# Stored data for newform 1014.2.b.e, downloaded from the LMFDB on 16 April 2024.
{"label": "1014.2.b.e", "space_label": "1014.2.b", "level": 1014, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014467262514166, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 625540834261423762, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [1, 0, 14, 0, 1]]], "qexp_display": "q+\\zeta_{12}q^{2}+q^{3}-q^{4}+(2\\zeta_{12}+\\zeta_{12}^{2}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 13, "char_orbit_label": "b", "char_is_real": true, "Nk2": 4056, "analytic_conductor": 8.096830764957831, "hecke_ring_index": 4, "level_radical": 78, "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": "0.518", "prec": 17}, "analytic_rank_proved": true, "char_values": [1014, 2, [677, 847], [2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 13], "conrey_indexes": [337], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.906", "prec": 17}, {"__RealLiteral__": 0, "data": "0.600", "prec": 17}, {"__RealLiteral__": 0, "data": "79.755", "prec": 20}, {"__RealLiteral__": 0, "data": "42.501", "prec": 20}, {"__RealLiteral__": 0, "data": "2313.737", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 4, 0, 0], "traces": [0, 4, 0, 4, -4, 0, 0, 0, 0, 4, -8, 0, -4, 0, -4, 0, 4, 16, 0, 0, 0, 0, 12, 4, 0, -8, 0, 4, 0, -4, -8, 0, 0, 0, 0, -20, -4, 0, -12, 0, 8, 0, -4, 4, 0, 0, 0, 0, 4, 12, 0, 16, 0, -12, 0, 12, 4, 0, 0, 0, 0, -16, 8, 0, -4, 0, 12, 0, -16, 4, 0, 0, 0, 0, 28, -8, 0, 0, 0, -24, 0, 4, -4, 0, 0, 0, 0, -4, -12, 0, -8, 0, -4, 0, -12, -36, 0, 0, 0, 0, 8, 20, 0, 68, 0, -20, 0, 20, -4, 0, 0, 0, 0, -40, -12, 0, 4, 0, 32, 0, 8, -4, 0, 0, 0, 0, -4, -16, 0, 4, 0, 40, 0, -24, -4, 0, 0, 0, 0, 16, 20, 0, -12, 0, 4, 0, -32, 12, 0, 0, 0, 0, 12, 16, 0, -8, 0, -32, 0, -12, -8, 0, 0, 0, 0, 12, -20, 0, 4, 0, -44, 0, -4, 24, 0, 0, 0, 0, -24, -12, 0, -56, 0, -16, 0, 32, 8, 0, 0, 0, 0, 0, -4, 0, 24, 0, -12, 0, 12, 36, 0, 0, 0, 0, -16, 64, 0, 4, 0, 24, 0, 24, 12, 0, 0, 0, 0, -16, 8, 0, -12, 0, 28, 0, -4, -8, 0, 0, 0, 0, 28, 0, 0, -24, 0, 12, 0, -24, -28, 0, 0, 0, 0, 4, 16, 0, -4, 0, -8, 0, 24, -40, 0, 0, 0, 0, 4, -72, 0, 4, 0, -4, 0, 36, -12, 0, 0, 0, 0, 8, -8, 0, 16, 0, 20, 0, -4, 16, 0, 0, 0, 0, -12, -68, 0, -36, 0, 68, 0, 8, 32, 0, 0, 0, 0, 64, -28, 0, -32, 0, 8, 0, 20, 20, 0, 0, 0, 0, 0, 68, 0, -28, 0, 40, 0, -20, 24, 0, 0, 0, 0, 20, 32, 0, -4, 0, -40, 0, 4, 24, 0, 0, 0, 0, -24, -92, 0, 28, 0, -40, 0, -48, -12, 0, 0, 0, 0, 84, 4, 0, 56, 0, 12, 0, 32, -36, 0, 0, 0, 0, 8, 28, 0, -4, 0, -52, 0, -52, 4, 0, 0, 0, 0, -48, 36, 0, 12, 0, -4, 0, 