# Stored data for newform 1470.2.g.e, downloaded from the LMFDB on 19 April 2024.
{"label": "1470.2.g.e", "space_label": "1470.2.g", "level": 1470, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014810859898302, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 16853605508532916, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [2, 1]], [17, [64, 0, 1]], [19, [2, 1]]], "qexp_display": "q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "g", "char_is_real": true, "Nk2": 5880, "analytic_conductor": 11.738009097128216, "hecke_ring_index": 1, "level_radical": 210, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [1470, 2, [491, 1177, 1081], [2, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [589], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "1.995", "prec": 17}, {"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "16.582", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "171.909", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 2, 0], "traces": [0, 2, 0, 0, -2, 2, 2, 0, 0, -2, 4, -4, 0, 0, 0, -4, 2, 0, 0, -4, -2, 0, 0, 0, -2, -6, -4, 0, 0, 12, 2, -12, 0, 0, 16, 0, 2, 0, 0, 4, -4, -12, 0, 0, 4, -2, 0, 0, 0, 0, 8, -16, 0, 0, -2, -4, 0, 0, 0, -16, 4, -20, 0, 0, -2, 8, -4, 0, 0, 0, 0, -28, 0, 0, -16, -8, 4, 0, 0, -8, 2, 2, 0, 0, 0, -32, 16, 0, 0, 20, -4, 0, 0, 0, 8, -4, 2, 0, 0, 4, 6, 20, 0, 0, 4, 0, -4, 0, 0, 12, -8, 16, 0, 0, -4, 0, -12, 0, 0, 0, -2, -14, 0, 0, 12, -22, 0, 0, 0, -16, -4, 40, 0, 0, 24, 4, -16, 0, 0, -4, 0, -8, 0, 0, -2, 12, 20, 0, 0, 36, -6, 16, 0, 0, 0, -12, -4, 0, 0, 4, 4, 0, 0, 0, 12, 8, -32, 0, 0, 18, 16, 4, 0, 0, 12, 0, -4, 0, 0, 4, 2, -44, 0, 0, 0, 32, -12, 0, 0, 0, -8, 28, 0, 0, 20, 4, 0, 0, 0, -52, -8, -24, 0, 0, 16, -12, 0, 0, 0, 8, 0, -16, 0, 0, 24, -32, 2, 0, 0, -20, 4, 32, 0, 0, 0, 6, 12, 0, 0, 52, 0, 0, 0, 0, 4, -16, 16, 0, 0, 44, -4, 20, 0, 0, 20, 0, -12, 0, 0, 32, -4, 0, 0, 0, -24, -16, 2, 0, 0, 0, -8, -12, 0, 0, 4, 8, 0, 0, 0, 28, -2, -4, 0, 0, 28, 12, 0, 0, 0, 12, 0, 44, 0, 0, 28, 8, 8, 0, 0, -94, 24, -20, 0, 0, 0, -16, 16, 0, 0, 0, 8, 0, 0, 0, -4, -20, -16, 0, 0, 0, -24, 16, 0, 0, -20, 0, 8, 0, 0, -24, -2, -24, 0, 0, -2, 16, 0, 0, 0, 0, -4, 0, 0, 0, -16, -48, 0, 0, 0, -12, 32, 24, 0, 0, -16, 0, 32, 0, 0, 36, 0, -4, 0, 0, -16, -28, -20, 0, 0, -28, 4, -30, 0, 0, 0, -40, -20, 0, 0, 12, -16, 0, 0, 0, -32, 4, -8, 0, 0, 56, 4, 24, 