# Stored data for newform 845.2.l.d, downloaded from the LMFDB on 19 April 2024. {"label": "845.2.l.d", "space_label": "845.2.l", "level": 845, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511554829910861, "dim": 12, "is_polredabs": true, "nf_label": "12.0.89539436150784.1", "trace_hash": 1789040408214432650, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [25, 5, 16, 7, 10, 3, 1]]], "qexp_display": "q+(-1+\\beta _{1}-\\beta _{7}+\\beta _{10})q^{2}-\\beta _{5}q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 65, "char_orbit_label": "l", "char_is_real": false, "Nk2": 3380, "analytic_conductor": 6.747358970798192, "hecke_ring_index": 16, "level_radical": 65, "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": [845, 6, [677, 171], [3, 1]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [5, 13], "conrey_indexes": [654, 699], "field_disc": 89539436150784, "field_disc_factorization": [[2, 16], [3, 6], [37, 4]], "field_poly": [4, -8, 8, -24, 20, 20, -8, 16, 4, -8, 2, -2, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.796", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "930.698", "prec": 24}, {"__RealLiteral__": 0, "data": "618.581", "prec": 24}, {"__RealLiteral__": 0, "data": "144061.399", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c6", "trace_display": [-6, 0, 4, 4], "traces": [0, 12, -6, 0, -10, 4, 0, 4, 36, 6, 2, 0, 0, 0, 16, -4, -10, 0, -20, 0, 14, 0, 0, 0, 0, -4, 0, 0, 4, 12, 8, 0, -22, 12, 0, -8, -22, 0, 0, 0, -68, 0, 0, 0, 0, 38, 0, -40, 0, 18, -22, -48, 0, 0, 0, 16, 40, 8, -24, 0, 8, -12, 0, 36, 132, 0, -32, -20, 0, -24, 40, 0, -90, -96, -4, 16, 0, 0, 0, 64, 58, -46, 0, -88, 0, -32, 0, 0, 0, 0, -140, 0, 0, -4, 32, 16, 0, 28, 50, 0, -2, -4, -8, 0, 0, -48, 0, 0, 0, 0, 36, 0, -40, 0, 8, -4, -24, 0, 0, 0, -40, -26, 32, 24, 0, 52, 40, 0, -50, 128, 0, 0, -12, 0, -96, 96, 0, 36, -8, 8, -16, 0, 0, 0, 252, -24, 44, 0, -64, 0, 40, 0, 0, 0, 0, -16, 0, 0, 24, 32, 58, 0, -106, -36, 0, 40, 24, -28, 0, 0, -48, 0, 0, 0, 0, -44, 0, 120, 0, -56, 54, -56, 0, 0, 0, -36, 40, 16, 36, 0, -8, -40, 0, 52, 104, 0, -140, -12, 0, 0, -124, 0, -4, 144, 0, -40, 0, 0, 0, -32, -8, 16, 0, 232, 0, 44, 0, 0, 0, 0, -128, 0, 0, 28, 16, 78, 0, -12, -4, 0, -88, 32, 120, 0, 0, -32, 0, 0, 0, 0, -20, 0, -52, 0, 12, -2, -48, 0, 0, 0, -86, 16, -56, -60, 0, -32, -10, 0, -60, 80, 0, -216, -72, 0, -72, -112, 0, 64, 232, 36, -16, 0, 0, 0, 168, -24, 32, 0, 224, 0, 4, 0, 0, 0, 0, -16, 0, 0, -110, -14, -60, 0, 112, -8, 0, 56, 108, -88, 0, 0, -64, 0, 0, 0, 0, -40, 0, 24, 0, 72, -76, -32, 0, 0, 0, 48, -8, -240, 88, 0, -44, -96, 0, -32, 180, 0, 80, 160, 0, 8, -136, 0, 36, -224, -40, 0, 0, 0, 0, 144, -8, -32, 0, 32, 0, -52, 0, 0, 0, 0, -16, 0, 0, 72, -32, 40, 0, -40, -136, 0, -10, -98, 24, 0, 0, 40, 0, 0, 0, 0, -72, 0, -72, 0, -16, 68, -64, 0, 0, 0, 24, -104, 240, 20, 0, 16, 204, 0, -4, -88, 0, 96, 78, 0, -12, 0, 0, 0, -320, 24, 30, 0, 0, 0, -184, -62, 24, 0, -96, 0, -56, 0, 0, 0, 0, -64, 0, 0, 36, 16, 0, 0, 144, -60, 0, 0, -144, -32, 0, 0, -32, 0, 0, 0, 