# Stored data for newform 45.2.l.a, downloaded from the LMFDB on 21 May 2022. {"level_primes": [3, 5], "is_polredabs": true, "sato_tate_group": "1.2.3.c12", "rm_discs": [], "conrey_indexes": [2, 23, 32, 38], "cm_discs": [], "trace_hash": 418696286611927058, "level_radical": 15, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 12, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 0.3593268090957617, "inner_twist_count": 4, "field_disc_factorization": [[2, 24], [3, 12], [127, 4]], "is_rm": false, "char_order": 12, "level_is_square": false, "weight_parity": 1, "label": "45.2.l.a", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "45.2.l.a", "field_poly_is_cyclotomic": false, "dim": 16, "trace_zratio": {"__RealLiteral__": 0, "data": "0.375", "prec": 17}, "traces": [0, 16, -6, -6, 0, -6, 0, -2, 0, 0, -8, 0, -6, -2, 0, -6, -8, 0, 36, 0, 18, -12, -10, 18, 0, 4, 0, 18, -16, 0, 30, -4, 30, -12, 0, 0, -48, 4, -30, 0, 6, -24, 6, -2, 0, -36, 32, -12, -30, 0, -54, 36, -14, 0, 0, -16, 36, -6, -6, 0, 18, 8, 0, 36, 0, 66, 36, 4, 42, 0, 18, 0, 18, -8, 0, 42, 24, -6, -42, 0, 0, -48, 32, -66, 0, 22, -48, -18, 18, 0, -66, -40, -60, -18, 0, -36, -24, 28, 0, 0, -24, -12, -60, 34, 0, -6, 8, 0, 78, 0, 18, 48, 10, 96, 0, -20, 0, 48, 24, 0, 18, -48, 84, 18, 0, 0, 0, -80, -24, 0, -40, 48, 6, -6, 0, -30, -96, 24, -36, 0, -30, 72, -22, 0, 0, 36, 132, -6, -10, 0, 84, -40, 0, -42, 0, 36, 84, -20, -24, 0, 4, 0, -24, 4, 0, -18, -4, -60, -42, 0, 0, 48, 52, -72, 0, 22, -84, -72, -30, 0, -54, 104, -66, -42, 0, -42, -60, 8, 0, 0, 108, -36, -12, -26, 0, -60, 44, 0, 24, 0, -36, -96, 56, -6, 0, -10, 0, 72, 100, 0, -6, 32, 36, 30, 0, 0, 24, 92, 72, 0, -12, -48, 60, 40, 0, 36, -112, 66, 18, 0, 78, -24, 48, 0, 0, -20, -60, 96, 10, 0, 60, 8, 0, -36, 0, 36, -84, 12, -66, 0, -68, 0, -30, -28, 0, 24, -8, -24, 6, 0, 0, 24, -184, 78, 0, -68, 60, -66, -58, 0, 60, -64, 6, 42, 0, 60, -60, -62, 0, 0, -12, -48, -12, -38, 0, 18, -32, 0, -24, 0, -108, -48, -92, 6, 0, 24, 0, -54, -96, 0, -84, -4, 42, 96, 0, 0, 108, 52, 42, 0, 14, 180, 18, -38, 0, 30, 216, 54, 120, 0, 102, 96, 20, 0, 0, 4, 0, 12, -18, 0, -36, 68, 0, -114, 0, -114, 84, 40, -90, 0, 50, 0, -66, 24, 0, -72, 128, -186, 24, 0, 0, -84, 20, 24, 0, 44, 24, -24, 90, 0, 60, 64, -6, -24, 0, -48, -108, 70, 0, 0, -120, -96, 36, 100, 0, -144, 0, 0, -78, 0, -84, 0, 26, -114, 