# Stored data for newform 210.2.u.a, downloaded from the LMFDB on 16 April 2024.
{"label": "210.2.u.a", "space_label": "210.2.u", "level": 210, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1374423089362, "dim": 16, "is_polredabs": true, "trace_hash": 2012953858187677387, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[13, [171295744, 51933184, 7872512, 9624320, 18339968, 7707968, 1764384, 370872, 304225, 126936, 29856, 4424, 1442, 536, 128, 16, 1]]], "qexp_display": "q+\\beta _{12}q^{2}-\\beta _{6}q^{3}+\\beta _{5}q^{4}+(\\beta _{1}+\\beta _{3}+\\cdots)q^{5}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 35, "char_orbit_label": "u", "char_is_real": false, "Nk2": 840, "analytic_conductor": 1.676858442446888, "hecke_ring_index": 1, "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": "0.095", "prec": 17}, "analytic_rank_proved": true, "char_values": [210, 12, [71, 127, 31], [12, 9, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [73, 103, 157, 187], "field_disc": 88982531009962573824, "field_disc_factorization": [[2, 32], [3, 8], [1777, 2]], "field_poly": [4, -40, 164, -344, 390, -336, 358, -180, 351, -176, 118, -24, 67, -48, 12, -4, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.268", "prec": 20}, {"__RealLiteral__": 0, "data": "1.568", "prec": 17}, {"__RealLiteral__": 0, "data": "766.063", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63123.374", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c12", "trace_display": [0, 0, 12, -8], "traces": [0, 16, 0, 0, 0, 12, 0, -8, 0, 0, 8, 4, 0, -16, 16, 4, 8, -12, 0, -8, -8, 8, 4, 32, -8, -32, -12, 0, -8, 0, -4, -24, 0, 8, 16, 4, -16, -8, -28, -12, 0, 0, -4, -24, 0, 4, -4, -24, 0, 52, 0, 8, -8, 44, -8, -56, 8, -8, 48, 8, 0, 24, 8, 4, 0, 16, 0, 36, -12, -8, 32, -32, 0, -40, -24, -24, 0, -44, -16, 12, 12, 8, 12, -16, 4, 8, -8, 12, 8, -16, 0, 8, 8, 40, 8, -48, 0, 44, -8, 0, -16, 24, 12, -20, -16, 16, 8, 28, 0, -48, 12, 0, -4, 96, -12, 8, 8, -8, -36, 32, 0, 12, -28, 36, 28, -24, -4, 12, 0, 8, -52, 36, 4, -48, 0, 0, 0, 84, 40, 48, 24, 16, 32, 0, 0, 28, 0, -40, -16, -24, 4, 12, 28, 24, 8, -88, -8, -40, 36, 4, 4, -76, 0, -16, 8, -12, -60, 0, 4, 0, -20, -12, 12, -52, 16, 96, 8, -12, -24, -72, -12, 0, -92, -56, 24, 92, -28, -60, 24, -8, 48, -16, 0, 36, -16, 16, -20, 8, -4, 56, -8, -24, 56, -56, 0, -72, 0, 32, -8, -64, 48, -8, 44, 16, -24, 88, 0, -84, 0, -48, 12, -32, -8, 20, 8, 20, -16, -116, 20, 40, 24, 4, -36, -68, 8, -108, 24, 0, -120, 0, -4, -12, 48, 0, -32, 100, 16, 100, -40, -60, -48, 0, 8, -64, -48, 20, -8, -44, 24, 64, -16, 8, -72, 0, 4, 52, 76, -24, -36, 48, -12, 60, -24, -52, 0, -32, 24, 144, 8, -56, 28, 8, 0, 64, -48, 0, 0, 24, 0, -144, 112, 16, 40, 104, 8, 100, -4, -8, 