0, 0, -2, 0, 0, 0, 0, -12, 8, 0, 0, 0, 12, -8, -4, 0, 0, 0, -6, 36, 0, 0, -20, 2, 0, 0, 0, 20, -24, -28, 0, 0, 0, 64, -4, 0, 0, 24, 0, 20, 0, 0, 4, -64, -28, 0, 0, -8, 16, -12, 0, 0, 0, -24, -12, 0, 0, 12, 8, 0, 0, 0, -16, 20, 32, 0, 0, 60, -8, 24, 0, 0, -16, 0, 4, 0, 0, 16, 0, -36, 0, 0, 12, 24, 12, 0, 0, 0, 8, 20, 0, 0, -8, 12, 0, 0, 0, 16, 2, -32, 0, 0, 14, -40, 2, 0, 0, 0, 0, -84, 0, 0, 8, 4, -12, 0, 0, 56, 22, 16, 0, 0, 0, 20, 0, 0, 0, 4, -32, 0, 0, 0, -40, 0, 16, 0, 0, -32, 4, 12, 0, 0, -40, 0, -48, 0, 0, 46, -4, 16, 0, 0, 20, -48, -24, 0, 0, 0, -4, -4, 0, 0, 16, 12, 0, 0, 0, 20, -16, -24, 0, 0, 16, 16, 4, 0, 0, 32, 0, 32, 0, 0, 8, -24, -8, 0, 0, -36, -4, -88, 0, 0, 0, 0, 2, 0, 0, 0, -12, 0, 0, 0, -20, -8, 32, 0, 0, 24, -32, -12, 0, 0, 4, 0, -36, 0, 0, -28, 6, 84, 0, 0, -16, -14, 20, 0, 0, 0, -40, 16, 0, 0, 56, 24, 0, 0, 0, -36, 12, 0, 0, 0, 4, -14, -20, 0, 0, 128, 0, 24, 0, 0, 4, 48, -4, 0, 0, 28, -4, 60, 0, 0, 0, -16, -32, 0, 0, 32, 12, 0, 0, 0, 12, 40, -12, 0, 0, 12, -8, -20, 0, 0, 32, 0, 16, 0, 0, -32, 24, 40, 0, 0, -64, 8, -18, 0, 0, 0, -16, 16, 0, 0, -4, -56, 0, 0, 0, -8, 0, 28, 0, 0, -8, -4, -12, 0, 0, -12, 0, -60, 0, 0, 4, -8, 0, 0, 0, 76, -56, 8, 0, 0, 0, -16, -4, 0, 0, -40, -2, 0, 0, 0, 44, -36, -14, 0, 0, -2, 20, -128, 0, 0, -64, 0, 0, 0, 0, -40, -32, -8, 0, 0, 12, 36, 72, 0, 0, 0, -22, 8, 0, 0, -24, 16, 0, 0, 0, 0, 8, -12, 0, 0, -28, 32, 0, 0, 0, -84, 0, 40, 0, 0, -16, 36, -20, 0, 0, 24, -4, 56, 0, 0, 0, 40, 40, 0, 0, 48, -16, 0, 0, 0, 4, 4, 52, 0, 0, -64, 8, -20, 0, 0, 24, 0, 24, 0, 0, -12, 4, -28, 0, 0, 32, 0, -16, 0, 0, 0, 12, -12, 0, 0, 0, 16, 0, 0, 0, -68, -32, -16, 0, 0, -4, 32, -8, 0, 0, 88, 0, 14, 0, 0, 16, 18, -8, 0, 0, 8, -48, 0, 0, 0, 0, 4, -24, 0, 0, -12, 32, 0, 0, 0, -2, -64, -52, 0, 0, 16, 12, 48, 0, 0, 0, 0, 20, 0, 0, -32, -4, 12, 0, 0, -32, 32, 72, 0, 0, 0, 40, -4, 0, 0, 36, 4, 0, 0, 0, -72, -6, 32, 0, 0, -12, -44, 16, 0, 0, -20, 0, 12, 0, 0, 56, 40, -52, 0, 0, 8, 0, -56, 0, 0, 0, 64, -24, 0, 0, -36, -12, 0, 0, 0, 32, 64, -4, 0, 0, 20, 16, 12, 0, 0, -16, 0, -32, 0, 0, 40, -16, -4, 0, 0, 4, 28, -44, 0, 0, 0, 4, 10, 0, 0, -20, 0, 0, 0, 0, 32, 20, -48, 0, 0, -72, -12, -20, 0, 0, -40, 0, -12, 0, 0, 12, -24, 96, 0, 0, 0, 8, -120, 0, 0, 0, -52, -32, 0, 0, -16, 4, 0, 0, 0, 0, -24, -48, 0, 0, -36, 40, 64, 0, 0, 18, 0, 24, 0, 0, -44, 16, 36, 0, 0, -2, 36, 4, 0, 0, 0, 