0, -22, 0, -30, -88, 0, -54, -28, -54, 24, 0, 0, 36, -224, 174, 0, 4, 48, 210, 56, 0, 174, -72, 84, 78, 0, 102, -84, -110, 0, 0, 40, 36, 96, -48, 0, 6, -88, 0, -66, 0, 66, -96, -52, -144, 0, 20, 0, -102, -44, 0, 84, -60, 42, -36, 0, 0, -84, 176, 72, 0, 42, -204, -18, -28, 0, 48, 88, 96, 156, 0, 48, -60, -2, 0, 0, 28, -276, 18, -14, 0, 48, 92, 0, -114, 0, -78, -60, 72, 72, 0, 84, 0, -36, 168, 0, -108, 44, -84, 72, 0, 0, 36, 196, 102, 0, 26, 216, 66, -54, 0, 108, -64, 90, 42, 0, 126, 216, 122, 0, 0, -160, -72, -66, 50, 0, -126, -52, 0, -36, 0, -66, 0, -22, -18, 0, -60, 0, -84, -128, 0, -96, -136, -24, -54, 0, 0, 48, -84, -126, 0, -116, 192, -78, -36, 0, 90, -160, -90, -42, 0, -54, 108, -122, 0, 0, 44, 180, -12, -84, 0, -84, -120, 0, -18, 0, -24, -12, -160, -156, 0, -44, 0, 60, -108, 0, -24, -4, 0, 0, 0, 0, 168, 16, -66, 0, 126, 12, 48, -16, 0, 114, 200, 162, -84, 0, 144, -60, -26, 0, 0, 48, 168, 30, 38, 0, -36, 116, 0, 60, 0, -54, 60, 76, 30, 0, 50, 0, -60, 196, 0, 54, 24, 24, -114, 0, 0, 156, 68, 66, 0, -8, -192, 12, 140, 0, -30, -112, -192, 78, 0, 30, -96, -8, 0, 0, -132, -12, 18, 64, 0, 36, -12, 0, 0, 0, -12, -72, 58, 126, 0, 20, 0, 12, 124, 0, -66, -40, 12, 60, 0, 0, 60, -60, 102, 0, 6, -108, -24, 46, 0, -66, -56, -102, 12, 0, -120, -36, -32, 0, 0, 160, -108, -60, 46, 0, -12, -136, 0, -24, 0, -120, -120, -34, 42, 0, 44, 0, 24, 168, 0, -78, -100, -120, 48, 0, 0, -276, 48, -66, 0, -4, -144, -60, -162, 0, -42, 224, 30, -246, 0, -168, 156, 88, 0, 0, 224, 0, 42, -56, 0, -36, 20, 0, 54, 0, 54, 36, 68, -42, 0, 42, 0, 0, -8, 0, 132, 128, 156, -42, 0, 0, -12, 148, -60, 0, -18, 36, -90, 12, 0, -108, -160, -12, 24, 0, 12, 84, 94, 0, 0, -160, 108, -36, 12, 0, 168, 52, 0, 42, 0, 240, 336, 34, 24, 0, -180, 0, 18, -220, 0, 216, -144, 66, 66, 0, 0, -24, -352, -72, 0, -46, 216, 60, 36, 0, -228, -256, 120, 42, 0, 126, 36, -72, 0, 0, -132, 360, -72, -68, 0, 54, -12, 0, 102, 0, 126, 276, -158, 96, 0, -62, 0, 54, -372, 0, 60, 64, 84, -54, 0, 0, -12, -60, -108, 0, -60, 24, 54, -14, 0, -48, 168, -222, -12, 0, -54, -120, -76, 0, 0, -56, -24, 6, 22, 0, 48, 164, 0, 48, 0, 48, -228, 70, 12, 0, 92, 0, 138, 136, 0, -84, 224, 150, 78, 0, 0, -120, 172, -66, 0, 84, -252, -96, 60, 0, -84, -16, -30, -102, 0, -234, -276, 148, 0, 0, -100, -264, 96, 50, 0, 102, -12, 0, 30, 0, 30, -288, 122, 48, 0, 46, 0, 108, 84, 0, 