# Stored data for newform 420.2.c.b, downloaded from the LMFDB on 25 April 2024.
{"label": "420.2.c.b", "space_label": "420.2.c", "level": 420, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503737099878820, "dim": 16, "is_polredabs": true, "trace_hash": 1872205695721738915, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[19, [1408, 6784, 1696, -2400, -352, 288, 6, -12, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+q^{3}+\\beta _{2}q^{4}-\\beta _{4}q^{5}+\\beta _{1}q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 28, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1680, "analytic_conductor": 3.353716884893776, "hecke_ring_index": 256, "level_radical": 210, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [420, 2, [211, 281, 337, 241], [1, 2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [391], "field_disc": 56333109072702135599104, "field_disc_factorization": [[2, 20], [7211, 2], [32143, 2]], "field_poly": [256, -256, 192, -128, 48, 16, -28, 24, -28, 12, -7, 2, 3, -4, 3, -2, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.787", "prec": 20}, {"__RealLiteral__": 0, "data": "5.517", "prec": 17}, {"__RealLiteral__": 0, "data": "954.184", "prec": 24}, {"__RealLiteral__": 0, "data": "507.912", "prec": 24}, {"__RealLiteral__": 0, "data": "111781.814", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c2", "trace_display": [2, 16, 0, 4], "traces": [0, 16, 2, 16, -2, 0, 2, 4, 2, 16, 0, 0, -2, 0, 10, 0, 6, 0, 2, 24, 0, 4, -12, 0, 2, -16, 12, 16, -22, 16, 0, -8, -18, 0, -24, 0, -2, 24, -28, 0, -12, 0, 10, 0, -8, 0, -20, -16, 6, -16, -2, 0, 20, -32, 2, 0, -2, 24, -32, -8, 0, 0, -16, 4, -2, -8, -12, 0, -4, 0, -20, 0, 2, 0, -4, -16, -16, -8, 12, 0, 16, 16, 4, -8, -22, 0, 64, 16, -52, 0, 0, -16, 64, -8, -16, 0, -18, 0, 2, 0, 2, 0, -24, -8, 44, 0, 44, 0, -2, 8, 28, 24, -50, -32, -28, 0, 52, 0, 20, 40, -12, -40, -12, 0, -64, 0, 10, 0, 2, 0, 8, 8, -8, 8, 8, 0, 64, 32, -20, -56, 28, -16, 0, -88, 6, 0, 56, -16, -32, -16, -2, 0, 20, 0, 12, 0, 20, 0, 44, -32, 0, -16, 2, 0, -4, 0, 8, 8, -2, -8, -8, 24, 44, 0, -32, -4, 0, -8, -12, 0, 0, 0, 24, 0, -12, 0, -16, 32, -36, 4, 12, 0, -2, 32, 88, -8, -2, -16, -12, 56, -2, 0, -32, -40, -4, 0, -36, 0, 68, 0, -20, 0, -48, 0, 20, -8, 2, 0, 4, 0, 0, -48, -4, 56, 86, -16, 4, -40, -16, 0, -16, -8, -32, -48, 12, 0, 36, 0, 8, 0, 16, 0, 22, 16, 80, -32, 4, 0, 40, -8, 0, -120, -22, 16, 72, 0, 102, 0, 64, -56, 16, 16, 36, 0, -52, 0, -4, 0, 100, 0, 0, -56, 28, -16, -28, 0, 64, 8, -84, -8, 60, -16, -16, 112, -16, 0, 80, 48, -18, 64, 8, 0, 8, 0, 2, 0, -124, 0, 112, 80, 2, 40, -116, 0, -72, 8, -24, 48, 32, -8, -36, -32, 44, 0, -84, 0, 12, 16, 44, 0, -48, 0, 56, 0, -2, 0, -80, 8, -68, 48, 28, 0, -104, 24, 112, 48, -50, 48, -6, -32, -44, 0, -28, 76, -32, 0, -16, 0, 52, 0, -10, 0, 44, 0, 20, 8, -132, 40, -12, 0, -12, -40, -36, -40, 32, 0, -12, -72, -128, 0, -20, 8, -64, 40, 72, 0, 80, 0, 10, 0, 32, 0, -144, -24, 2, 24, -108, 0, -40, 48, 8, 64, -46, 8, -28, 0, -8, 0, 64, 8, -6, 48, 8, 0, -96, 0, 100, 0, 64, 0, 64, 32, 12, 56, -20, 0, -60, -56, -184, 56, 28, -144, -12, -16, -20, 0, 0, -24, -40, -88, 16, 0, 6, 0, -208, 0, -100, 0, 56, -152, 20, -16, 40, 0, -32, 56, -148, -16, -6, -128, -2, 48, 8, 0, -96, -16, 20, -80, -68, 0, -60, 0, 12, 0, -84, 0, -60, 152, 20, 0, -28, 0, -60, 80, 44, -24, -76, -32, -64, 112, 0, 0, -80, -16, 26, 48, 2, 0, 156, 