 0, 140, -20, 0, 0, -32, 0, -16, -32, 0, 0, -36, 0, -72, 0, 0, 0, -12, 0, 0, 0, 0, 0, -32, 0, -12, -48, 0, 0, 0, 0, -144, 0, 0, 0, -56, 0, 32, -48, 0, 80, -32, 0, 24, 0, 0, 0, 72, 0, 0, 0, 0, 0, 52, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, -168, 0, 0, -56, 96, 0, -108, 0, 0, 48, -72, 0, 0, 40, 0, -16, -96, 0, -8, 0, 0, 24, 0, 0, 48, -24, 0, 0, 96, 0, 28, 0, 0, 0, -68, 0, -96, 0, 0, 60, -16, 0, 0, 168, 0, 0, 40, 0, -120, 104, 0, -48, 0, 0, -100, -112, 0, 0, -36, 0, -120, -144, 0, 0, 24, 0, -20, 0, 0, 0, -68, 0, 0, 0, 0, 0, -96, 0, 60, -92, 0, 0, 0, 0, -64, 0, 0, 0, 32, 0, 64, -88, 0, -100, 38, 0, 56, 0, 0, 0, -48, 0, 0, 0, 0, 40, -28, 0, 112, 0, 0, 0, 0, 0, -40, 0, 0, 0, -100, 0, -24, 0, 0, 96, -8, 0, -60, 0, 0, 96, -92, 0, 0, -72, 0, -60, -24, 0, -108, 0, 0, -144, 0, 0, -64, -88, 0, 0, -32, 0, -16, 0, 0, 0, 96, 0, 96, 0, 0, -4, -120, 0, 0, -120, 0, 0, -148, 0, 144, 24, 0, -192, 0, 0, 0, 80, 0, 0, 124, 0, -96, 192, 0, 0, -180, 0, -76, 0, 0, 0, -108, 0, 0, 0, 0, 0, 88, 0, -136, 236, 0, 0, 0, 0, 96, 0, 0, 0, 120, 0, -96, 8, 0, -104, 120, 0, 16, 0, 0, 0, -96, 0, 0, 0, 0, -24, -76, 0, -72, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 24, 0, 0, -24, -32, 0, -48, 0, 0, 120, -40, 0, 0, 48, 0, -80, 16, 0, 0, 0, 0, 36, 0, 0, -52, 96, 0, 0, 0, 0, 16, 0, 0, 0, -12, 0, 96, 0, 0, -84, -60, 0, 0, 72, 0, 0, -44, 0, 24, -64, 0, 16, 0, 0, 64, -40, 0, 0, -8, 0, -16, -168, 0, 0, 56, 0, 60, 0, 0, 0, 72, 0, 0, 0, 0, 0, 48, 0, 4, 76, 0, 0, 0, 0, 160, 0, 0, 0, -96, 0, -64, 160, 0, -96, 78, 0, 48, 0, 0, 0, -48, 0, 0, 0, 0, 8, -20, 0, 56, 0, 0, 0, 0, 0, -84, 0, 0, 0, 56, 0, 36, 0, 0, -40, -80, 0, -44, 0, 0, -8, 56, 0, 0, -64, 0, -144, 40, 0, 100, 0, 0, 96, 0, 0, 0, 72, 0, 0, -96, 0, 116, 0, 0, 0, -64, 0, 0, 0, 0, -4, 16, 0, 0, -128, 0, 0, -148, 0, -112, -120, 0, 64, 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": "40.2.d.a", "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], [1, 0, 0, 0], [0, 0, -1, 1], [0, 0, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [1, -1, 1, 1], [-2, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [0, 2, -2, 2], [-2, 1, -2, -1], [0, 0, 0, 0], [0, 2, 0, -2], [-2, 2, 0, -2], [0, 0, 0, 0], [-2, 2, -4, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, -2, 0], [-3, 3, 1, -3], [0, 0, 0, 0], [0, 0, 0, 0], [4, -2, -2, 0], [0, 0, 0, 0], [2, -2, 4, 0], [-4, 4, 0, -4], [0, 0, 0, 0], [-2, -2, 2, -2], [4, 0, 0, 4], [0, 0, 0, 0], [4, 0, 2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [4, -4, 6, 2], [0, 0, 0, 0], [0, 0, 0, 0], [2, -2, 2, -2], [0, 0, 0, 0], [7, -1, 1, -1], [4, -2, 0, 2], [0, 0, 0, 0], [6, 1, 2, 3], [1, -1, 5, 1], [0, 0, 0, 0], [3, 2, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-4, -2, 0, 2], [8, 2, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 4, -4, 0], [0, 0, 0, 0], [8, 0, 4, 4], [2, -2, -4, 2], [0, 0, 0, 0], [4, -4, -2, 4], [-4, 2, 4, -2], [0, 0, 0, 0], [0, 0, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [9, 1, -1, 1], [0, 2, -8, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-2, -2, 2, -2], [0, 0, 0, 0], [-2, 2, 4, -2], [0, 0, 2, -2], [0, 0, 0, 0], [-8, 6, -8, -2], [-2, 2, -2, 2], [0, 0, 0, 0], [8, -4, 4, -4], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 2, 0, 2], [3, -1, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 1, -6, 7], [0, 0, 0, 0], [-4, 0, -4, 0], [2, 4, -4, 4], [0, 0, 0, 0], [-2, 2, -6, -2], [2, 2, -12, 4], [0, 0, 0, 0], [-2, 5, -6, -1], [0, 0, 0, 0], [0, 0, 0, 0], [-6, 6, 4, -6], [4, -2, -5, 3], [0, 0, 0, 0], [0, 0, 0, 0]]}