# Stored data for newform 1014.2.i.b, downloaded from the LMFDB on 23 May 2025.
{"Nk2": 4056, "analytic_conductor": 8.096830764957831, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 6, "char_parity": 1, "char_values": [1014, 6, [677, 847], [6, 5]], "cm_discs": [], "conrey_index": 361, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[5, [9, 0, 1]], [7, [16, 0, -4, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504149416739830, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 2, 1, 2, 0], [1, 1, 13, 3, 1, 3, 0], [1, 1, 13, 5, 1, 6, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1014.2.i.b", "level": 1014, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 13], "level_radical": 78, "minimal_twist": "78.2.e.a", "nf_label": "4.0.144.1", "prim_orbit_index": 5, "qexp_display": "q+(-\\zeta_{12}+\\zeta_{12}^{3})q^{2}-\\zeta_{12}^{2}q^{3}+(1+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1014.2.i", "trace_display": [0, -2, 0, 0], "trace_hash": 1830147567866241296, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.837", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "86.990", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3077.461", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.515", "prec": 17}, "traces": [0, 4, 0, -2, 2, 0, 0, 0, 0, -2, -6, 0, -4, 0, -8, 0, -2, -6, 0, 0, 0, 0, 12, -12, 0, -16, 0, 4, 0, -6, -6, 0, 0, 0, 0, -12, 2, 0, 8, 0, -12, 0, 4, -20, 0, 0, 0, 0, -2, -6, 0, 12, 0, 12, 0, -36, -4, 0, 0, 0, 0, 14, 8, 0, -4, 0, -24, 0, 6, -12, 0, 0, 0, 0, -14, 8, 0, -48, 0, -16, 0, -2, 6, 0, 0, 0, 0, -6, -12, 0, 12, 0, -24, 0, 12, 12, 0, 0, 0, 0, -8, 30, 0, -56, 0, 24, 0, 12, 2, 0, 0, 0, 0, 6, -4, 0, -12, 0, 0, 0, 6, 50, 0, 0, 0, 0, 4, -8, 0, 40, 0, 0, 0, -8, 20, 0, 0, 0, 0, 8, 12, 0, 24, 0, 4, 0, -26, -6, 0, 0, 0, 0, 4, -6, 0, 48, 0, 20, 0, -6, -6, 0, 0, 0, 0, -36, 12, 0, 8, 0, 36, 0, 20, -12, 0, 0, 0, 0, 36, 12, 0, 28, 0, -28, 0, 42, 8, 0, 0, 0, 0, 24, 2, 0, 56, 0, -12, 0, 12, -20, 0, 0, 0, 0, 6, -18, 0, 24, 0, 48, 0, 32, 6, 0, 0, 0, 0, 16, -28, 0, -72, 0, 28, 0, 4, 8, 0, 0, 0, 0, -36, 24, 0, 24, 0, 72, 0, 8, 12, 0, 0, 0, 0, -2, -14, 0, -12, 0, 16, 0, -6, -24, 0, 0, 0, 0, -2, -6, 0, 56, 0, 12, 0, 12, -12, 0, 0, 0, 0, -36, -6, 0, 12, 0, -36, 0, 12, 34, 0, 0, 0, 0, 12, 28, 0, -24, 0, -24, 0, 16, -18, 0, 0, 0, 0, 0, 14, 0, -36, 0, 16, 0, -20, 30, 0, 0, 0, 0, -24, 28, 0, 120, 0, -40, 0, -12, -8, 0, 0, 0, 0, 12, 24, 0, -4, 0, 16, 0, -6, 24, 0, 0, 0, 0, 0, -60, 0, -92, 0, -12, 0, 48, -4, 0, 0, 0, 0, 60, 6, 0, 32, 0, -24, 0, 0, 36, 0, 0, 0, 0, 6, -30, 0, -100, 0, -156, 