36, -16, 0, 0, 0, 0, -40, 4, 0, 36, 0, -20, 0, 40, 16, 0, 0, 0, 0, -24, -8, 0, -4, 0, -20, 0, 28, -108, 0, 0, 0, 0, -68, 32, 0, -4, 0, 16, 0, -56, 20, 0, 0, 0, 0, -80, -12, 0, -20, 0, -68, 0, 4, 4, 0, 0, 0, 0, -32, 36, 0, 12, 0, 104, 0, -72, 80, 0, 0, 0, 0, 84, 40, 0, 28, 0, 12, 0, 8, 16, 0, 0, 0, 0, -4, -8, 0, -12, 0, -88, 0, -32, -32, 0, 0, 0, 0, -12, 4, 0, -8, 0, -8, 0, 4, 48, 0, 0, 0, 0, 0, -28, 0, -40, 0, 12, 0, -24, -20, 0, 0, 0, 0, 60, 4, 0, 48, 0, 16, 0, -44, -20, 0, 0, 0, 0, -4, 72, 0, 24, 0, 48, 0, 28, -40, 0, 0, 0, 0, 20, 48, 0, 24, 0, -24, 0, 4, -12, 0, 0, 0, 0, -32, -56, 0, -8, 0, 4, 0, -16, 24, 0, 0, 0, 0, 32, -16, 0, 8, 0, -20, 0, -20, -112, 0, 0, 0, 0, 12, 16, 0, 20, 0, 0, 0, 136, -4, 0, 0, 0, 0, 16, 24, 0, 32, 0, 32, 0, -12, 0, 0, 0, 0, 0, 12, -116, 0, 36, 0, -24, 0, 4, -64, 0, 0, 0, 0, -80, -12, 0, 68, 0, -16, 0, -28, 64, 0, 0, 0, 0, 8, 4, 0, -48, 0, 68, 0, 24, 32, 0, 0, 0, 0, 24, -48, 0, 12, 0, 12, 0, 8, 0, 0, 0, 0, 0, -60, -8, 0, -96, 0, -16, 0, -56, 8, 0, 0, 0, 0, 56, -12, 0, -80, 0, 20, 0, 28, 68, 0, 0, 0, 0, -4, -84, 0, -8, 0, -168, 0, 24, 44, 0, 0, 0, 0, 88, -16, 0, 4, 0, 28, 0, -24, 0, 0, 0, 0, 0, -8, -24, 0, -56, 0, 60, 0, 12, 4, 0, 0, 0, 0, -24, 24, 0, -28, 0, 12, 0, 44, 104, 0, 0, 0, 0, 56, 104, 0, 20, 0, 4, 0, 76, 16, 0, 0, 0, 0, -72, -4, 0, -32, 0, 36, 0, -8, -100, 0, 0, 0, 0, 24, 68, 0, -40, 0, 52, 0, 56, 8, 0, 0, 0, 0, -16, 0, 0, -8, 0, 4, 0, -24, -72, 0, 0, 0, 0, -24, 4, 0, 60, 0, 24, 0, -4, 12, 0, 0, 0, 0, 36, 24, 0, -12, 0, 40, 0, -36, 136, 0, 0, 0, 0, 60, 108, 0, 88, 0, 8, 0, -152, -8, 0, 0, 0, 0, -104, 16, 0, -64, 0, -64, 0, 20, 0, 0, 0, 0, 0, -4, 0, 0, 16, 0, 24, 0, -72, -24, 0, 0, 0, 0, -64, -20, 0, -24, 0, -12, 0, -12, -68, 0, 0, 0, 0, 52, -36, 0, -40, 0, -140, 0, 68, -4, 0, 0, 0, 0, 8, 16, 0, 32, 0, -8, 0, 24, 84, 0, 0, 0, 0, 12, -48, 0, -144, 0, 64, 0, 96, -28, 0, 0, 0, 0, 0, -32, 0, 4, 0, -24, 0, 8, -72, 0, 0, 0, 0, 20, -104, 0, 20, 0, -24, 0, 96, -40, 0, 0, 0, 0, -24, -28, 0, -96, 0, 0, 0, -36, 68, 0, 0, 0, 0, 24, -28, 0, 60, 0, 76, 0, 40, -12, 0, 0, 0, 0, -20, -48, 0, 24, 0, 72, 0, 28, 0, 0, 0, 0, 0, 120, 68, 0, 60, 0, 20, 0, -92, 32, 0, 0, 0, 0, 24, -4, 0, -36, 0, -16, 0, -40, 48, 0, 0, 0, 0, 4, 128, 0, 24, 0, -176, 0, 28, 8, 0, 0, 0, 0, 120, -128, 0, -24, 0, -24, 0, 40, -92, 0, 0, 0, 0, 8, 28, 0, 220, 0, 92, 0, -40, -48, 0, 0, 0, 0, -48, -4, 0, -12, 0, 72, 0, -124, -104, 0, 0, 0, 0, -4, -100, 0, 144, 0, 84, 0, -68, 4, 0, 0, 0, 0, -192, 56, 0, -36, 0, 8, 0, 12, 32, 0, 0, 0, 0, 32, 48, 0, -36, 0, -72, 0, 8, -76, 0, 0, 0, 0, -248, -8, 0, 60, 0, 8, 0, 92, 28, 0, 0, 0, 