# Stored data for newform 1890.2.j.h, downloaded from the LMFDB on 05 May 2024. {"label": "1890.2.j.h", "space_label": "1890.2.j", "level": 1890, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525815900440418, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1581128687085473164, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [1, -4, 15, -4, 1]], [13, [36, 36, 30, 6, 1]]], "qexp_display": "q+(-1+\\zeta_{12})q^{2}-\\zeta_{12}q^{4}+\\zeta_{12}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "j", "char_is_real": false, "Nk2": 7560, "analytic_conductor": 15.091725982021993, "hecke_ring_index": 3, "level_radical": 210, "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": "0.020", "prec": 17}, "analytic_rank_proved": true, "char_values": [1890, 3, [1541, 757, 1081], [1, 3, 3]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [631, 1261], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.010", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.816", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1597.088", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 0, 2, 2], "traces": [0, 4, -2, 0, -2, 2, 0, 2, 4, 0, -4, 4, 0, -6, 2, 0, -2, -4, 0, -12, 2, 0, 4, 6, 0, -2, 12, 0, -4, -6, 0, -4, -2, 0, 2, 4, 0, -4, 6, 0, 2, 8, 0, -2, -8, 0, -12, 8, 0, -2, -2, 0, -6, -20, 0, 8, 2, 0, -6, 10, 0, -2, 8, 0, 4, 6, 0, 18, 2, 0, -2, -28, 0, 20, 2, 0, 6, -4, 0, 28, -4, 0, -16, -4, 0, -2, -2, 0, 4, 16, 0, -12, 6, 0, 8, -6, 0, 2, 4, 0, 4, 12, 0, 10, -6, 0, 10, -60, 0, -12, -4, 0, 2, 8, 0, -6, 12, 0, -20, -2, 0, 8, -2, 0, -4, -4, 0, 28, -2, 0, 6, -4, 0, -6, -36, 0, -4, 12, 0, -2, -2, 0, 14, -36, 0, -12, -10, 0, 2, 24, 0, -4, -12, 0, 8, 4, 0, -2, 28, 0, 2, 12, 0, 32, 8, 0, -4, -6, 0, 2, 4, 0, 4, 20, 0, 2, 4, 0, -8, 0, 0, 16, 6, 0, 6, -2, 0, -4, -16, 0, 12, -12, 0, -28, 2, 0, -2, -4, 0, -52, -2, 0, 12, 6, 0, -8, -20, 0, 12, -24, 0, 4, 10, 0, 30, -4, 0, -8, 6, 0, -4, 6, 0, 22, -4, 0, -16, 32, 0, -14, -6, 0, -6, -48, 0, 16, 10, 0, -2, -8, 0, -8, -16, 0, 4, 2, 0, 30, -4, 0, 2, -12, 0, 12, -14, 0, -2, 26, 0, -2, -12, 0, 8, 38, 0, -10, -6, 0, 18, 84, 0, -12, 2, 0, 12, 4, 0, -36, 4, 0, 4, 20, 0, 8, 14, 0, 18, 16, 0, -64, 6, 0, -10, 10, 0, -10, -4, 0, -48, 12, 0, 2, -4, 0, 6, -4, 0, -32, -4, 0, 4, 24, 0, -34, 4, 0, -56, 22, 0, 30, 2, 0, -6, 12, 0, 12, -16, 0, 8, -8, 0, 52, 8, 0, 12, -18, 0, -56, 2, 0, -2, -64, 0, -4, -2, 0, 20, -2, 0, -14, -4, 0, -8, -30, 0, -14, -8, 0, 0, 20, 0, 8, -8, 0, 6, 10, 0, -26, -12, 0, 4, -10, 0, 8, -4, 0, 8, 72, 0, 24, -6, 0, -12, -12, 0, 4, 56, 0, -4, 32, 0, -6, -2, 0, 2, 56, 0, 52, 26, 0, -2, -14, 0, -36, -24, 0, -12, -34, 