# Stored data for newform 144.2.x.b, downloaded from the LMFDB on 13 May 2024. {"label": "144.2.x.b", "space_label": "144.2.x", "level": 144, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505180208890000, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 510189560401720571, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [16, 16, 20, 8, 1]]], "qexp_display": "q+(\\zeta_{12}-\\zeta_{12}^{2}-\\zeta_{12}^{3})q^{2}+(-2+\\zeta_{12}^{2}+\\cdots)q^{3}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 144, "char_orbit_label": "x", "char_is_real": false, "Nk2": 576, "analytic_conductor": 1.1498457891064375, "hecke_ring_index": 1, "level_radical": 6, "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": "0.098", "prec": 17}, "analytic_rank_proved": true, "char_values": [144, 12, [127, 37, 65], [12, 9, 4]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [13, 61, 85, 133], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.956", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "47.795", "prec": 20}, {"__RealLiteral__": 0, "data": "7.117", "prec": 17}, {"__RealLiteral__": 0, "data": "918.859", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c12", "trace_display": [-2, -6, -8, -6], "traces": [0, 4, -2, -6, 0, -8, 6, -6, -8, 6, 0, -10, 0, -10, 8, 12, 8, -16, -12, -6, 16, 6, 18, 6, 12, 24, -8, 0, -8, -6, -12, -8, 8, 12, 14, 8, 0, 12, 6, 24, 8, 0, -12, -16, -4, -12, -12, -2, -24, -6, -18, 24, -20, -16, 18, 0, 16, 12, 0, 6, -24, -12, 16, 0, 0, 28, -36, 16, -12, -12, -8, 0, -12, 0, -12, -24, 0, 22, 12, -24, -16, -18, -12, -2, 12, 20, 18, 6, 4, 0, 36, 20, 12, 0, -32, 0, 0, -20, 12, -6, -24, -8, -30, -42, 48, -12, 24, -2, 0, 36, -28, -12, -24, 0, -18, 12, 0, -42, 0, 30, 0, 18, 12, 0, 24, -40, 12, -4, -16, 30, 64, -14, 24, 18, -4, 0, 32, 12, 24, -12, -8, 6, 32, 68, 48, 24, 22, 0, 24, 2, 48, -6, 0, -24, -40, 16, 12, -12, -24, 12, -48, -24, -18, -28, 12, 12, -4, -12, -24, -48, 0, -18, -28, -26, 0, -18, -32, 6, 4, 20, 24, 12, -12, 0, 0, -24, -36, 52, 0, -18, 0, -10, 0, -40, -14, -84, 24, 20, 54, 0, -36, -30, 24, 0, 24, 24, 12, 18, 16, 12, 24, 6, -40, -24, -90, 0, 0, 0, -36, -6, -32, 46, 12, 6, 16, 0, 0, -30, 12, 10, 0, -24, 24, 0, -12, 64, -12, 72, -44, -42, 48, -36, -12, 54, -24, 12, 18, 30, -8, 6, 40, -6, -12, -24, -16, -36, -32, 10, -36, -12, 0, 0, 32, -42, -12, 24, -24, 0, 32, 12, -72, 40, -32, -24, 14, -18, -36, 42, 0, 24, 0, 0, 60, 66, 16, 0, -28, -12, -24, 