0, -16, -4, 0, 8, 0, -144, 0, -52, -20, 0, 0, 0, 0, -52, 36, 0, 4, 0, 0, 0, -16, 132, 0, 0, 0, 0, 24, 208, 0, 184, 0, -48, 0, 96, 36, 0, 0, 0, 0, 84, 12, 0, 20, 0, 68, 0, -4, 92, 0, 0, 0, 0, 36, -64, 0, -16, 0, -80, 0, -104, -68, 0, 0, 0, 0, -20, -8, 0, -8, 0, -40, 0, -32, 4, 0, 0, 0, 0, -12, 36, 0, -48, 0, 92, 0, -20, -64, 0, 0, 0, 0, 40, -64, 0, 16, 0, 28, 0, -92, -60, 0, 0, 0, 0, 32, -56, 0, -52, 0, -24, 0, -48, -8, 0, 0, 0, 0, 92, -4, 0, -20, 0, -64, 0, -20, 0, 0, 0, 0, 0, 28, 60, 0, -108, 0, -48, 0, 72, -4, 0, 0, 0, 0, -80, 0, 0, -44, 0, -68, 0, 56, 32, 0, 0, 0, 0, 28, -4, 0, -124, 0, 92, 0, 16, -40, 0, 0, 0, 0, -56, 88, 0, 20, 0, 80, 0, -24, -24, 0, 0, 0, 0, -64, 152, 0, -96, 0, -80, 0, 116, -12, 0, 0, 0, 0, 48, -20, 0, 0, 0, -32, 0, -68, 64, 0, 0, 0, 0, 4, -124, 0, 4, 0, 72, 0, 68, 40, 0, 0, 0, 0, 24, -56, 0, -4, 0, -32, 0, -24, 36, 0, 0, 0, 0, 4, 12, 0, 120, 0, -80, 0, 104, 96, 0, 0, 0, 0, -72, 24, 0, 80, 0, 92, 0, -12, -72, 0, 0, 0, 0, -28, -48, 0, -52, 0, 84, 0, -160, 40, 0, 0, 0, 0, 96, 28, 0, 48, 0, -96, 0, 12, -96, 0, 0, 0, 0, 8, -12, 0, 16, 0, 112, 0, 120, -140, 0, 0, 0, 0, -84, -84, 0, -128, 0, -4, 0, 56, -8, 0, 0, 0, 0, -56, -12, 0, 92, 0, 80, 0, -88, -12, 0, 0, 0, 0, -32, 28, 0, -32, 0, 108, 0, 36, 36, 0, 0, 0, 0, 80, 12, 0, -40, 0, -12, 0, -56, 4, 0, 0, 0, 0, 56, -8, 0, -56, 0, -28, 0, -8, -32, 0, 0, 0, 0, 4, 104, 0, 48, 0, 96, 0, 16, 52, 0, 0, 0, 0, 220, -76, 0, 52, 0, 0, 0, -4, -28, 0, 0, 0, 0, -16, -40, 0, -48, 0, -184, 0, 12, 152, 0, 0, 0, 0, -24, 48, 0, -20, 0, -36, 0, -56, 8, 0, 0, 0, 0, -12, -200, 0, -12, 0, 60, 0, 132, 4, 0, 0, 0, 0, 172, 48, 0, -36, 0, -24, 0, 16, 176, 0, 0, 0, 0, -44, -52, 0, -20, 0, -164, 0, 60, 120, 0, 0, 0, 0, -20, 40, 0, 168, 0, -4, 0, 80, 72, 0, 0, 0, 0, -36, 24, 0, -40, 0, 128, 0, 48, 20, 0, 0, 0, 0, 28, -44, 0, -40, 0, 88, 0, -16, -24, 0, 0, 0, 0, -20, -148, 0, -156, 0, 20, 0, 64, 48, 0, 0, 0, 0, -36, 24, 0, -12, 0, 8, 0, -24, -88, 0, 0, 0, 0, 4, -196, 0, -12, 0, -72, 0, -204, 20, 0, 0, 0, 0, 8, 56, 0, -28, 0, -32, 0, 108, -56, 0, 0, 0, 0, -72, -8, 0, 104, 0, 60, 0, 4, -24, 0, 0, 0, 0, -16, 68, 0, 24, 0, -32, 0, 120, -160, 0, 0, 0, 0, 4, -48, 0, -96, 0, 32, 0, 0, -16, 0, 0, 0, 0, -56, 8, 0, 56, 0, 112, 0, -20, -272, 0, 0, 0, 0, -20, 100, 0, -112, 0, -96, 0, -160, -68, 0, 0, 0, 0, -4, 80, 0, 100, 0, 12, 0, -92, 16, 0, 0, 0, 0, 20, 20, 0, -128, 0, 32, 0, 0, 68, 0, 0, 0, 0, 136, 20, 0, -4, 0, 24, 0, -4, 236, 0, 0, 0, 0, -96, 156, 0, 32, 0, 16, 0, 104, 24, 0, 0, 0, 0, 260, 32, 0, -68, 0, -36, 0, 32, -16, 0, 0, 0, 0, -12, 152, 0, 0, 0, 88, 0, -72, -104, 0, 0, 0, 