0, -60, -8, 0, 10, 20, 0, -8, -6, 0, -24, -24, 0, 2, -8, 0, -20, 2, 0, 2, 30, 0, 2, -24, 0, 20, 4, 0, 6, -6, 0, -38, 8, 0, -12, -14, 0, 8, 22, 0, 2, -12, 0, 44, 8, 0, 32, -6, 0, 16, 28, 0, 12, 10, 0, -40, -6, 0, 24, -16, 0, 36, -8, 0, 10, 40, 0, 6, 4, 0, 16, -30, 0, 36, -8, 0, 8, 4, 0, -16, -2, 0, 2, 48, 0, 6, -60, 0, 8, -14, 0, -12, 2, 0, 6, -24, 0, 24, -6, 0, -14, -38, 0, 10, 4, 0, -52, -10, 0, -16, -2, 0, 6, -88, 0, 112, -4, 0, 38, 4, 0, 22, 20, 0, 12, 30, 0, -30, 18, 0, -42, -8, 0, -24, 6, 0, 2, -6, 0, 6, -24, 0, -8, 54, 0, -28, -36, 0, -2, -80, 0, 84, -2, 0, 20, -52, 0, -8, -16, 0, -28, 6, 0, -12, 18, 0, -8, -12, 0, 52, 32, 0, 6, 4, 0, -38, 20, 0, -20, -40, 0, 60, -10, 0, 2, -24, 0, -4, 24, 0, 12, 0, 0, -12, -4, 0, 8, -8, 0, -32, 6, 0, 2, -48, 0, 120, 16, 0, -4, 32, 0, -34, -8, 0, -48, 8, 0, -2, -34, 0, -2, 4, 0, -76, 28, 0, 22, 14, 0, -6, -60, 0, -4, 38, 0, 16, -6, 0, -6, -20, 0, 64, -6, 0, -16, -28, 0, 4, -16, 0, 16, 4, 0, 4, 52, 0, -4, -12, 0, 0, -6, 0, -18, -2, 0, -44, 112, 0, -4, -66, 0, -2, -2, 0, 32, -28, 0, 24, 2, 0, -2, 48, 0, -8, -40, 0, 4, 2, 0, -8, -14, 0, 2, -20, 0, 132, 4, 0, -30, -12, 0, -26, 28, 0, 16, -12, 0, -18, 0, 0, -10, 36, 0, 20, -4, 0, -8, -6, 0, 54, -12, 0, -20, 2, 0, -26, -26, 0, 6, 72, 0, 40, -2, 0, -10, -12, 0, -24, -16, 0, 8, -30, 0, 50, 8, 0, -36, -8, 0, 28, -12, 0, -6, 36, 0, -6, 24, 0, 24, 42, 0, -8, 4, 0, -28, -60, 0, 8, 2, 0, 32, -36, 0, -34, 12, 0, 4, 2, 0, -32, 2, 0, -28, 16, 0, 0, -26, 0, 26, -24, 0, -8, 4, 0, 28, -4, 0, 6, -36, 0, 12, -132, 0, -148, 6, 0, -34, 16, 0, 78, 120, 0, 16, 42, 0, -50, 10, 0, -10, 104, 0, -40, 4, 0, -6, 2, 0, 6, 48, 0, 48, 26, 0, -14, 2, 0, 4, 4, 0, 16, 10, 0, 2, 24, 0, -28, -4, 0, -60, -72, 0, -6, 2, 0, 12, 64, 0, 40, -10, 0, 4, -56, 0, 54, -12, 0, 12, -2, 0, -10, -38, 0, -4, 128, 0, -108, 6, 0, -14, -4, 0, 14, -16, 0, -44, -24, 0, 0, 2, 0, 6, 168, 0, 20, -22, 0, 8, 8, 0, 26, -64, 0, 12, -42, 0, -4, 16, 0, -14, -8, 0, -100, -6, 0, 10, 48, 0, 2, 80, 0, 12, -44, 0, 6, 24, 0, 8, -8, 0, -88, -18, 0, -8, -52, 0, -18, -20, 0, -80, -10, 0, -6, 6, 0, -2, 96, 0, -24, -8, 0, -30, -12, 0, -42, -72, 0, 16, 28, 0, 52, 8, 0, -2, -48, 0, -4, 8, 0, -2, 0, 0, 4, -4, 0, -96, -16, 0, -2, 6, 0, 30, 60, 0, -56, -4, 0, -14, -26, 0, 20, 24, 0, -4, -18, 0, -10, 6, 0, 12, 132, 0, 136, -12, 0, -6, -14, 0, -6, 28, 0, 76, -52, 0, 38, 10, 0, -2, -16, 0, -168, 26, 0, -10, 60, 0, 0, 32, 0, 4, 2, 0, 14, 6, 0, 44, 48, 0, -48, -56, 0, -4, -68, 0, 76, -76, 0, -8, -4, 0, 4, 22, 0, -10, 12, 0, -88, -6, 0, 30, -4, 0, -14, 60, 0, -36, 96, 0, -2, -42, 0, 4, 0, 0, 48, 12, 0, 6, -4, 0, -4, -4, 0, 12, -6, 0, -46, 6, 0, 