8, 0, 60, 32, 30, -30, -48, -48, -18, 0, -36, 36, 46, 4, 0, 0, 48, 48, -26, 44, 84, -72, 66, -96, 12, 0, 12, 0, 74, -24, 18, 32, 48, 36, 30, 0, -108, 28, -60, 12, -24, 60, 10, 8, 0, 16, -28, 48, -6, 22, 0, -40, -28, 36, 0, 28, -12, -16, -40, -12, -24, 36, 54, 0, -6, -6, -16, 8, -30, -20, 0, -24, 0, 72, -36, 32, -32, 0, 8, 0, 0, 0, 16, -24, -26, -78, 48, 64, 0, 0, -30, -24, 6, 56, -20, 48, -4, 80, -42, 0, 34, -72, -42, -12, 12, -60, 48, -60, -44, 16, -30, 96, 24, 6, 92, 16, 36, 0, -60, -60, -108, 12, -12, -12, 24, -36, 8, -16, -6, -18, -30, 0, -60, -24, -12, 64, -78, -48, -12, 88, -102, 20, -44, -72, -16, -16, -36, -24, -6, -54, 36, 64, 18, -16, 24, -24, -8, 72, 12, -16, -48, -90, -6, -96, 6, -18, -48, -12, 36, 0, 0, 0, -14, 60, -16, -24, 24, -22, 14, 24, -32, 72, 24, -36, 72, 0, -30, 56, 12, 84, 34, 48, -12, -18, 36, 12, 28, 0, 0, 72, 42, -60, -44, -36, 18, -12, -36, -64, -16, 0, 14, 64, 24, 30, 0, 24, 0, 24, 48, 36, -32, 36, 10, 64, 18, -20, 60, 60, 38, 24, 42, -128, 0, 0, -44, -28, 0, 12, 20, 72, -22, -16, -36, 24, -30, -12, 96, -60, -6, -12, -30, 0, -12, 16, -54, -8, -24, 12, -80, -104, 36, 132, 18, 24, 72, -24, 48, 24, -80, 60, 44, 16, -78, -20, 56, -60, 0, 0, 54, -32, 84, 12, -38, -12, 30, 24, 12, 0, 60, -52, 0, -24, 4, -12, 84, -64, 168, 0, -56, -24, 0, 36, 0, 48, 56, -54, -32, -4, -42, 60, 24, 12, 6, -64, 42, 8, -12, -48, 28, -24, 12, -24, -124, -36, -28, 26, -36, -48, 78, -60, -52, -80, -18, -12, 4, 24, 34, 38, -36, -24, -60, -48, 0, 48, 0, 16, 44, 48, 78, -36, 72, 64, -48, 90, 42, -48, -24, -30, 0, 36, 0, -120, 12, 28, -58, 108, -4, 0, 18, 56, -22, 0, -12, -48, -84, 0, 0, 0, -12, -16, -18, -52, 60, -48, 56, 12, 72, 104, -12, 48, 66, -8, 48, -60, -50, -36, -76, -40, 0, -8, 32, 0, 42, 32, 6, 0, 84, -24, -18, 12, 18, -12, 8, 0, -48, 64, -132, -66, 8, 48, 84, -128, -144, -16, 12, 60, -148, -68, 0, -32, -24, -96, 96, 44, 108, -60, -42, 36, -6, -80, -108, -88, 94, 0, -6, -76, 24, 0, -92, -18, 26, 0, -60, -40, -54, 48, -36, 0, -12, 52, 2, -120, 20, 8, -6, 36, 16, 0, -52, -78, 66, 24, -36, 12, -84, 0, 48, 40, -6, 0, -8, 32, 0, -12, 80, 54, 0, 28, -12, -24, 0, 72, -56, 60, -18, -48, 24, -48, 54, 80, 42, 144, 0, 24, 0, 44, -48, -52, -32, 48, -22, 48, 0, -48, -70, -36, 0, 64, -12, -16, 0, 108, -18, 0, -60, 84, 28, 96, 30, 4, 12, -24, -38, 24, -36, 72, -30, -24, 84, 72, 8, 8, -102, -112, 12, 6, -8, 0, -72, -72, 24, 0, 0, 72, 0, 12, 148, -84, -48, -80, -120, 78, 60, 0, 10, 0, 