# Stored data for newform 1638.2.j.i, downloaded from the LMFDB on 25 April 2024.
{"label": "1638.2.j.i", "space_label": "1638.2.j", "level": 1638, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029415527810662, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 149967398693796722, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [0, 1]], [11, [25, 5, 1]], [17, [49, -7, 1]]], "qexp_display": "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}+(-2-\\zeta_{6})q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "j", "char_is_real": false, "Nk2": 6552, "analytic_conductor": 13.079495851085728, "hecke_ring_index": 1, "level_radical": 546, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [1638, 3, [911, 703, 379], [3, 2, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [235, 1171], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "2.060", "prec": 17}, {"__RealLiteral__": 0, "data": "0.285", "prec": 17}, {"__RealLiteral__": 0, "data": "13.638", "prec": 20}, {"__RealLiteral__": 0, "data": "3.102", "prec": 17}, {"__RealLiteral__": 0, "data": "135.868", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 0, 0, -5], "traces": [0, 2, 1, 0, -1, 0, 0, -5, -2, 0, 0, -5, 0, -2, -1, 0, -1, 7, 0, -7, 0, 0, -10, 2, 0, 5, -1, 0, 4, 18, 0, 0, 1, 0, 14, 0, 0, -4, 7, 0, 0, -8, 0, 4, -5, 0, -2, -3, 0, 11, 10, 0, 1, 1, 0, 0, 5, 0, 9, 7, 0, -13, 0, 0, 2, 0, 0, -3, 7, 0, 0, -18, 0, 10, 4, 0, 14, 20, 0, -14, 0, 0, -4, -32, 0, 0, 2, 0, 5, -12, 0, 5, -4, 0, 3, 0, 0, 12, -2, 0, 5, -6, 0, 10, 2, 0, 2, 0, 0, -8, 0, 0, 1, -2, 0, 0, -9, 0, 14, -28, 0, -14, 13, 0, 0, 0, 0, 44, 1, 0, 0, 18, 0, 7, -6, 0, -7, -12, 0, 32, 0, 0, -9, 5, 0, 0, 20, 0, 8, 10, 0, 17, 7, 0, 25, 0, 0, -11, 14, 0, 0, -2, 0, -13, 4, 0, -16, 10, 0, 2, 0, 0, -2, -13, 0, -20, 10, 0, 12, -10, 0, -22, 1, 0, -2, 0, 0, 35, 6, 0, 0, -12, 0, 8, 6, 0, -13, -44, 0, -18, -5, 0, -12, -45, 0, 0, -10, 0, 1, 70, 0, -52, 1, 0, 0, 0, 0, 0, -16, 0, 0, -7, 0, -2, -4, 0, -1, 12, 0, -18, 0, 0, -18, -3, 0, 0, 7, 0, -35, 2, 0, 0, 14, 0, 26, 0, 0, 7, 0, 0, 0, -36, 0, -20, 22, 0, -1, -14, 0, 4, 0, 0, -18, -4, 0, 0, -28, 0, -3, 23, 0, -3, -14, 0, -24, 25, 0, -19, 16, 0, 0, 48, 0, 10, 9, 0, 10, 20, 0, -32, 0, 0, 10, 60, 0, 0, 4, 0, -10, -2, 0, -10, 34, 0, -7, 0, 0, 38, 5, 0, 0, 20, 0, 6, -22, 0, 28, 26, 0, -45, 0, 0, 8, -98, 0, -5, 13, 0, 8, 3, 0, -4, 16, 0, 5, 0, 0, -66, 1, 0, 0, 0, 0, -20, -4, 0, 13, -16, 0, 4, -25, 