12, 44, 0, -4, 4, 0, 54, 84, 0, -6, 56, 0, 72, 24, 0, -36, -2, 0, 40, 44, 0, 4, -42, 0, -2, -54, 0, -52, -40, 0, 104, 6, 0, 46, -8, 0, 8, 52, 0, 64, 14, 0, 6, -18, 0, 16, 24, 0, -36, 14, 0, 124, -8, 0, 6, -12, 0, -36, -26, 0, 32, -12, 0, -6, -12, 0, -8, -14, 0, -24, -38, 0, -10, -12, 0, -80, 10, 0, -40, 8, 0, -72, -120, 0, 20, -22, 0, -2, 2, 0, 12, 36, 0, -84, 2, 0, 24, -18, 0, 8, -24, 0, 0, -18, 0, 10, -12, 0, 2, -16, 0, 28, -4, 0, -8, -20, 0, -32, 64, 0, -12, -66, 0, -12, 2, 0, 24, -52, 0, 4, -60, 0, 16, -14, 0, -22, 8, 0, -64, -30, 0, 12, -34, 0, 4, -20, 0, -64, 24, 0, 8, -114, 0, 72, 4, 0, 68, 0, 0, -6, -2, 0, -2, 12, 0, -12, 38, 0, 28, 6, 0, 8, -44, 0, -28, 40, 0, -54, -6, 0, 30, -4, 0, 56, 2, 0, 38, -30, 0, -26, -32, 0, 12, -78, 0, 26, -6, 0, 10, -4, 0, -48, -32, 0, -6, -78, 0, 4, 32, 0, 56, 68, 0, 4, 4, 0, 8, -96, 0, 76, -8, 0, 4, -72, 0, 104, -8, 0, -104, 10, 0, 16, -4, 0, 6, 72, 0, 296, 0, 0, -6, 12, 0, 36, 36, 0, 4, -28, 0, 42, -44, 0, -56, 108, 0, -56, 2, 0, -66, -6, 0, -18, 4, 0, 4, 36, 0, 24, 32, 0, 14, 16, 0, 156, -12, 0, 2, 0, 0, -4, 4, 0, -96, -2, 0, 56, -8, 0, 20, -72, 0, 36, -2, 0, 2, 102, 0, -26, 16, 0, 28, -2, 0, 44, 2, 0, 10, -24, 0, 40, -66, 0, 4, 114, 0, 4, 60, 0, 24, -8, 0, 24, -26, 0, -14, 12, 0, 72, -8, 0, -12, -112, 0, -70, 36, 0, 0, 4, 0, 8, -10, 0, -18, -100, 0, -112, -10, 0, -4, -32, 0, -74, 16, 0, 12, -40, 0, -44, 54, 0, 6, -32, 0, -144, 10, 0, 2, 24, 0, -10, 52, 0, 52, -24, 0, 64, 6, 0, -36, -20, 0, 8, -20, 0, -2, 66, 0, 112, 20, 0, 24, -12, 0, -32, -24, 0, 8, 140, 0, 24, -4, 0, -30, -76, 0, -84, -100, 0, -16, -2, 0, -18, -36, 0, 4, 184, 0, -16, -14, 0, -12, -38, 0, -4, 12, 0, -72, 70, 0, -2, -6, 0, -12, 16, 0, 32, -12, 0, 42, -16, 0, 84, 16, 0, -8, -54, 0, -30, -28, 0, 30, 12, 0, -116, -4, 0, 2, -42, 0, -24, -64, 0, 72, -18, 0, -22, -34, 0, -6, -68, 0, -268, -2, 0, 2, 42, 0, 0, 64, 0, -4, -12, 0, 8, -28, 0, -8, 200, 0, 44, 0, 0, -26, -32, 0, 182, -52, 0, 48, -30, 0, -62, -8, 0, -2, -216, 0, -28, -14, 0, -4, 18, 0, 48, -12, 0, 72, -102, 0, 6, 12, 0, 66, -80, 0, -16, 74, 0, 6, 6, 0, -32, 68, 0, -32, -24, 0, -36, 78, 0, -60, 132, 0, 96, -8, 0, 42, 92, 0, 8, 100, 0, -20, -2, 0, -12, -10, 0, -52, 104, 0, 60, 20, 0, 4, -40, 0, -24, 12, 0, -4, -2, 0, -8, 6, 0, -24, -16, 0, -36, -24, 0, 26, 54, 0, 44, 28, 0, -4, 56, 0, 8, 4, 0, -2, 0, 0, 200, -8, 0, 10, -48, 0, 26, -4, 0, -48, -60, 0, -32, -28, 0, 2, 24, 0, -132, 30, 0, -72, -2, 0, -12, 12, 0, -4, 32, 0, -2, 12, 0, -32, -140, 0, 60, -20, 0, -10, 66, 0, 2, -8, 0, 112, -8, 0, 48, 54, 0, 6, -28, 0, -48, -6, 0, -2, -10, 0, -22, 20, 0, 76, -6, 0, -6, -4, 0, -64, -88, 0, -60, 54, 