0, -4, -12, 0, 0, 0, 0, -58, 36, 0, 24, 0, -8, 0, -12, -8, 0, 0, 0, 0, 46, -20, 0, -156, 0, 72, 0, 0, -12, 0, 0, 0, 0, -8, 8, 0, -40, 0, 60, 0, 12, -84, 0, 0, 0, 0, -28, 0, 0, 72, 0, -16, 0, -48, 12, 0, 0, 0, 0, 24, -12, 0, 24, 0, 120, 0, -2, -26, 0, 0, 0, 0, -26, 28, 0, 12, 0, -144, 0, -108, -16, 0, 0, 0, 0, 36, -6, 0, 72, 0, -8, 0, -44, -6, 0, 0, 0, 0, -6, -24, 0, 72, 0, -80, 0, -10, 0, 0, 0, 0, 0, -6, -12, 0, 12, 0, 4, 0, -50, 84, 0, 0, 0, 0, -18, -36, 0, 36, 0, 72, 0, -24, 12, 0, 0, 0, 0, -12, -4, 0, -144, 0, -16, 0, -18, -52, 0, 0, 0, 0, 20, 72, 0, 24, 0, 132, 0, 68, 0, 0, 0, 0, 0, -26, -18, 0, -16, 0, -72, 0, -20, 12, 0, 0, 0, 0, -32, -14, 0, -168, 0, -136, 0, 14, -48, 0, 0, 0, 0, 42, -8, 0, -16, 0, 24, 0, 18, 0, 0, 0, 0, 0, 12, 12, 0, 88, 0, -48, 0, 48, 2, 0, 0, 0, 0, 24, -28, 0, -52, 0, 84, 0, 6, -16, 0, 0, 0, 0, 12, -36, 0, 40, 0, 96, 0, 74, 40, 0, 0, 0, 0, -64, -4, 0, -84, 0, -12, 0, -20, -18, 0, 0, 0, 0, 24, -12, 0, -144, 0, -116, 0, -24, 10, 0, 0, 0, 0, 32, -6, 0, -12, 0, -72, 0, 6, -6, 0, 0, 0, 0, -12, 48, 0, 0, 0, -32, 0, -84, -28, 0, 0, 0, 0, -48, 36, 0, -16, 0, 24, 0, -14, -36, 0, 0, 0, 0, 4, -26, 0, -16, 0, 72, 0, -56, 18, 0, 0, 0, 0, -54, 40, 0, 40, 0, 72, 0, 12, 24, 0, 0, 0, 0, -20, -12, 0, 120, 0, -56, 0, -36, 30, 0, 0, 0, 0, 8, -36, 0, -24, 0, 24, 0, 12, 0, 0, 0, 0, 0, 14, 24, 0, -56, 0, 4, 0, -60, -14, 0, 0, 0, 0, 120, 6, 0, 84, 0, -24, 0, -8, -54, 0, 0, 0, 0, -6, 28, 0, 48, 0, -120, 0, 68, -40, 0, 0, 0, 0, -56, -24, 0, 96, 0, 4, 0, 72, -6, 0, 0, 0, 0, 28, -28, 0, 24, 0, 144, 0, -6, -6, 0, 0, 0, 0, 12, 24, 0, 24, 0, -56, 0, 20, 60, 0, 0, 0, 0, -6, -156, 0, 144, 0, 72, 0, 102, -6, 0, 0, 0, 0, 24, -6, 0, -4, 0, -36, 0, 18, -80, 0, 0, 0, 0, 12, 34, 0, -68, 0, 36, 0, 0, 24, 0, 0, 0, 0, 40, -58, 0, 64, 0, -24, 0, -6, 28, 0, 0, 0, 0, -28, 12, 0, -84, 0, 104, 0, 12, 12, 0, 0, 0, 0, 16, -16, 0, 36, 0, -56, 0, -24, -12, 0, 0, 0, 0, -36, 66, 0, -32, 0, 0, 0, 96, 14, 0, 0, 0, 0, -24, 18, 0, 8, 0, -72, 0, -8, -18, 0, 0, 0, 0, -20, 88, 0, -60, 0, -96, 0, 72, -22, 0, 0, 0, 0, 32, 36, 0, 60, 0, 48, 0, 76, 28, 0, 0, 0, 0, 12, -60, 0, 216, 0, 188, 0, 20, 36, 0, 0, 0, 0, -12, 120, 0, 16, 0, -32, 0, -12, 108, 0, 0, 0, 0, 0, 36, 0, 60, 0, -24, 0, -138, 24, 0, 0, 0, 0, -120, 2, 0, 8, 0, -28, 0, -8, 216, 0, 0, 0, 0, -6, 36, 0, -48, 0, 240, 0, -76, 8, 0, 0, 0, 0, -10, -64, 0, -12, 0, 0, 0, 24, -60, 0, 0, 0, 0, 90, 46, 0, -60, 0, 72, 0, 6, -6, 0, 0, 0, 0, 48, 2, 0, 8, 0, -12, 0, 84, 72, 0, 0, 0, 0, 28, 42, 0, -128, 0, -120, 0, 36, 6, 0, 0, 0, 0, -90, -16, 0, 24, 0, -48, 0, 12, -40, 0, 0, 0, 0, 0, -128, 