0, 5, 2, 0, 0, 24, 0, -20, 0, 0, -30, -11, 0, -4, 0, 0, -2, 2, 0, 0, -4, 0, 21, -35, 0, 3, -18, 0, -8, 0, 0, 12, 8, 0, 0, 16, 0, -6, -23, 0, 28, -11, 0, -22, 0, 0, 2, -36, 0, -10, -38, 0, 0, -6, 0, -9, 40, 0, 4, 0, 0, -20, -28, 0, 0, -1, 0, 35, -52, 0, 76, -26, 0, -1, -35, 0, 13, 0, 0, 0, -16, 0, -22, 0, 0, -8, 14, 0, 22, 0, 0, -14, -4, 0, 0, -1, 0, -5, -8, 0, 20, 1, 0, 24, 0, 0, 10, 18, 0, 0, 16, 0, 64, -9, 0, 3, -6, 0, 12, 0, 0, -7, -10, 0, -70, -7, 0, 1, -11, 0, 4, 0, 0, 28, 0, 0, 5, 13, 0, 0, 44, 0, 63, -7, 0, 0, 45, 0, -40, 0, 0, -18, 48, 0, 0, -10, 0, -22, 24, 0, -40, -2, 0, 14, 0, 0, 30, -16, 0, 0, -38, 0, -26, -36, 0, -8, 0, 0, 19, 0, 0, -35, 8, 0, 0, 3, 0, 46, -65, 0, -16, 3, 0, -7, 0, 0, -76, -12, 0, -25, -63, 0, 14, -38, 0, -16, 18, 0, -4, 0, 0, 24, -12, 0, 0, 20, 0, 18, -31, 0, 32, 5, 0, 4, 20, 0, 14, 32, 0, 0, 80, 0, 5, -10, 0, 30, 90, 0, 0, 0, 0, -4, 0, 0, 0, -20, 0, 2, -16, 0, 50, -2, 0, 17, 0, 0, 14, -14, 0, 0, 3, 0, -8, 19, 0, -20, 12, 0, 20, 0, 0, 40, 12, 0, -25, -6, 0, -11, -56, 0, -32, 14, 0, -26, 0, 0, -11, -90, 0, 0, 18, 0, -18, 10, 0, -49, -6, 0, 35, -10, 0, 26, -22, 0, 0, 4, 0, -12, 0, 0, 4, 4, 0, 32, 0, 0, 18, -5, 0, 0, 130, 0, 44, -33, 0, -1, 25, 0, -30, 0, 0, 0, -40, 0, 0, 17, 0, -2, -1, 0, -5, 26, 0, -32, 0, 0, -28, 2, 0, -5, 84, 0, -28, -5, 0, 4, 24, 0, 46, 0, 0, 12, 0, 0, 0, -10, 0, 0, 6, 0, -10, -60, 0, 11, 45, 0, -16, -5, 0, 0, 14, 0, -14, -4, 0, 4, -15, 0, 28, 0, 0, -5, 10, 0, 0, -21, 0, -70, 0, 0, -32, -3, 0, -9, 0, 0, 58, -4, 0, 0, -8, 0, 32, 24, 0, -8, -7, 0, 4, 0, 0, 8, -34, 0, 0, -12, 0, -46, 28, 0, 45, 14, 0, 2, 0, 0, -17, 22, 0, 0, 5, 0, 13, -2, 0, -18, -12, 0, -42, -5, 0, 38, 50, 0, 0, 0, 0, 6, 25, 0, 24, 36, 0, 20, 0, 0, -14, 8, 0, 0, -20, 0, -16, -10, 0, -35, -42, 0, 41, 0, 0, -2, 91, 0, 0, -35, 0, -26, -10, 0, 104, 38, 0, 26, 0, 0, 14, -2, 0, 35, 8, 0, -20, -52, 0, 0, 13, 0, 8, 0, 0, -32, 12, 0, 0, -11, 0, 0, 140, 0, 3, 8, 0, 28, 0, 0, 12, -22, 0, 0, 28, 0, 88, -7, 0, 4, 42, 0, -110, 0, 0, 1, -21, 0, 0, -1, 0, -4, 0, 0, -7, 40, 0, 2, 0, 0, -54, 12, 0, 0, 60, 0, 80, -10, 0, 36, -18, 0, 14, 0, 0, 8, 18, 0, -40, 32, 0, 9, 18, 0, 14, 6, 0, 6, 0, 0, -2, 15, 0, 0, -8, 0, -8, -14, 0, -20, -5, 0, -10, -35, 0, 28, -18, 0, 0, -1, 0, -22, 48, 0, 31, -4, 0, 0, 0, 0, 2, 14, 0, 0, -36, 0, -80, 10, 0, -13, 2, 0, 120, 0, 0, 22, 59, 0, 0, 126, 0, -14, 4, 0, 32, 0, 0, 9, 0, 0, -21, 40, 0, 0, -20, 0, -49, 18, 0, 24, -14, 0, 