0, -56, 0, -4, 0, -56, 0, -72, 80, 8, 0, 0, 8, -52, -40, -2, 8, 72, -8, -96, 0, -8, -48, 110, 24, 96, 0, 44, 0, -8, 0, 48, 0, -32, 0, 164, -4, -44, 0, 0, -16, 88, -8, 80, 176, -12, 0, 56, 0, 136, 80, 0, -48, 48, 0, -184, 0, 24, 0, 40, 0, 12, 0, -12, 0, 100, 0, 32, 0, -16, 0, 32, 32, 84, 32, -36, 0, 88, 4, -8, 144, 12, 0, 80, 0, -136, 0, -2, 0, 98, 32, 52, -80, 88, 0, -104, -8, -120, 32, -2, 40, -52, -16, 104, 0, -12, 16, 36, 56, -24, 0, -2, 0, 8, 0, -12, 0, -32, -24, -124, -40, 24, 0, -4, 8, 176, 0, -172, 32, -36, -136, -84, 0, 16, 72, 68, 16, 128, 0, 220, 0, -20, 0, 12, 0, -28, 40, -48, -112, 152, 0, -28, 80, 20, 16, 172, -8, 80, 40, 2, 0, -12, 0, -76, 16, 4, 0, 68, 0, 8, 0, 0, 0, 4, -48, 184, 48, -4, 0, 84, 56, 72, 272, 86, 16, 52, -16, 78, 0, 4, 96, 56, -40, 32, 0, -16, 0, 70, 0, 36, 0, -16, -40, -80, -8, 76, 0, -32, -80, -164, -48, 22, 192, 12, -64, 152, 0, 64, -200, 36, -192, 20, 0, 28, 0, 8, 0, 16, 0, 208, -64, 16, -32, -102, 0, -104, -16, 22, -120, -8, 16, -36, 256, 80, 0, -140, -32, 84, -112, 4, 0, -104, 0, 40, 0, 40, 0, -140, -8, -184, -32, 0, 0, 140, -120, 336, -32, -22, -152, -100, 16, -4, 0, 72, -40, -136, 0, -56, 0, 102, 0, -52, 0, -84, 0, 64, 8, -56, -56, 8, 0, 16, -56, -88, 16, 86, 40, 36, -176, -80, 0, -72, -56, -52, 0, 20, 0, 96, 0, -4, 0, 18, 0, -116, -88, 100, -40, -48, 0, 40, -112, 0, -328, -136, -56, 40, -8, 28, 0, 136, -16, -40, -48, -28, 0, -308, 0, 104, 0, 64, 0, 120, 8, -76, -112, -84, 0, 8, -8, -252, -176, 60, 192, 44, -16, -28, 0, -16, 44, -144, 112, 24, 0, -16, 0, -196, 0, -52, 0, 80, 184, 76, 48, 136, 0, -18, -96, -72, 64, -96, 160, 8, -144, -28, 0, -216, 0, 8, 120, -64, 0, -112, 0, 2, 0, -104, 0, -116, -176, -124, -120, -56, 0, 148, -256, 112, 160, -138, 80, -148, -128, 2, 0, 96, 40, 116, -136, -116, 0, 208, 0, -132, 0, -72, 0, -164, 8, 80, -184, -24, 0, -32, 48, 8, -24, 32, -24, 48, -8, -192, 0, -36, 104, 216, -32, 24, 0, 44, 0, 48, 0, 0, 0, -84, 144, 220, 0, -104, 0, 12, 8, 28, 16, 120, -240, 44, 8, 80, 0, 152, -200, -48, 136, -88, 0, -232, 0, 56, 0, 150, 0, 36, -136, -2, 88, 168, 0, 96, 48, -80, 96, 32, 8, 36, 176, -68, 0, 48, 48, 8, -32, 28, 0, -8, 0, -52, 0, -104, 0, 76, 24, 12], "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, 28, 4, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 4, "minimal_twist": "420.2.c.a", "char_is_minimal": true, "conrey_index": 391, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, 0, 1, -1, -1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, -1, 0, -1, 1, 0, -1, 0, 1, 1, -1, -1, 1], [1, 0, 1, 0, -1, -1, 1, 1, -1, 1, -1, 0, 0, 1, -1, -1], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, 0, 0, -1, -1, 0, 0, 1, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, 0, 2, 1, 1, 1, 0, 1, -1, 1, 1, 2, 0, -1], [0, 1, -2, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, -2, 1, 1], [0, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 1, 1, 0, 2, 1, -1, 0, 1, 0, -1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 2, -1, 0, -1, -1, 0, 2, 0, -1, 1, -1, -1], [2, -1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [-1, -1, -3, -1, 0, 1, -1, -2, 1, 0, 1, 0, -1, 1, 2, 1], [-1, 0, 1, 1, 0, -1, 1, 0, -1, 0, -1, 2, 1, 1, 0, -1], [0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, 0, 1, -1, -1, 1], [-2, 0, 0, 1, 0, 1, -1, 0, 1, -1, 0, -1, -1, -2, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -2, -2, 