0, 72, 0, 8, 0, -64, 100, 52, 0, 0, 0, 48, 208, -112, 60, 0, -180, -56, 0, -4, -64, 0, 80, -44, 0, 56, 248, 0, 48, -88, 60, 0, 0, 0, 0, 112, 12, -64, 0, -40, 0, -8, 0, 0, 0, 0, 32, 0, 0, 0, 34, -20, 0, -4, 72, 0, -22, 80, 40, 0, 0, -32, 0, 0, 0, 0, -106, 0, 16, 0, 0, -100, 304, 0, 0, 0, 8, -72, -4, -48, 0, 56, -40, 0, -32, 64, 0, 200, 120, 0, -16, -64, 0, -56, 232, 6, 32, 0, 0, 0, -272, 28, -80, 0, -392, 0, -40, 0, 0, 0, 0, 176, 0, 0, -164, 124, -80, 0, 60, 88, 0, 40, -112, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 152, 0, 92, 20, -192, 0, 0, 0, 64, -38, 224, -190, 0, 96, -32, 0, 88, -504, 0, -40, -132, 0, 8, 8, 0, 136, 136, -152, 88, 0, 0, 0, -224, -8, -124, 0, -152, 0, -34, 0, 0, 0, 0, 136, 0, 0, 100, -136, 8, 0, 92, 148, 0, -104, 56, -144, 0, 0, 44, 0, 0, 0, 0, 60, 0, 256, 0, 116, -44, 0, 0, 0, 0, -6, -12, 24, -100, 0, 168, 24, 0, 2, -48, 0, -96, -28, 0, 136, 112, 0, 64, -48, 16, 40, 0, 0, 0, -160, -32, 180, 0, 296, 0, 20, 0, 0, 0, 0, 96, 0, 0, -120, -128, -128, 0, -100, -92, 0, 116, 40, 8, 0, 0, 160, 0, 0, 0, 0, 8, 0, -128, 0, -88, 4, -104, 0, 0, 0, -8, 68, 192, -28, 0, -40, -56, 0, 116, -144, 0, 288, -20, 0, -8, 76, 0, -110, -96, -20, -132, 0, 0, 0, -108, -88, -112, 0, -8, 0, -12, 0, 0, 0, 0, 136, 0, 0, -164, -16, 32, 0, -76, -48, 0, 24, 40, 20, 0, 0, 112, 0, 0, 0, 0, 76, 0, 344, 0, -216, -56, 240, 0, 0, 0, -16, -200, -504, 40, 0, -144, 172, 0, 92, 80, 0, 16, 112, 0, 126, 96, 0, 4, 40, 8, 32, 0, 0, 0, -120, 120, 200, 0, 16, 0, 10, 0, 0, 0, 0, 96, 0, 0, 284, 140, -78, 0, 0, 100, 0, -48, -56, 44, 0, 0, 272, 0, 0, 0, 0, 76, 0, -360, 0, -12, 20, 176, 0, 0, 0, 80, 64, 112, 24, 0, -96, -42, 0, 0, -176, 0, 160, 44, 0, 192, -128, 0, -68, 224, -48, 24, 0, 0, 0, -240, 100, -16, 0, -168, 0, 88, 0, 0, 0, 0, 48, 0, 0, 140, -88, -40, 0, 100, -104, 0, 136, 36, 10, 0, 0, 128, 0, 0, 0, 0, 16, 0, -568, 0, 48, -48, 96, 0, 0, 0, 34, -80, 304, -16, 0, -144, 0, 0, -76, -600, 0, -96, -20, 0, 52, -64, 0, -128, 208, 88, -112, 0, 0, 0, -48, -80, 200, 0, -96, 0, 4, 0, 0, 0, 0, -48, 0, 0, 56, -256, -40, 0, -136, 72, 0, 56, 80, 164, 0, 0, 96, 0, 0, 0, 0, 56, 0, -192, 0, -40, -60, 132, 0, 0, 0, 4, -104, 56, -2, 0, 136, 0, 0, -120, -208, 0, -232, -144, 0, 88, 180, 0, -80, -88, 72, -4, 0, 0, 0, -16, 60, 56, 0, 168, 0, -40, 0, 0, 0, 0, 172], "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, 13, 3, 1, 3, 0], [1, 1, 65, 4, 1, 2, 0], [1, 1, 65, 12, 1, 6, 0]], "char_orbit_index": 12, "prim_orbit_index": 12, "minimal_twist": "65.2.b.a", "char_is_minimal": false, "conrey_index": 654, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0], [0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0], [4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 0], [1, 0, 2, 0, 0, -1, 0, 1, 0, -2, 0, -2], [0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, 1, -2, 0, -1, -1, 1, -1, 0], [-3, 2, -4, 0, 0, 0, 0, -3, 0, 4, 2, 0], [0, 0, 0, -1, 2, 0, 1, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, -1, 0, 3, -3, 0, 2, 1, 0], [0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, -1], [0, 