0, -60, 0, 0, -16, 0, 0, 0, 0, 116, 8, 8, 0, 0, 12, 8, 24, 0, 0, -116, 0, -96, 0, 0, -96, -16, -4, 0, 0, 0, -8, 44, 0, 0, 0, 56, 24, 0, 0, -52, 24, 0, 0, 0, 4, -64, -28, 0, 0, -64, 2, 0, 0, 0, 4, 0, -44, 0, 0, 14, 24, 64, 0, 0, -40, -20, -28, 0, 0, 0, -12, 64, 0, 0, 0, 32, 0, 0, 0, 52, 32, -40, 0, 0, -12, -64, -12, 0, 0, -72, 0, 32, 0, 0, -44, 22, -24, 0, 0, -28, 12, 24, 0, 0, 0, 32, -28, 0, 0, -192, -8, 0, 0, 0, -8, 52, 28, 0, 0, 0, 0, -120, 0, 0, 36, 0, 94, 0, 0, 40, -24, 16, 0, 0, 20, -24, 8, 0, 0, 0, 4, -24, 0, 0, 8, -32, 0, 0, 0, -40, 16, 132, 0, 0, -16, 16, 64, 0, 0, -72, 0, -4, 0, 0, -52, 44, 0, 0, 0, -24, -8, -60, 0, 0, 0, 20, -24, 0, 0, -24, -28, 0, 0, 0, -32, -4, 4, 0, 0, 0, 20, -32, 0, 0, 16, 0, 64, 0, 0, 108, -12, 4, 0, 0, 36, -16, 0, 0, 0, 0, 24, -160, 0, 0, -16, 32, 0, 0, 0, 76, -48, 4, 0, 0, 8, 0, 20, 0, 0, -32, 0, 40, 0, 0, -8, 0, -16, 0, 0, 8, -24, 72, 0, 0, 0, 48, 24, 0, 0, 52, 2, 0, 0, 0, 24, 80, 40, 0, 0, -60, -32, -36, 0, 0, 32, 0, 2, 0, 0, 52, -16, -20, 0, 0, 0, -12, -28, 0, 0, 0, 80, 0, 0, 0, -20, 96, 0, 0, 0, 72, 4, -92, 0, 0, 0, 16, 32, 0, 0, -72, 0, 72, 0, 0, 0, -40, 16, 0, 0, 0, 48, -36, 0, 0, 0, 28, 24, 0, 0, 56, 6, 0, 0, 0, 0, -4, 12, 0, 0, -16, -32, 20, 0, 0, -24, 0, 56, 0, 0, -54, 28, -56, 0, 0, 52, 44, 16, 0, 0, 0, 0, 52, 0, 0, -32, -32, 0, 0, 0, 24, -8, 48, 0, 0, -96, 12, -36, 0, 0, -68, 0, -32, 0, 0, 4, 44, 32, 0, 0, 100, -16, 256, 0, 0, 0, 16, 16, 0, 0, 32, 28, 0, 0, 0, 20, 16, 0, 0, 0, -148, 8, -4, 0, 0, 44, 0, 28, 0, 0, -12, -4, -80, 0, 0, 30, -94, 20, 0, 0, 0, 48, -36, 0, 0, 32, -20, 0, 0, 0, 92, 40, 72, 0, 0, 20, -64, 60, 0, 0, 24, 0, 64, 0, 0, -48, 48, -12, 0, 0, -96, 16, -132, 0, 0, 0, -8, 32, 0, 0, -12, 72, 0, 0, 0, 32, 0, 32, 0, 0, 52, -4, 16, 0, 0, 8, 0, 0, 0, 0, 48, 32, -24, 0, 0, 8, -40, -56, 0, 0, 0, -4, -18, 0, 0, -24, 60, 0, 0, 0, 8, -16, 116, 0, 0, 32, -112, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 64, 0, 0, 20, -48, 16, 0, 0, 0, 16, 12, 0, 0, 88, -8, 0, 0, 0, 0, 40, -12, 0, 0, -24, -20, 56, 0, 0, -88, 0, -12, 0, 0, 32, 8, 96, 0, 0, 4, -8, 40, 0, 0, 0, 8, 128, 0, 0, 0, -24, 0, 0, 0, -24, 6, -76, 0, 0, -36, -24, -40, 0, 0, 52, 0, -4, 0, 0, 28, 64, 20, 0, 0, 36, -2, 36, 0, 0, 0, -8, -4, 0, 0, 44, 0, 0, 0, 0, -32, -24, -20, 0, 0, -72, 24, 40, 0, 0, 28, 0, -8, 0, 0, -160, 12, -48, 0, 0, 72, 0, 0, 0, 0, 0, -64, -32, 0, 0, 4, -32, 0, 0, 