# Stored data for newform 1530.2.f.e, downloaded from the LMFDB on 19 April 2024. {"label": "1530.2.f.e", "space_label": "1530.2.f", "level": 1530, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014742140421626, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1315725731004515042, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [2, 1]], [23, [4, 1]]], "qexp_display": "q+iq^{2}-q^{4}+(2+i)q^{5}-2q^{7}-iq^{8}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 85, "char_orbit_label": "f", "char_is_real": true, "Nk2": 6120, "analytic_conductor": 12.217111509255899, "hecke_ring_index": 1, "level_radical": 510, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [1530, 2, [1361, 307, 1261], [2, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 17], "conrey_indexes": [1189], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "1.931", "prec": 17}, {"__RealLiteral__": 0, "data": "0.140", "prec": 17}, {"__RealLiteral__": 0, "data": "15.139", "prec": 20}, {"__RealLiteral__": 0, "data": "1.377", "prec": 17}, {"__RealLiteral__": 0, "data": "150.205", "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, 4, -4], "traces": [0, 2, 0, 0, -2, 4, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, -10, -4, 0, 0, -8, 0, 6, 2, 0, 4, 0, 0, 0, 0, 0, -8, -8, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, -8, 0, 0, 0, 0, 0, 0, 0, -18, 10, 0, 0, -10, 0, -2, 2, 0, 0, -2, 0, 4, 0, 0, -22, 0, 0, 10, 0, 0, 0, 4, 0, -20, 0, 0, -4, 12, 0, 0, -10, 0, 0, 8, 0, 14, -20, 0, -14, 0, 0, -6, 16, 0, 0, -2, 0, -2, 24, 0, 0, 0, 0, -4, -18, 0, -16, 0, 0, 0, -4, 0, 22, -10, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 20, -4, 0, 8, 0, 0, 0, 8, 0, 10, 0, 0, -18, 0, 0, 4, -40, 0, -16, 0, 0, 0, -10, 0, 0, -32, 0, -2, 16, 0, 8, 0, 0, -12, -36, 0, 24, -18, 0, 0, 32, 0, -12, 0, 0, 0, -40, 0, 0, -4, 0, 0, -8, 0, 0, 0, 0, 10, 36, 0, 28, 0, 0, 6, -16, 0, 0, 8, 0, 0, 0, 0, -20, 32, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 18, 0, 0, 8, 0, 0, 0, 0, 0, 54, 0, 0, 8, 0, 18, 42, 0, 14, -10, 0, 16, 0, 0, 0, 0, 0, 0, -12, 0, 0, 10, 0, -22, 16, 0, 0, -14, 0, 2, 0, 0, 8, -2, 0, -40, 0, 0, -2, 0, 0, 0, 0, 0, 44, 2, 0, 4, 0, 0, 36, 28, 0, -4, 46, 0, -42, 0, 0, 0, 0, 0, -30, -36, 0, 22, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, 0, 0, 0, 0, -20, 0, 0, 28, 36, 0, 0, 24, 0, 0, -4, 0, 0, -10, 0, 8, 0, 0, 20, 0, 0, 14, 0, 0, 0, -4, 0, 46, 0, 0, 4, 0, 0, 40, -12, 0, 