0, -72, 0, 336, 0, 20, 36, 0, 0, 0, 0, 80, 36, 0, -72, 0, -12, 0, 58, -30, 0, 0, 0, 0, 6, 50, 0, 0, 0, 116, 0, 78, -18, 0, 0, 0, 0, -4, -12, 0, 24, 0, 32, 0, -34, -90, 0, 0, 0, 0, 6, 48, 0, 136, 0, 116, 0, 0, 36, 0, 0, 0, 0, -36, -12, 0, -36, 0, 56, 0, 4, 108, 0, 0, 0, 0, -12, -16, 0, 16, 0, -264, 0, -56, -12, 0, 0, 0, 0, -70, -22, 0, 32, 0, -92, 0, 18, -20, 0, 0, 0, 0, 36, 78, 0, 0, 0, -88, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 28, 0, 18, -12, 0, 0, 0, 0, -18, 36, 0, -72, 0, 16, 0, -168, 8, 0, 0, 0, 0, 6, 20, 0, -40, 0, -300, 0, -30, 10, 0, 0, 0, 0, 12, -36, 0, 168, 0, -48, 0, 24, 62, 0, 0, 0, 0, 80, 24, 0, -60, 0, 56, 0, 16, 0, 0, 0, 0, 0, 60, -36, 0, 120, 0, -244, 0, 8, -20, 0, 0, 0, 0, -48, -42, 0, -24, 0, -80, 0, 8, -216, 0, 0, 0, 0, -24, 24, 0, 80, 0, -48, 0, -54, -12, 0, 0, 0, 0, -72, -12, 0, -64, 0, 48, 0, -60, -80, 0, 0, 0, 0, -2, -26, 0, 52, 0, -24, 0, -4, 8, 0, 0, 0, 0, 72, 0, 0, -12, 0, 52, 0, -24, 28, 0, 0, 0, 0, 10, -6, 0, -48, 0, 32, 0, 72, -24, 0, 0, 0, 0, -108, 0, 0, 32, 0, -120, 0, -84, 24, 0, 0, 0, 0, -46, 24, 0, -184, 0, -72, 0, 96, -6, 0, 0, 0, 0, 54, -36, 0, 96, 0, 192, 0, 4, 24, 0, 0, 0, 0, -44, -36, 0, 12, 0, 48, 0, -58, -52, 0, 0, 0, 0, 52, -60, 0, -48, 0, 12, 0, 18, -24, 0, 0, 0, 0, 16, -36, 0, -168, 0, 108, 0, 40, -12, 0, 0, 0, 0, -10, -60, 0, 0, 0, -20, 0, -36, -18, 0, 0, 0, 0, 48, 36, 0, -164, 0, 12, 0, -114, -12, 0, 0, 0, 0, 72, -6, 0, 112, 0, -60, 0, -2, 40, 0, 0, 0, 0, -50, -134, 0, -168, 0, -96, 0, 8, -78, 0, 0, 0, 0, 126, 62, 0, -8, 0, 36, 0, 12, -36, 0, 0, 0, 0, -32, -18, 0, -84, 0, -64, 0, -36, 72, 0, 0, 0, 0, -24, 58, 0, -24, 0, 72, 0, -24, -48, 0, 0, 0, 0, 12, -120, 0, -216, 0, 24, 0, 60, -4, 0, 0, 0, 0, -42, 72, 0, -24, 0, 120, 0, 8, -56, 0, 0, 0, 0, -18, 148, 0, 104, 0, -120, 0, -18, -28, 0, 0, 0, 0, -28, -46, 0, -120, 0, -40, 0, -32, 72, 0, 0, 0, 0, -78, -12, 0, 144, 0, 64, 0, -66, 36, 0, 0, 0, 0, 68, -30, 0, 0, 0, 112, 0, 12, -24, 0, 0, 0, 0, -12, 12, 0, -36, 0, 52, 0, -72, -18, 0, 0, 0, 0, -108, 8, 0, -72, 0, 16, 0, 36, -88, 0, 0, 0, 0, -20, -122, 0, -24, 0, 120, 0, 36, 30, 0, 0, 0, 0, -76, 8, 0, 24, 0, 64, 0, 84, -14, 0, 0, 0, 0, -40, 84, 0, 216, 0, -216, 0, 68, -36, 0, 0, 0, 0, 14, 28, 0, 96, 0, 0, 0, -96, -24, 0, 0, 0, 0, 36, -120, 0, -176, 0, -84, 0, -120, -8, 0, 0, 0, 0, -24, 8, 0, -96, 0, 48, 0, -12, -64, 0, 0, 0, 0, 18, -4, 0, 0, 0, 144, 0, -82, -100, 0, 0, 0, 0, 68, -24, 0, 168, 0, -24, 0, -38, 12, 0, 0, 0, 0, 12, -44, 0, 240, 0, -180, 0, 24, 60, 0, 0, 0, 0, 48, -36, 0, -4, 0, 72, 0, 26, 102, 0, 0, 0, 0, -48, -84, 0, -68, 0, -48, 0, 60, -28, 