120, 24, -90, -210, 0, 0, -156, -128, -162, 0, -40, -252, -180, -40, 0, -96, -80, -36, -120, 0, -150, 108, -30, 0, 0, 296, -288, 30, -24, 0, 60, 72, 0, 144, 0, 210, 0, -62, 180, 0, -12, 0, 162, 0, 0, 108, 44, 42, -60, 0, 0, -108, 128, 102, 0, 100, 240, 84, 0, 0, -126, 32, -54, 144, 0, -72, 48, 28, 0, 0, 276], "hecke_ring_index_factorization": [], "field_poly": [1, 12, 72, 288, 502, -432, 144, -102, -93, 132, -72, 18, 34, -36, 18, -6, 1], "has_non_self_twist": 1, "char_values": [45, 12, [11, 37], [2, 3]], "Nk2": 180, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "l", "weight": 2, "trace_display": [-6, -6, -6, -2], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-\\beta _{5}q^{2}+(-1+\\beta _{9}-\\beta _{11}-\\beta _{12}+\\cdots)q^{3}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 2319475750231496196096, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [], "space_label": "45.2.l", "level": 45, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 0], [1, 1, 9, 4, -1, 6, 0], [1, 1, 45, 12, 1, 12, 0]], "char_degree": 4, "char_conductor": 45, "char_orbit_index": 12, "hecke_ring_generator_nbound": 3, "hecke_orbit_code": 755947798573, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.799", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1221.410", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "159903.933", "prec": 34}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "nf_label": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, -1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [-1, 1, -1, 0, 0, 1, 0, -1, 1, 0, -1, 1, 1, 0, 0, -1], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0], [1, -1, 1, 0, 0, 0, 0, 0, -1, -2, 0, 2, 1, 1, 1, -1], [0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -2], [1, -1, 1, 1, 0, -2, 0, 1, -1, -1, 2, -1, 0, 0, -1, -1], [-1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, -1, -1, -1, 0, 1], [-1, 0, 0, -2, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, -1, 0], [0, 1, -1, -1, -2, -1, -1, 0, 0, 2, 0, 0, 0, 2, -1, -1], [1, 0, 2, 1, 0, -2, -1, 1, -1, 0, 1, -1, -1, 0, -1, 0], [0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1, 0, 1], [-1, -1, 0, 1, -1, 0, -1, -2, 0, 0, -1, 1, 1, -1, 1, -1], [1, 0, -1, 1, 1, 1, 0, 1, 1, 0, 0, 1, -1, 0, 1, 1], [1, 2, 0, 1, 2, 1, 1, 0, 1, 0, 0, -1, 1, -2, 0, 1], [-2, 