0, -108, -16, 12, 0, 0, 12, -96, -24, 0, 0, 0, 0, -10, 0, 0, -20, 128, 44, 0, 0, 24, 36, -40, 0, 0, 0, -12, -4, 0, 0, -108, 64, 0, 0, 0, 28, 24, -20, 0, 0, -132, 8, -96, 0, 0, 40, 0, 8, 0, 0, -28, -16, -116, 0, 0, 12, 0, 96, 0, 0, 0, 32, -36, 0, 0, -94, 16, 0, 0, 0, 64, 24, 68, 0, 0, 12, 36, -20, 0, 0, -8, 0, 0, 0, 0, 96, -4, -12, 0, 0, -152, -8, -8, 0, 0, 0, 0, 104, 0, 0, -120, -16, 0, 0, 0, 72, 84, 16, 0, 0, -64, -20, 56, 0, 0, -32, 0, -16, 0, 0, 60, 8, 52, 0, 0, 0, -28, -60, 0, 0, 0, 8, -116, 0, 0, -24, -30, 0, 0, 0, 24, -88, 0, 0, 0, 88, 28, 16, 0, 0, -192, 0, 32, 0, 0, -4, -80, 64, 0, 0, 96, -20, 120, 0, 0, 0, 128, -16, 0, 0, -64, 0, 0, 0, 0, 36, 12, 56, 0, 0, -42, 48, -36, 0, 0, 0, 0, -12, 0, 0, -36, -24, 132, 0, 0, -12, -144, 16, 0, 0, 0, -32, 156, 0, 0, -52, 48, 0, 0, 0, 12, -8, -8, 0, 0, -20, 48, 0, 0, 0, 60, 0, 120, 0, 0, -24, 56, 8, 0, 0, 16, -12, -60, 0, 0, 0, 24, -36, 0, 0, 0, 56, 0, 0, 0, -24, 0, -16, 0, 0, -40, -2, -96, 0, 0, 32, 0, -24, 0, 0, -40, 0, -152, 0, 0, 48, 32, -14, 0, 0, 0, 40, -32, 0, 0, -2, -12, 0, 0, 0, -156, 16, 28, 0, 0, 36, 0, 0, 0, 0, 28, 0, -32, 0, 0, 84, -80, -24, 0, 0, -8, 12, 20, 0, 0, 0, 24, -8, 0, 0, -32, -4, 0, 0, 0, 12, -8, 0, 0, 0, -32, -104, 88, 0, 0, -76, 0, -56, 0, 0, -160, -22], "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, 5, 2, 1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 2, "minimal_twist": "210.2.g.a", "char_is_minimal": true, "conrey_index": 589, "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, -1], [-1, 0], [1, -2], [1, 0], [0, 0], [0, -1], [-1, 0], [2, 1], [-2, 0], [0, 1], [0, 2], [0, 0], [-2, -1], [1, 0], [0, -8], [0, -1], [-2, 0], [-1, 2], [0, 0], [0, -2], [0, 0], [-1, 0], [-3, -4], [-2, 0], [0, 1], [0, 0], [6, 0], [1, -2], [-6, 0], [0, 1], [0, 2], [8, 0], [0, 0], [1, 0], [0, 8], [0, -2], [2, 0], [-2, -1], [-6, 0], [0, 0], [0, -8], [2, 0], [-1, 2], [0, 0], [0, -4], [0, -1], [0, 0], [4, -3], [-8, 0], [0, -2], [0, 2], [-1, 0], [-2, 4], [0, 0], [0, 2], [0, 6], [-8, 0], [2, 1], [-10, 0], [0, -6], [0, 0], [-1, 0], [4, 2], [-2, 0], [0, -12], [0, 8], [0, 0], [0, 0], [-14, 0], [0, 1], [0, -10], [-8, 0], [-4, 3], [2, 0], [0, 0], [0, 2], [-4, 0], [1, -2], [1, 0], [0, -6], [0, 16], [0, 0], [-16, -8], [8, 0], [0, -6], [0, 2], [10, 0], [-2, -1], [0, 0], [0, 0], [0, 6], [4, 0], [-2, 4], [1, 0], [0, -10], [0, 0], [2, 0], [3, 4]]}