0, 8, 48, 96, 54, -8, 18, 40, -48, 72, 104, 14, -12, -8, 96, 24, 18, 0, -120, 0, 56, 0, 64, -68, -48, 48, 40, 54, -54, 92, 48, 6, -84, 72, -12, -16, 72, 0, 30, -12, -68, 32, 48, -6, 24, -36, 88, 6, -60, 96, -108, -12, 18, 36, 24, -16, -4, 24, -2, -10, -72, -20, 28, -54, 0, -48, 6, 56, 128, -84, 48, 32, -126, 0, -60, 144, -6, -8, -132, -14, 0, 144, 0, 36, -12, -8, 20, 0, 18, 72, 0, -68, 8, 0, 130, 54, -90, -88, 0, 0, -112, 36, 0, 64, 14, -96, 6, 24, -138, 0, 80, -60, -54, -24, -66, 108, 76, 0, -36, -40, 222, -96, -64, -84, -16, -72, 72, 0, 0, 0, 0, -12, 48, 12, -60, -96, 8, -16, 18, -16, 52, -12, -76, -44, 36, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 144, 24, 1, 12, 0]], "char_orbit_index": 24, "prim_orbit_index": 24, "minimal_twist": "144.2.x.b", "char_is_minimal": true, "conrey_index": 13, "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, 1, -1, -1], [-2, 0, 1, 0], [0, -2, 0, 0], [-2, -2, 0, 2], [1, -1, 1, 2], [-2, 1, 1, -1], [-2, 0, 0, 2], [3, 0, -3, 0], [-2, 0, 4, 2], [-3, 2, 1, 1], [0, 4, 0, -2], [-1, 1, -3, -4], [2, -2, 0, 2], [4, 2, -2, -4], [0, 0, 4, 0], [-4, 2, 0, -1], [-3, 0, 0, -3], [-1, 1, -1, 1], [4, 4, 0, 0], [3, -1, -3, 2], [3, -1, 3, 0], [1, -3, 1, 0], [4, -2, -2, -2], [8, 3, -4, -3], [-2, -8, 0, 4], [-3, 0, 6, 0], [-2, 4, 0, -2], [-2, -1, 1, -1], [0, -2, -6, -2], [-4, -2, 4, 4], [4, 4, -4, 0], [5, -5, -4, 1], [2, -5, 3, 3], [2, 0, 0, -2], [0, -6, 0, 6], [4, -2, -2, 4], [0, -1, 3, -1], [5, 2, 2, 5], [4, 4, -4, -8], [0, -3, 0, 0], [-4, 2, 2, -4], [-3, 5, -2, -2], [2, 6, -6, -2], [-6, 0, 6, 6], [-2, 2, -2, 2], [0, -5, -1, -5], [-4, 0, -4, 0], [-3, -2, 3, 4], [-1, 1, -7, -8], [8, -3, -4, 3], [-8, 2, 6, 6], [-6, 4, 4, -6], [6, 3, -3, 3], [2, 0, -4, -8], [4, -4, 0, 0], [3, -3, 0, 0], [0, -2, 0, 4], [4, 4, -5, 1], [-8, -8, 4, 4], [-6, 0, 6, -6], [2, 4, 4, 2], [-3, 0, 6, -3], [0, 0, 0, -8], [0, 6, 14, 6], [-9, 2, 0, -1], [3, -3, 2, 5], [-2, 8, -2, 0], [-3, 6, 0, -3], [0, 0, -4, 0], [-4, 0, 8, 4], [-6, 6, 6, 0], [-1, 0, 2, 8], [-4, 6, 2, -6], [-12, -3, 12, 6], [2, 2, -4, 2], [7, -7, -3, 4], [4, 12, -2, -12], [0, 0, -12, 0], [0, -8, -8, 0], [0, 0, -9, 0], [-3, 0, 0, 3], [0, -1, -1, 1], [4, -6, -2, 6], [4, 4, 2, -6], [3, -7, 3, 0], [3, 3, -3, 0], [0, -6, 2, -6], [0, 0, 0, 2], [6, 6, 6, 0], [6, -2, -2, 6], [0, -2, 6, -2], [4, 0, -8, -6], [-6, -6, -4, 10], [0, 2, 0, -4], [-4, -8, 8, 4], [0, 1, -10, 1], [1, 4, 4, 1], [-6, 9, 9, -6], [-6, -16, 0, 8]]}