0, -46, 0, 20, 16, 0, 0, 0, 0, 10, 10, 0, 0, 60, 0, 12, -20, 0, 0, -44, 0, -4, -8, 0, 4, 0, 0, 0, 0, 0, -14, 18, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 14, 20, 0, -8, 0, 0, 0, -32, 0, 36, -2, 0, 6, 0, 0, 10, -16, 0, 36, 0, 0, -50, -40, 0, 0, -20, 0, -12, 2, 0, 0, 0, 0, 4, 40, 0, 2, -26, 0, 0, -24, 0, 24, 0, 0, 0, 20, 0, 0, 40, 0, 0, 0, 0, 2, 0, 0, -20, -18, 0, 4, 0, 0, 0, 18, 0, 0, -4, 0, 0, 0, 0, 16, -64, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, -30, 4, 0, 0, 0, 0, 0, -20, 0, -22, -28, 0, -64, 10, 0, 6, 66, 0, -72, -10, 0, 0, 0, 0, 0, -4, 0, 0, 12, 0, 32, 0, 0, 0, 40, 0, 44, 0, 0, -36, 32, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -42, -40, 0, -14, -4, 0, -20, 20, 0, 48, 4, 0, 2, 0, 0, 0, 0, 0, -8, 18, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -8, 0, 0, 0, 0, -36, 0, 0, -10, -30, 0, 0, 0, 0, 40, -24, 0, 0, -16, 0, 18, 0, 0, 0, 0, 0, 58, 0, 0, 0, -10, 0, -4, 0, 0, 8, 40, 0, -8, -40, 0, 0, -24, 0, 16, 44, 0, 76, 0, 0, -20, -14, 0, 0, -4, 0, 0, -66, 0, 0, 10, 0, 40, 20, 0, -14, 0, 0, 0, -4, 0, 4, 32, 0, 0, -14, 0, 0, 0, 0, 2, 0, 0, -72, -16, 0, 40, 0, 0, 0, 6, 0, -8, -48, 0, -40, 0, 0, -28, 10, 0, -16, 0, 0, 12, 40, 0, 0, 36, 0, -8, 0, 0, -2, 0, 0, -24, 4, 0, 28, 18, 0, 0, -78, 0, 4, 0, 0, 0, 2, 0, 0, -32, 0, 0, 28, 0, -80, 0, 0, 12, 96, 0, 20, 0, 0, 8, -32, 0, 0, 20, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 4, 0, 22, 48, 0, 0, 0, 0, 0, 0, 0, -30, 8, 0, 4, -68, 0, -80, -68, 0, 0, -48, 0, 0, 0, 0, 0, -32, 0, 0, 8, 0, -10, -44, 0, 0, -36, 0, -62, 0, 0, 70, 0, 0, -28, 0, 0, -40, 0, 0, 0, 0, 0, 0, 32, 0, -6, 36, 0, -14, 16, 0, -64, 36, 0, 10, 0, 0, 0, 0, 0, 56, -8, 0, -20, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 20, 0, 0, -92, -32, 0, 0, 24, 0, 20, -24, 0, 0, -6, 0, -72, 0, 0, -48, 0, 0, -104, 0, 0, 0, 48, 0, -44, 0, 0, -32, 16, 0, -32, 20, 0, 0, 34, 0, -50, -12, 0, 0, 0, 0, 64, 12, 0, 0, 0, 0, 4, -18, 0, 0, -8, 0, -64, 48, 0, 0, 0, 0, 0, -8, 0, -52, -16, 0, 0, 10, 0, 0, 0, 0, -80, 0, 0, 32, -90, 0, -8, 0, 0, 0, -20, 0, -14, -54, 0, -8, 0, 0, 0, 36, 0, 0, 0, 0, 0, -8, 0, 0, -10, 0, -12, -58, 0, -18, 0, 0, 30, -42, 0, 24, 0, 0, 0, 8, 0, -14, 0, 0, 0, 10, 0, 0, -6, 0, 0, 40, 0, -16, 0, 0, 72, 0, 0, 42, 0, 0, 12, -4, 0, 0, 56, 0, 0, 0, 0, 14, -114, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -48, 0, -32, -18, 0, 0, 0, 0, 0, -10, 0, -20, -2, 0, 36, -12, 0, 22, 0, 0, 10, -16, 0, 0, 0, 0, 