0, -200, -80, 0, 72, 0, 12, 0, -80, -116, 0, 0, 0, 0, -108, 36, 0, 96, 0, 4, 0, -24, 40, 0, 0, 0, 0, 4, -84, 0, -64, 0, -40, 0, 148, 12, 0, 0, 0, 0, -28, -96, 0, 116, 0, -80, 0, -124, -12, 0, 0, 0, 0, -64, 68, 0, -8, 0, -16, 0, -16, 48, 0, 0, 0, 0, -28, 72, 0, 64, 0, -32, 0, 132, 40, 0, 0, 0, 0, 132, 4, 0, 60, 0, 8, 0, -12, 4, 0, 0, 0, 0, 12, -48, 0, -76, 0, 12, 0, 68, 88, 0, 0, 0, 0, 24, 88, 0, 32, 0, -220, 0, 32, 80, 0, 0, 0, 0, 112, 40, 0, -128, 0, 24, 0, -120, -48, 0, 0, 0, 0, -284, 12, 0, 48, 0, -4, 0, 12, 8, 0, 0, 0, 0, 8, -100, 0, 0, 0, -96, 0, -228, 8, 0, 0, 0, 0, 168, 124, 0, -4, 0, -60, 0, -48, -8, 0, 0, 0, 0, -112, -96, 0, 68, 0, -48, 0, -16, -156, 0, 0, 0, 0, -56, 0, 0, 8, 0, 28, 0, 0, 100, 0, 0, 0, 0, 40, 108, 0, -48, 0, 56, 0, -256, -12, 0, 0, 0, 0, 152, -80, 0, 24, 0, -108, 0, 20, -12, 0, 0, 0, 0, 28, 44, 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, 13, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "78.2.i.a", "char_is_minimal": false, "conrey_index": 337, "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, 0, 0], [1, 0, 0, 0], [-1, 0, 0, 0], [0, 2, 1, 0], [0, 1, 0, 0], [0, 1, 1, 0], [0, -1, 0, 0], [1, 0, 0, 0], [-2, 0, 0, -1], [0, -3, 1, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, -1], [0, 2, 1, 0], [1, 0, 0, 0], [4, 0, 0, 1], [0, 1, 0, 0], [0, 3, 1, 0], [0, -2, -1, 0], [0, 1, 1, 0], [3, 0, 0, -1], [1, 0, 0, -3], [0, -1, 0, 0], [-2, 0, 0, -4], [0, 0, 0, 0], [1, 0, 0, 0], [0, -1, -1, 0], [-1, 0, 0, -2], [-2, 0, 0, -1], [0, -2, 2, 0], [0, 1, 0, 0], [0, -3, 1, 0], [0, 4, 1, 0], [-5, 0, 0, -3], [-1, 0, 0, 0], [0, -7, 2, 0], [-3, 0, 0, -1], [0, 0, 0, 0], [2, 0, 0, 1], [0, 1, -6, 0], [-1, 0, 0, -1], [1, 0, 0, 5], [0, 3, -1, 0], [0, 2, 1, 0], [0, 1, -3, 0], [0, 3, -3, 0], [1, 0, 0, 0], [3, 0, 0, -2], [0, -2, -4, 0], [4, 0, 0, 1], [0, 0, 0, 0], [-3, 0, 0, -2], [0, 1, 0, 0], [3, 0, 0, 1], [1, 0, 0, 1], [0, 3, 1, 0], [0, -1, -2, 0], [0, -8, 0, 0], [0, -2, -1, 0], [-4, 0, 0, -3], [2, 0, 0, -2], [0, 1, 1, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, -1], [0, 1, 7, 0], [-4, 0, 0, -1], [1, 0, 0, -3], [0, -5, -3, 0], [0, 3, 1, 0], [0, -1, 0, 0], [0, 8, -1, 0], [7, 0, 0, -2], [-2, 0, 0, -4], [0, -3, -1, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-6, 0, 0, 2], [0, 2, 1, 0], [1, 0, 0, 0], [-1, 0, 0, 6], [0, 5, -3, 0], [0, -1, -1, 0], [0, 11, 6, 0], [0, 1, 5, 0], [-1, 0, 0, -2], [-3, 0, 0, 1], [0, 6, 2, 0], [-2, 0, 0, -1], [0, 0, 0, 0], [-1, 0, 0, 3], [0, -2, 2, 0], [-3, 0, 0, 3], [-9, 0, 0, -5], [0, 1, 0, 0], [0, -6, 0, 0], [0, 3, -2, 0], [0, -3, 1, 0], [2, 0, 0, 4]]}