0, 6, 12, 0, 6, 28, 0, 8, 14, 0, 122, 14, 0, 8, -60, 0, -268, 22, 0, -24, 8, 0, 20, 0, 0, -4, -4, 0, 10, 6, 0, -84, 52, 0, -60, -10, 0, -22, 4, 0, 6, -16, 0, -16, 10, 0, 2, 26, 0, 32, 168, 0, 60, -6, 0, -42, -98, 0, -10, 8, 0, -32, 68, 0, -40, -14, 0, 4, -52, 0, 60, 50, 0, -6, -38, 0, -6, -20, 0, -96, 18, 0, -132, 2, 0, -40, 12, 0, -20, -6, 0, -44, 32, 0, -36, -12, 0, -48, -8, 0, 128, 8, 0, 4, -252, 0, 16, 44, 0, -18, 42, 0, -4, 16, 0, 104, 42, 0, 36, -18, 0, 10, 24, 0, -40, 40, 0, -10, 12, 0, -6, 12, 0, -12, -12, 0, -16, -2, 0, -48, 296, 0, -48, 12, 0, -8, -8, 0, 12, 60, 0, 24, -60, 0, -8, -42, 0, 36, 8, 0, 64, -8, 0, 28, 2, 0, -120, -104, 0, -16, 72, 0, 36, -2, 0, 24, -108, 0, 64, 2, 0, 8, 78, 0, 94, 4, 0, 0, 6, 0, -42, 4, 0, 2, 200, 0, -72, 48, 0, -16, -20, 0, 84, 4, 0, -12, -116, 0, 28, 30, 0, -30, 0, 0, 16, 28, 0, -4, 26, 0, 104, 28, 0, 52, 64, 0, 18, 20, 0, -12, -148, 0, -164, 2], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 10, "prim_orbit_index": 3, "minimal_twist": "630.2.j.f", "char_is_minimal": false, "conrey_index": 631, "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], [-1, 1, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [1, -1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [2, -2, -1, 1], [0, 0, 0, 0], [0, -3, -1, 0], [0, 1, 0, 0], [0, 0, 0, 0], [-1, 1, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, -2], [1, -1, 0, 0], [0, 0, 0, 0], [0, 2, 1, 0], [0, 3, -1, 0], [0, 0, 0, 0], [-1, 1, 0, 0], [3, 0, 0, 1], [0, 0, 0, 0], [-1, 0, 0, 0], [-3, 3, 3, -3], [0, 0, 0, 0], [0, -2, -4, 0], [0, -1, 0, 0], [0, 0, 0, 0], [1, -1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, -5], [3, -3, -2, 2], [0, 0, 0, 0], [0, 1, 0, 0], [0, 4, 1, 0], [0, 0, 0, 0], [-1, 1, 6, -6], [-2, 0, 0, -1], [0, 0, 0, 0], [-3, 0, 0, 1], [4, -4, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-3, 3, 1, -1], [-5, 0, 0, -3], [0, 0, 0, 0], [2, 0, 0, 1], [1, -1, 0, 0], [0, 0, 0, 0], [0, -3, -3, 0], [0, 5, 2, 0], [0, 0, 0, 0], [-1, 1, -1, 1], [2, 0, 0, 4], [0, 0, 0, 0], [1, 0, 0, 0], [3, -3, -1, 1], [0, 0, 0, 0], [0, 9, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [-1, 1, 0, 0], [-7, 0, 0, -1], [0, 0, 0, 0], [5, 0, 0, -4], [1, -1, -5, 5], [0, 0, 0, 0], [0, 3, 2, 0], [0, -2, -1, 0], [0, 0, 0, 0], [14, -14, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, -1], [-2, 2, -2, 2], [0, 0, 0, 0], [0, -1, 0, 0], [0, -1, -6, 0], [0, 0, 0, 0], [2, -2, -1, 1], [4, 0, 0, -2], [0, 0, 0, 0], [-3, 0, 0, -1], [3, -3, 1, -1], [0, 0, 0, 0], [0, 4, 0, 0], [0, -3, -2, 0], [0, 0, 0, 0], [1, -1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0]]}