2, -2, 0, 1, 2, 2, -1, 2, 1, -2, 1, -1, -1, 2, 1], [0, 0, -2, -1, 0, 3, 1, 0, 2, 1, -2, 1, -2, -1, 1, 2], [1, -1, 0, -1, -2, -1, -1, 0, 0, -1, -1, 3, 1, 1, 0, -1], [-1, 0, 1, 0, 1, 1, 0, 1, 1, 0, -1, -1, 1, 0, 1, 1], [1, -3, -1, -1, -1, 0, 0, 0, -1, 0, 0, -1, 1, 0, 1, 1], [0, 2, -3, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1], [1, 0, 2, -1, 1, -1, -1, 2, -2, -1, 1, -1, -1, -1, -1, 1], [-3, 2, 0, -1, -2, -2, 0, -1, 0, 3, 0, -5, 0, -1, -4, 0], [2, 0, 0, 3, -1, -3, 0, -1, 0, 0, 1, 0, -2, 0, 0, -1], [-2, 1, -1, 0, 2, 2, 2, 0, 1, 0, 0, 0, -2, -1, 1, 1], [2, -1, 3, 0, -2, -3, -2, 0, -2, -1, 2, 0, 4, 2, -2, -2], [3, 1, 0, 2, 0, -1, -1, -1, -1, 1, 0, 3, -1, 1, 0, -1], [1, -2, 0, 1, 3, 1, 0, 0, 0, -4, 0, 1, 0, 0, 3, 0], [1, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0], [0, 1, 2, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, -1, -1, 0], [-1, -2, -1, -4, -1, 2, 1, -2, -1, 0, -1, 2, 1, 1, 1, -1], [-2, 0, -1, 0, 1, 1, 0, 0, 1, 2, 0, -4, -1, -1, 1, 1], [0, -1, 0, -1, -1, -2, 1, 2, 0, 0, 1, 2, -1, 1, -1, 1], [0, 0, 1, -1, -1, 1, 0, 1, -1, 0, 2, -1, 0, 0, -1, -1], [0, -2, 0, 1, -2, -3, -3, 0, -2, -3, 0, 0, 0, 3, -1, -4], [0, -1, 3, 3, 1, 0, 0, 1, -1, -3, 0, -1, 4, -1, 0, 0], [-1, 1, 2, 1, -1, -1, 0, 0, -2, 2, 0, -1, 2, 0, -1, -2], [0, 1, 0, 0, 3, 0, 2, 2, 0, 0, 2, 0, -2, 0, -1, 2], [0, 0, -2, -1, -1, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1], [0, 2, 0, -1, 0, 1, 1, 0, 1, -1, 0, 2, 0, 1, 0, 0], [0, -1, -2, 0, 0, -1, 0, 0, -2, -1, 0, 0, -1, 0, 0, -1], [-3, 1, 0, -3, 0, 1, 1, -1, -2, -1, 1, 2, 2, 1, 1, 0], [2, 0, 0, 1, 0, 0, -2, -1, 0, -1, -2, 1, 2, 1, 0, -2], [-3, 0, 0, 0, -1, 3, 0, 0, 1, 0, -3, 0, 3, 0, 1, -1], [-2, -2, -3, 2, 1, -1, -1, 0, -1, -2, 0, -3, -2, 1, 0, -3], [0, 0, -3, 0, 0, 1, 0, 0, 1, 0, 0, 0, -3, 0, 0, 1], [-3, 0, -3, 0, -1, 1, 2, 0, 1, 0, 0, 3, 1, 0, 3, 1], [0, 2, 0, -1, -1, 0, -1, -1, 0, 1, -1, -2, 1, 0, -2, -1], [1, 0, 0, 4, 1, 0, 0, 2, 2, 0, 1, 0, -1, 0, 2, 1], [2, 2, 6, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, -2, -2, 2], [-1, 0, 0, -3, 2, 4, 1, 1, 3, 4, -1, -1, -6, -2, 1, 6], [0, -2, 0, 0, -2, -2, -2, -1, 0, 0, -2, 1, 3, 1, 0, 0], [3, 0, 0, 1, 3, 1, 1, 0, 0, -1, 1, 1, -1, -1, 1, 1], [-2, 0, 3, 0, 1, 3, 0, 1, 3, 0, -1, -3, 2, 0, 3, 1], [-2, 1, 0, -1, 1, 2, 2, 0, 3, 2, 0, -2, -2, -4, -1, 5], [-1, 0, 2, -1, 0, 1, 1, -1, 0, 0, -1, 