0, 0, 0, 0, 84, 26, 0, 164, 0, 56, 0, -42, 136, 0, 0, 0, 0, 6, -90, 0, 32, 0, -84, 0, 144, -72, 0, 0, 0, 0, 116, 16, 0, -216, 0, -24, 0, 16, -36, 0, 0, 0, 0, 36, -20, 0, 96, 0, 72, 0, -48, 24, 0, 0, 0, 0, 74, -36, 0, -80, 0, -12, 0, -42, -12, 0, 0, 0, 0, 36, 48, 0, -72, 0, 128, 0, -12, -4, 0, 0, 0, 0, 0, 42, 0, -88, 0, 0, 0, 6, 0, 0, 0, 0, 0, -20, 56, 0, 36, 0, -336, 0, -114, 56, 0, 0, 0, 0, -36, 6, 0, 132, 0, -48, 0, -12, -12, 0, 0, 0, 0, 36, 72, 0, 168, 0, -148, 0, 58, -40, 0, 0, 0, 0, -24, -84, 0, -20, 0, -72, 0, 0, 18, 0, 0, 0, 0, 48, 120, 0, 128, 0, -64, 0, 156, -6, 0, 0, 0, 0, -36, 6, 0, -144, 0, -24, 0, 36, 144, 0, 0, 0, 0, 6, 18, 0, 12, 0, 192, 0, 36, 2, 0, 0, 0, 0, -28, 44, 0, -100, 0, 24, 0, -84, 48, 0, 0, 0, 0, -16, 0, 0, 276, 0, 32, 0, 16, 6, 0, 0, 0, 0, -84, 18, 0, 56, 0, -72, 0, -72, 36, 0, 0, 0, 0, 18, 150, 0, 64, 0, 96, 0, 24, 36, 0, 0, 0, 0, -84, 8, 0, -48, 0, 120, 0, -12, -50, 0, 0, 0, 0, -14, 148, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, 1], [0, 0, -1, 0], [1, 0, -1, 0], [0, 0, 0, 3], [0, 1, 0, 0], [0, 2, 0, 0], [0, 0, 0, 1], [-1, 0, 1, 0], [0, 0, -3, 0], [0, -6, 0, 6], [-1, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 3, 0, -3], [0, 0, -1, 0], [-3, 0, 3, 0], [0, 0, 0, -1], [0, -2, 0, 0], [0, 3, 0, 0], [0, 0, 0, -2], [6, 0, -6, 0], [0, 0, -6, 0], [0, 1, 0, -1], [-4, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 2, 0, -2], [0, 0, -3, 0], [-3, 0, 3, 0], [0, 0, 0, -4], [0, 1, 0, 0], [0, 6, 0, 0], [0, 0, 0, -3], [-6, 0, 6, 0], [0, 0, 1, 0], [0, 7, 0, -7], [2, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, 0], [0, -3, 0, 3], [0, 0, 2, 0], [-10, 0, 10, 0], [0, 0, 0, 6], [0, -3, 0, 0], [0, 6, 0, 0], [0, 0, 0, -6], [-1, 0, 1, 0], [0, 0, -3, 0], [0, 4, 0, -4], [3, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, -1, 0, 1], [0, 0, -18, 0], [-2, 0, 2, 0], [0, 0, 0, 2], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3], [7, 0, -7, 0], [0, 0, 4, 0], [0, -2, 0, 2], [-1, 0, 0, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, -10, 0, 10], [0, 0, 3, 0], [-6, 0, 6, 0], [0, 0, 0, -6], [0, -6, 0, 0], [0, -1, 0, 0], [0, 0, 0, 13], [-7, 0, 7, 0], [0, 0, 4, 0], [0, -2, 0, 2], [-12, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 3, 0, -3], [0, 0, -1, 0], [3, 0, -3, 0], [0, 0, 0, -6], [0, -2, 0, 0], [0, -9, 0, 0], [0, 0, 0, -10], [-3, 0, 3, 0], [0, 0, -6, 0], [0, -18, 0, 18], [3, 0, 0, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, -4, 0, 4], [0, 0, 6, 0], [6, 0, -6, 0], [0, 0, 0, -1], [0, -14, 0, 0], [0, 3, 0, 0], [0, 0, 0, -6], [-4, 0, 4, 0]]}