0, -1, 0, 0, 1, 1, 0, -1, 0, 2, 1, 1], [-2, 3, 0, 0, 0, 1, -1, 1, 0, 0, -1, -1, 1, -2, -1, 1], [0, 1, 1, 1, -1, 0, -1, 1, 0, -1, 0, 1, 1, -1, -1, 1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1], [0, -2, -2, -2, 0, -2, 2, -2, -1, 1, -1, 0, -2, 2, 0, -1], [1, 0, 1, 0, -1, -1, 1, 1, -1, 1, -1, 0, 0, 1, -1, -1], [0, -2, 0, 1, 0, 1, 0, 1, 1, -1, -2, -1, 0, 0, 0, -1], [0, -2, -2, -1, 0, -1, 1, -2, 1, 1, 0, 1, -1, 2, 1, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, -1, -1, -2, 1, 1, -1, 0, -1, 0, 1, 1, 0, -1], [0, -2, 2, 1, 0, 1, 2, 1, -1, 1, -2, 3, 2, 2, 0, -1], [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0], [-1, -2, 0, 0, -2, -2, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 1, -3, -2, 1, -1, 0, -1, 2, -1, 1, -1, -2, -1, 1, 1], [-3, 2, -1, -1, 0, 0, -1, 0, 0, -1, 3, -1, -1, -1, -1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 0, 0, 0, -1, -1, 0, -1, 1, -1, -1, -1, 0, 0], [0, -1, 1, 1, 3, 1, -1, 0, 0, 0, -2, -1, 0, -3, -1, 1], [1, -1, -1, 0, 0, 0, -1, -1, 0, 0, 1, -1, -1, -1, 0, 0], [-3, -1, -5, -3, 1, 0, 1, -3, 1, 0, 1, -2, -3, 1, 2, -1], [0, 1, 2, 1, 0, -2, 2, 1, -2, 1, -4, 0, 2, 2, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, -2, 1, 2, -3, 2, 1, -1, 0, 0, 1, -2, 2, 0, -1], [0, 1, -2, -1, -2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 3, -2, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, -1], [-1, 0, -1, 0, 0, 1, -1, -1, 1, -1, 1, 0, -1, -1, 1, 1], [0, -1, 2, 0, 2, 1, 1, 1, 0, 1, -1, 1, 1, 2, 0, -1], [0, 1, -2, 0, 2, -1, 0, 0, 0, -1, -1, 1, 0, -2, -1, 2], [0, 0, 0, -1, -4, 1, -1, 0, 1, -1, 0, -1, 1, -2, -1, 2], [0, 1, -2, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, -2, 1, 1], [-1, 1, 1, 1, -1, 0, 0, 1, 0, -1, 0, 1, 1, -1, -1, 1], [0, 0, 3, 2, 1, 2, -1, 2, 1, 0, -3, -1, 1, 1, -1, -2], [0, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, -1, 2, -1, -1, 1, -1, 1, -1, 1, -3, 1, 2], [-1, 1, -1, -1, -1, 0, -1, -1, -1, 0, 3, 2, -1, 1, 2, 1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 4, -1, 2, -1, 1, 2, -1, 1, -2, 1, 1, 2, -1, -2], [-1, 1, 3, 0, 2, 0, -1, 1, 0, 0, -3, -3, -1, -1, 0, -2], [1, 0, 1, 1, 1, 1, 0, 2, 1, -1, 0, 1, 0, -1, 0, 0], [0, -1, -2, -1, 0, 0, 0, -1, 1, -1, 3, 0, 0, -2, 2, 1], [1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -3, 0, 5, -1, 0, -3, -2, 1, 1, -3, -2, 3, 1, -1], [0, -1, 0, 1, 0, 0, 2, -1, -1, 1, 3, 2, 2, 4, -2, -1], [-2, 0, 0, 0, 2, -1, 0, -1, -1, 0, 2, 0, -1, 1, -1, -1], [0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [4, 2, -2, -1, 0, -1, -1, 0, 1, -1, 2, 1, 1, 0, -1, 2], [2, -1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, -2, 0, 1], [-4, 0, -4, 1, 2, 1, -1, -2, 1, -1, 2, -1, -1, 0, 3, 2], [0, -1, 2, -1, 4, 0, 0, -1, 0, 1, 2, 0, 0, 2, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [-1, 2, 1, 0, 0, -1, -1, 1, 1, -1, 1, 0, -1, 1, 2, 1], [3, -3, 1, 1, -3, 0, -1, -1, -1, 0, 1, 0, -1, 1, 0, -3], [-1, -1, -3, -1, 0, 1, -1, -2, 1, 0, 1, 0, -1, 1, 2, 1], [0, -2, -2, 1, 0, -3, 3, 0, 1, 1, 0, 1, -1, 4, 1, -2], [0, -1, -1, 0, -1, -1, 1, 0, 0, 0, -1, 0, -1, 1, 0, -1], [-1, 0, 1, 1, 0, -1, 1, 0, -1, 0, -1, 2, 1, 1, 0, -1], [0, -3, 3, 1, 3, 2, -1, 1, 1, -1, -3, -1, 1, 1, -1, -2], [-1, 0, -1, 2, -3, 1, -2, 1, 0, -1, 1, -1, 0, -1, -1, -1], [0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, 0, 1, -1, -1, 1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}