112, 0, 0, 10, -21, 0, 0, -44, 0, -24, -53, 0, 0, -50, 0, -1, -20, 0, 14, 28, 0, 0, -50, 0, -48, 15, 0, -20, -182, 0, -36, 0, 0, -76, -10, 0, 0, 26, 0, -18, 10, 0, 110, -4, 0, 0, 0, 0, -68, 38, 0, 0, 48, 0, -88, -7, 0, 4, -30, 0, 61, 0, 0, 6, -36, 0, 10, 23, 0, -55, 32, 0, 6, 16, 0, 6, 0, 0, -41, 7, 0, 0, -60, 0, 74, -38, 0, 12, -36, 0, 44, -50, 0, 63, -65, 0, 0, -56, 0, -19, 6, 0, -30, -32, 0, 36, 0, 0, 43, -2, 0, 0, -98, 0, -52, -24, 0, -24, -4, 0, -28, 0, 0, 10, -100, 0, 0, 9, 0, 31, 21, 0, 13, 64, 0, -5, 0, 0, 0, -16, 0, 10, -9, 0, -29, 28, 0, 64, 12, 0, -91, 0, 0, 16, 30, 0, 0, -5, 0, -20, -25, 0, -2, -30, 0, 45, -30, 0, 0, 0, 0, 0, -18, 0, -5, -8, 0, 0, 18, 0, -72, 0, 0, -10, 45, 0, 0, 4, 0, -32, -40, 0, -24, 25, 0, 8, 0, 0, -63, -17, 0, 0, 13, 0, 50, -14, 0, -7, 52, 0, 4, 0, 0, -3, -10, 0, 65, -16, 0, -19, 4, 0, 80, -25, 0, 6, 0, 0, 32, 40, 0, 0, -70, 0, 5, 20, 0, -48, 36, 0, 38, 25, 0, -12, 40, 0, 0, 11, 0, -28, 56, 0, -12, -16, 0, -14, 0, 0, 55, -52, 0, 0, 0, 0, 42, 2, 0, -45, -42, 0, -9, 0, 0, 36, -34, 0, 0, -9, 0, 2, 36, 0, 58, 49, 0, -12, 0, 0, -29, -35, 0, -5, -106, 0, -32, 13, 0, 22, 33, 0, -35, 0, 0, -4, 6, 0, 0, -15, 0, 0, -8, 0, -50, 8, 0, 8, -5, 0, -12, 16, 0, 0, 30, 0, 0, -18, 0, -10, 12, 0, -10, 0, 0, 65, -196, 0, 0, 22, 0, 33, 63, 0, -32, -2, 0, -25, 0, 0, 28, -6, 0, 0, 19, 0, -27, 0, 0, -80, 21, 0, 21, 0, 0, 37, 36, 0, 0, 2, 0, -2, 110, 0, 43, 5, 0, 13, 0, 0, -140, -16, 0, 0, 0, 0, 72, -56, 0, -2, -110, 0, 72, 20, 0, 42, 26, 0, 0, -56, 0, -10, 6, 0, -112, 2, 0, 30, 0, 0, 8, -46, 0, 0, 99, 0, 16, -12, 0, 0, 36, 0, 30, 0, 0, 10, -74, 0, 0, 0, 0, -6, 48, 0, -180, 40, 0, -30, 0, 0, -38, 22, 0, 90, -3, 0, -21, -8, 0, -1, 0, 0, 6, 0, 0, 28, -175, 0, 0, 14, 0, -2, 2, 0, -6, 2, 0, 15, -35, 0, 130, 56, 0, 0, 11, 0, 108, -1, 0, 5, 4, 0, 6, 0, 0, -42, 46, 0, 0, -35, 0, 0, 100, 0, -98, 32, 0, -6, 0, 0, -60, 9, 0, 0, -108, 0, -168, 29, 0, 4, 16, 0, 0, 0, 0, 8, 29, 0, -130, 40, 0, 12, -80, 0, -36, -16, 0, -14, 0, 0, 9, 2, 0, 0, -12, 0, -60, -8, 0, -68, 28, 0, 30, 0, 0, -6, -80, 0, 0, -23, 0, -28, -26, 0, 5, 90, 0, -14, 0, 0, 22, 13, 0, 0, 7, 0, 14, -34, 0, 44, 112, 0, -15, 0, 0, 1, -40, 0, 0, -13, 0, -4, -48, 0, -8, 18, 0, -6, 0, 0, -24, -21, 0, 5, 48, 0, 18, 76, 0, -50, 25, 0, -42, 0, 0, 0, 11, 0, 0, 12, 0, 50, 4, 0, -11, 12, 0, 45, 0, 0, -17, -20, 0, 0, 3, 0, -18, 14, 0, 4, -50, 0, -100, 0, 0, 20, 0, 0, 0, -32, 0, 10, 42, 0, -44, -7, 0, -21, 