0, -16, 0, 0, 12, 0, 36, 14, 0, 0, 30, 0, 84, 0, 0, -2, -80, 0, 32, 0, 0, 64, 0, 0, 0, 0, 0, -8, -40, 0, 20, 2, 0, -80, 80, 0, 0, -68, 0, 40, 0, 0, 0, 0, 0, -10, 40, 0, 32, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 20, -24, 0, 0, 0, 0, 48, 0, 0, 0, 12, 0, 0, 20, 0, -44, 20, 0, 0, -2, 0, 36, 0, 0, 108, 0, 0, -4, 0, 0, 0, 0, 0, 90, 0, 0, 18, 64, 0, -36, 20, 0, 0, -28, 0, -6, -18, 0, -44, 0, 0, 4, -50, 0, 0, -46, 0, 48, 24, 0, 0, 18, 0, 42, 0, 0, 108, 0, 0, 0, -16, 0, -16, 40, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 28, 56, 0, 30, 0, 0, 0, 36, 0, 24, 122, 0, 84, 0, 0, -22, 72, 0, -46, 0, 0, 24, 56, 0, 0, 50, 0, -20, -24, 0, -48, 0, 0, -12, -6, 0, -180, 36, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, -20, 0, 40, 0, 0, -22, -64, 0, 28, 0, 0, 10, 54, 0, 0, 10, 0, 0, 0, 0, -18, 82, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, -52, 0, 20, -22, 0, 0, 0, 0, 0, 108, 0, 130, -48, 0, -28, 80, 0, 32, -36, 0, 16, 40, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -28, -100, 0, 0, -6, 0, 0, 0, 0, -140, 4, 0, -20, 0, 0, -36, 0, 0, 0, 0, 0, -46, 10, 0, 74, 16, 0, 106, 0, 0, -8, -24, 0, -52, 0, 0, 0, 0, 0, 0, -80, 0, -20, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, 0, -14, -8, 0, 0, 0, 0, -20, 0, 0, 60, 72, 0, 0, -72, 0, -32, 4, 0, 0, -128, 0, 2, 0, 0, -46, 0, 0, -56, 0, 0, 0, 88, 0, -40, 0, 0, -4, 6, 0, 126, 0, 0, 0, 64, 0, -66, 8, 0, -40, 0, 0, 0, 12, 0, 0, 32, 0, -16, -60, 0, 0, 72, 0, 110, 46, 0, 56, 0, 0, 0, -20, 0, -20, 0, 0, 0, -16, 0, 0, 0, 0, 92, 0, 0, 0, 140, 0, -48, 0, 0, 0, -84, 0, -18, -62, 0, -10, 0, 0, 48, -10, 0, 40, 0, 0, 80, 0, 0, 0, 2, 0, 40, -60, 0, 102, 0, 0, 0, -64, 0, -12, -76, 0, 0, 20, 0, -54, 0, 0, 0, 66, 0, 0, 70, 0, 0, 44, 0, 12, 0, 0, 58, 12, 0, 4, 0, 0, -36, 8, 0, 0, 30, 0, 0, 0, 0, -4, -54, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, -68, 0, -8, 0, 0, 0, 0, 0, 0, 50, 0, 14, -24, 0, 0, -18, 0, 16, -124, 0, -10, 26, 0, 0, 0, 0, 0, -20, 0, 0, 2, 0, -40, -36, 0, 0, 0, 0, 64, 0, 0, 10, -4, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, -52, -16, 0, -20, -30, 0, -14, -38, 0, 40, -20, 0, 100, 0, 0, 0, 0, 0, 8, 56, 0, -64, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 120, 32, 0, 0, 0, 0, 48, 0, 0, -36, -108, 0, 0, 2, 0, 4, 0, 0, 0, 14, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -10, 0, 0, 20, 16, 0, -48, 90, 0, 0, -60, 0, -36, 22, 0, 56, 0, 0, -8, -84, 0, 0, -60, 0, 