0, 0, -2, -2, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3], [0, 0, 0, 0, -3, 2, 0, 0, 3, 0, 0, 0], [-1, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, -3, -1, 0, -4, 0, 0, 1], [1, -1, 1, 0, 0, 0, 0, 1, 0, -1, -1, 0], [3, 3, 3, 0, 0, 0, 0, 3, 0, -3, 3, 0], [0, 0, 0, -3, -2, 0, 0, -1, 0, -1, -1, 0], [0, 0, 0, -1, 0, -1, 3, 0, 1, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 5, 0, -4, -3, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 1, 0], [0, 0, 0, -1, 0, -1, 3, 0, 2, 0, 0, -3], [0, 0, 0, -1, 2, 0, 1, 1, 0, 1, -1, 0], [-5, 2, -4, 0, 0, 0, 0, -5, 0, 4, 2, 0], [1, 1, 3, 0, 0, 0, 0, 1, 0, -3, 1, 0], [0, 0, 0, 1, 0, 1, -2, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 3, -1, 0, 0, 0, -3, 0, 4, 0, 0, 3], [0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1], [0, 0, 0, 2, -2, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 2, -6, 0, 3, 0, 0, 6], [0, 0, 0, 1, -1, 0, 1, -5, 0, -4, 3, 0], [0, 0, 0, 2, 5, 0, -4, 0, 0, 0, 0, 0], [-3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 2, 0, -2, 0, 0, 0, 0, 0], [3, -2, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0], [-3, -1, 2, 0, -2, 0, 0, -3, 2, -2, -1, 4], [-4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, -2, 7, 0, 0, 2, 0, 0, 3], [3, -1, 1, 0, 0, -1, 0, 3, 0, -1, -1, 2], [0, 0, 0, 0, 0, 0, 0, -7, 0, 1, -1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0], [0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, 1, 0, 1, -1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 3, -1, 0], [0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 3], [5, -1, -3, 0, 0, 0, 0, 5, 0, 3, -1, 0], [12, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 5, 1, 0, 0, 0, 0, -3, 0, -1, 5, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 1, 0], [3, -1, -1, -1, 0, -1, 3, 0, 2, 0, 0, -3], [0, 0, 0, 4, -1, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 15, 0, 0, -5, 0], [-9, -1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 5, 1, 0], [2, -2, -2, 0, 4, -3, 0, 2, -4, 2, -2, 2], [0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, -3], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10, -4, 1, 0, 1, -2, 0, 10, -1, -1, -4, -8], [-6, 5, 5, 0, 0, 0, 0, -6, 0, -5, 5, 0], [0, 0, 0, 2, 2, 0, -8, 0, 0, 0, 0, 0], [-7, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 1, 6, 0, -2, 4, 0], [0, 0, 0, 0, 0, 0, -8, 0, -1, 0, 0, 8], [0, 0, 0, -3, -6, 0, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, -1, 0, 0, -4, 0, 0, -10], [0, 0, 0, 0, 4, -3, 0, 0, -4, 0, 0, 1], [-10, 5, 5, 0, 0, 0, -5, 0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, -3, 10, 0, -6, 0, 0, -10], [-1, -3, -1, 0, 0, 0, 0, -1, 0, 1, -3, 0], [5, -3, -1, 0, 0, 0, 0, 5, 0, 1, -3, 0], [0, 0, 0, 0, 0, 0, -1, -3, 0, 1, -1, 0], [0, 0, 0, -3, 0, -3, 3, 0, -1, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, -6, 0, 4, -6, 0], [0, 0, 0, 0, 0, 0, 0, -9, 0, 2, 3, 0], [0, 0, 0, -4, 0, -4, -4, 0, -1, 0, 0, 4], [0, 0, 0, 2, 4, 0, -8, 0, 0, 1, 1, 0]]}