0, 0, 2, 82, 0, 0, 85, 0, 34, -1, 0, 77, 68, 0, -54, 0, 0, -70, -5, 0, 15, 26, 0, -5, 40, 0, -50, 52, 0, -38, 0, 0, 0, 52, 0, 0, -84, 0, -156, -56, 0, -1, -74, 0, 34, 70, 0, 16, -18, 0, 0, -10, 0, -65, 0, 0, 63, 0, 0, 26, 0, 0, 42, -8, 0, 0, 44, 0, 136, -16, 0, -12, -55, 0, -7, 0, 0, 11, -9, 0, 0, 0, 0, 70, -12, 0, 14, 6, 0, 16, 0, 0, -13, 14, 0, 0, 140, 0, -52, -12, 0, -44, 90, 0, 26, 0, 0, 14, -16, 0, 0, 44, 0, 7, -117, 0, 50, 8, 0, -42, -45, 0, 92, -22, 0, 0, 12, 0, -65, 2, 0, -42, -5, 0, -28, 0, 0, 4, 130, 0, 0, 4, 0, 0, 14, 0, 22, 7, 0, 20, 0, 0, -32, 1, 0, 0, 16, 0, 8, -108, 0, -12, 28, 0, 0, 0, 0, 30, 26, 0, -50, 160, 0, -20, 0, 0, 32, 18, 0, 72, 0, 0, -25, -14, 0, 0, 16, 0, -42, -8, 0, 9, -20, 0, -78, -20, 0, -32, 56, 0, 0, 18, 0, -18, -5, 0, 4, 91, 0, 3, 0, 0, -37, 12, 0, 0, -28, 0, -19, -1, 0, 3, -60, 0, 57, 0, 0, -16, -92, 0, 0, 8, 0, -7, 62, 0, 0, -10, 0, 5, 0, 0, 3, -20, 0, 35, -71, 0, 130, 35, 0, -9, 0, 0, -32, 0, 0, -2, -18, 0, 0, -11, 0, 60, 84, 0, -7, -31, 0, -8, -25, 0, 12, 0, 0, 0, -166, 0, -12, 1, 0, -14, -10, 0, 76, 0, 0, 36, -27, 0, 0, -16, 0, 5, -39, 0, -12, -26, 0, 4, 0, 0, 70, 60, 0, 0, -8, 0, -17, -22, 0, 118, -120, 0, -50, 0, 0, 63, -130, 0, -140, -7, 0, -4, 18, 0, -40, 64, 0, 0, 0, 0, -88, -36, 0, 0, 55, 0, 71, -42, 0, 80, 24, 0, 4, 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, 7, 3, 1, 3, 0]], "char_orbit_index": 10, "prim_orbit_index": 3, "minimal_twist": "546.2.i.d", "char_is_minimal": true, "conrey_index": 235, "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], [1, 0], [0, 1], [0, 0], [-1, 1], [0, 0], [0, 0], [-2, -1], [-1, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [-1, 0], [1, -3], [0, 0], [0, -1], [7, -7], [0, 0], [0, -7], [0, 0], [0, 0], [-5, 0], [0, 2], [0, 0], [5, -5], [0, -1], [0, 0], [3, -2], [9, 0], [0, 0], [0, 0], [1, -1], [0, 0], [7, 0], [0, 0], [0, 0], [0, -4], [7, -7], [0, 0], [0, 0], [-4, 0], [0, 0], [2, 0], [0, -5], [0, 0], [-2, 2], [0, -3], [0, 0], [3, 5], [5, 0], [0, 0], [1, -1], [1, -1], [0, 0], [0, 0], [2, 1], [0, 0], [0, 9], [7, -7], [0, 0], [0, -13], [0, 0], [0, 0], [1, 0], [0, 0], [0, 0], [-3, 3], [0, 7], [0, 0], [0, 0], [-9, 0], [0, 0], [10, -10], [4, -4], [0, 0], [7, 0], [15, -10], [0, 0], [0, -14], [0, 0], [0, 0], [0, -4], [-16, 0], [0, 0], [0, 0], [0, 2], [0, 0], [5, -5], [0, -12], [0, 0], [2, 1], [-2, 0], [0, 0], [3, -3], [0, 0], [0, 0], [6, 0], [-5, 8], [0, 0], [0, 5]]}