50, 24, 0, 0, 40, 0, 30, -10, 0, -28, 0, 0, 0, -14, 0, 14, 20, 0, 0, 28, 0, 0, 0, 0, 12, 0, 0, -52, -2, 0, 24, 0, 0, 0, 36, 0, 0, 0, 0, -16, 0, 0, -18, 88, 0, -118, 0, 0, -4, 92, 0, 0, -40, 0, -24, 50, 0, -112, 0, 0, -2, 14, 0, 120, 26, 0, 0, 40, 0, 0, 0, 0, 0, 60, 0, 0, 24, 0, 0, 80, 0, 16, 0, 0, -24, -54, 0, -42, 0, 0, -72, 0, 0, 0, -32, 0, 0, 0, 0, -92, -20, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, -40, 0, 44, 128, 0, 0, 0, 0, 0, -32, 0, 20, 0, 0, 60, 120, 0, 8, -88, 0, -2, -90, 0, 0, 0, 0, 0, 40, 0, 0, 28, 0, 20, -4, 0, 0, 18, 0, -70, 0, 0, 120, 40, 0, -4, 0, 0, 120, 0, 0, 0, 0, 0, 54, -2, 0, 0, 24, 0, -28, -18, 0, -40, -34, 0, 12, 0, 0, 0, 0, 0, 24, 4, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, 0, 0, 0, 80, -8, 0, 0, 0, 0, -16, 0, 0, 70, 64, 0, 0, 24, 0, 14, 16, 0, 0, 72, 0, 4, 0, 0, -48, 0, 0, -76, 0, 0, 0, -68, 0, -104, 0, 0, 0, -44, 0, -2, -44, 0, 0, 104, 0, 80, -28, 0, -90, 0, 0, 36, 80, 0, 0, -70, 0, -50, 0, 0, 0, 8, 0, -88, -22, 0, 30, 0, 0, 0, -4, 0, -92, -146, 0, 0, -36, 0, 0, 0, 0, -62, 0, 0, -8, -80, 0, -18, 0, 0, 0, 0, 0, 140, 20, 0, -28, 0, 0, 108, 16, 0, 22, 0, 0, -72, 28, 0, 0, -36, 0, 40, -56, 0, 64, 0, 0, -56, -10, 0, -16, 16, 0, 0, 0, 0, -6, 0, 0, 0, -66, 0, 0, -92, 0, 0, 16, 0, 72, 0, 0, -128, 10, 0, -48, 0, 0, 84, 70, 0, 0, 72, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], "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, 85, 3, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "170.2.d.a", "char_is_minimal": true, "conrey_index": 1189, "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, 0], [2, 1], [0, 0], [-2, 0], [0, -1], [0, 0], [-1, 2], [0, 0], [0, 0], [0, -1], [0, -2], [0, 0], [1, 0], [1, 4], [0, 0], [-5, 0], [-2, -1], [0, 0], [0, 0], [-4, 0], [0, 0], [3, 4], [1, 0], [0, 0], [2, 0], [0, 9], [0, 0], [0, 5], [0, 1], [0, 0], [-4, 1], [-4, -2], [0, 0], [-2, 0], [0, -5], [0, 0], [1, -2], [0, 10], [0, 0], [0, -6], [0, 0], [0, 0], [0, -4], [0, -7], [0, 0], [-3, 0], [-4, 3], [0, 0], [0, 1], [0, 1], [0, 0], [0, 0], [0, 2], [0, 0], [-9, 0], [5, 0], [0, 0], [0, 5], [-5, 0], [0, 0], [-1, 0], [1, -2], [0, 0], [0, 2], [-1, -4], [0, 0], [2, -4], [0, -5], [0, 0], [-11, 0], [0, -2], [0, 0], [5, 0], [0, 0], [0, 0], [0, 16], [2, 1], [0, 0], [-10, 0], [0, 6], [0, 0], [-2, 9], [6, 0], [0, 0], [0, 0], [-5, 0], [0, 0], [0, 2], [4, 0], [0, 0], [7, 0], [-10, -5], [0, 0], [-7, 0], [0, -3], [0, 0], [-3, -4]]}