1, -3, 0, 1, 1], [-1, -2, 2, -2, -3, -3, -1, -2, -2, 0, 0, -4, 2, -1, -1, -2], [0, 0, 0, 3, 0, -3, 0, 0, 0, 3, 0, -4, 0, 0, -3, 0], [1, 0, -5, -1, -1, 1, 0, -3, 1, 0, 0, 5, -1, 0, 1, -1], [2, -2, -3, -1, -2, -1, -1, 0, -1, 0, 0, -2, 2, 2, 0, -1], [4, 1, 4, 2, -2, -9, -4, 2, -4, 1, 4, -2, 0, 2, -4, -1], [7, 1, -1, 2, 3, -3, 0, 0, -1, -1, 1, 3, -3, 0, 1, -1], [2, 1, 0, -2, 2, 2, 2, 2, 0, -1, 2, -1, -2, 0, 1, 2], [1, 0, -1, -2, -4, -6, 0, -3, -4, 0, 3, 1, -1, 0, -4, -4], [2, 5, 1, 3, 0, -3, -3, 0, 0, 0, 0, -2, 2, 0, -3, -3], [0, 0, -1, 2, 2, -4, 0, 2, -4, 0, 0, -2, -3, -2, 0, -1], [0, 1, -3, 1, 0, 0, 1, 0, 1, 0, 0, -2, 0, 1, 0, 0], [1, -2, 0, 0, 2, 2, 0, 1, 0, -4, 0, 1, 0, 1, 4, 0], [-1, 0, 3, 0, 2, 3, 0, 2, 0, 0, -2, -3, 1, 0, 0, 2], [1, -6, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3], [-3, 1, 1, 0, 3, 5, 3, 0, 3, 1, -3, 0, 5, -3, 3, 3], [2, 0, -6, -5, -2, 3, 3, 0, 2, 4, 0, 2, -4, -1, -1, 2], [3, 1, 0, -2, -3, -2, 0, 0, 0, 2, 0, 3, 0, 0, -3, 0], [-2, 0, -2, 1, -2, 1, 0, -3, 2, 0, -3, 2, 2, 0, 2, -2], [1, -7, 5, 0, 1, 1, 1, 0, -3, -6, 0, 6, 1, 0, 4, 0], [1, 4, 0, 3, 1, 1, -1, 2, 6, 3, 1, -2, -1, -1, -1, 1], [1, 1, 7, -1, 0, 0, 0, 3, 1, -2, 0, -1, 3, 2, -1, 1], [-6, 0, 0, 3, 0, 3, -3, -3, 0, 0, -3, 0, 3, 0, 3, -3], [1, 0, -1, -1, 2, 3, 0, -1, 1, 0, -2, 1, -1, 0, 1, 2], [-8, 3, -4, 0, 2, 2, 2, 0, 1, 3, 0, -4, -8, -2, 1, 2], [0, 2, 3, 0, -1, 0, 0, -1, 2, 1, 0, 1, 2, 1, 0, -1], [2, -1, 0, 3, 3, 4, 0, 1, 1, -2, -1, 2, 0, 0, 3, 1], [-2, -1, 0, 1, -1, -1, -1, -1, 0, 0, -1, 2, 1, 0, 0, -1], [2, 0, -3, 1, 3, 0, 0, 2, -1, 0, 1, 3, -2, 0, -1, 3], [0, 0, -3, -1, 0, 1, 1, 0, 0, -1, 0, -1, 0, 1, 1, 0], [0, -1, -8, -1, -3, -1, 0, -3, -2, -3, 0, 3, -1, 3, 0, -4], [-5, 1, 0, 2, -3, -1, -4, -1, 2, 0, -2, -2, 3, -1, -3, -2], [-5, 3, 0, -2, -1, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [-3, 0, 4, 0, 1, -3, 0, 0, -2, 0, 5, -4, 3, 0, -2, 1], [-5, 6, -6, -3, 0, 3, 3, 0, 3, 5, 0, -2, -5, 1, 0, 2], [1, -3, 5, 2, -2, -4, -1, -1, -6, -6, 1, 1, 6, 2, -1, -7], [2, -2, 4, 1, 2, -4, -3, 3, -3, 0, 3, -2, -1, 0, -5, 0], [-3, 0, 0, 0, 0, 0, 2, -1, 0, 2, 2, -2, -2, -3, 0, 2], [0, 0, 3, -2, 0, 0, 0, 0, -1, 0, 0, -3, 0, 0, -1, 0], [1, -1, 1, 0, 0, 0, 0, 0, -1, 3, 0, 2, 1, 1, 1, -1], [3, -1, 3, 0, -3, -3, -3, 0, -1, -1, 3, 0, 0, 3, -3, -2], [-4, 0, -2, -2, 5, 8, 2, -1, 2, -1, -2, 1, -4, -1, 2, 3]]}