0, 88, -16, 104, 24, 4, 8, -84, 0, 8, 28, 0, -24, 48, 8, 16, 32, 24, 16, 56, 28, 24, -4, 0, -20, 152, 0, 96, 56, 48, 24, -48, 36, -12, 4, 8, -8, 8, -8, -84, 32, 16, 16, -48, -8, -8, 0, -12, 36, 164, 12, -48, 0, 16, 8, -48, 24, 16, 0, -60, 24, -24, -8, -44, -52, -48, -16, -104, -16, 12, 40, 8, -64, -108, -8, -64, 48, -96, -12, -8, 4, 0, -80, -48, 108, -120, -16, 104, -16, 12, 8, 24, -44, 0, -48, -36, -24, -28, -4, 16, -16, 56, -16, 4, -84, 64, 56, 0, -52, 184, -12, 76, -132, -48, -64, -104, 0, -128, -12, -8, 76, -16, 32, -16, -28, -24, -60, 140, 0, -236, 8, 84, 44, 0, 0, 72, 32, 80, -16, -116, -16, -48, 0, 28, -40, 12, 4, -88, 72, 48, -4, 0, -8, 12, -48, -24, -24, 40, 16, 16, -116, 0, -60, 0, 44, -80, 0, -24, -8, -132, 16, 8, -72, 16, -12, 44, 8, 8, 32, -16, 116, 16, 4, -132, 64, -16, 0, -64, 0, 84, -28, 112, 4, -128, 36, -56, 72, 24, 0, -16, -16, 24, -4, 8, -76, 24, -16, -68, 20, 16, 72, 0, 32, -68, 0, -28, 0, -16, 0, -40, 12, 0, 20, 36, 48, 76, -32, -12, 64, 8, 4, -48, 88, 0, -48, 88, -48, -36, 8, 84, 92, 200, -4, -24, 128, 28, 8, -120, -32, 80, -84, 16, -68, 120, 8, 92, 0, -20, 72, -4, 32, -80, -4, 96, -4, -8, -12, -64, 0, -4, 16, 24, -64, 64, 0, 24, 64, 8, -8, 32, -64, -8, 44, 24, -44, 100, 0, -28, 12, 48, -24, 0, 16, -24, 8, -20, -8, 56, -80, 4, 120, -168, 16, 0, -52, -48, 144, 96, -56, 156, -8, -20, -24, 116, 12, 144, -104, -72, 20, -48, -44, -72, 8, -24, -32, 0, 0, 60, -120, -52, -40, 32, 4, -16, 36, 4, 0, -132, 0, -64, 24, 48, 0, -68, -20, 8, -40, 88, 48, -64, 0, 36, -80, 112, 8, 108, 16, -20, -12, -56, -4, 0, -48, -48, -36, 28, -16, 24, 8, -56, -24, 72, 52, 0, 4, -76, 0, 8, 4, 20, -96, -112, 0, -12, 8, -80, 8, 48, 92, -64, -12, 16, -12, -24, 16, 16, 0, 8, 0, -92, -72, -16, 36, 112, 8, -204, 0, -12, 0, 56, -36, -24, 80, -8, 24, -104, 64, 8, 36, 100, -40, -56, 8, 128, 48, 128, 32, 64, 60, 4, 64, 0, 156, -24, 28, -32, -32, -40, -8, 36, 12, -24, 32, 0, 84, -64, 24, 48, 96, -20, 24, 56, -8, -96, 0, -32, -16, 40, -8, -128, 84, -20, 52, 84, 12, -24, 0, 16, 36, -32, 0, 32, -136, 0, 36, -116, 0, 4, 0, -72, 8, 216, -20, 64, 28, 36, -4, -16, -16, -88, 100, 32, -20, -152, -4, 124, -96, 56, 0, 40, -72, 0, -24, -48, 4, -28, 16, -32, -48, 100, -4, -72, 4, 0, -48, -8, -216, 16, -8, -68, 0, -16, 72, -56, -60, 44, 24, -28, -132, -16, -32, -88, 20, -48, -16, 12, 0, 60, -156, 40, 12, 176, -8, 32, -188, -44, -72, -32, 0, 144, 16, -72, -184, -4, -16, -64, 24, 16, 20, -68, -72, -104, 40, -16, 56, 48, 8, -32, -144, 64, 16, 0, 28, -216, -48, -52, 16, 104, 0, -40, -8, 12, 8, 0, 24, 24, 96, 32, -48, -144, 16, 76, 0, -4, -80, -76, -40, -100, 4, 72, 20, 8, 32, -48, -112, -44, 0, 92, 144, -188, -116, -112, -12, -320, 20, 92, 144, -96, 0, 124, 24, 72, 60, 104, -44, -176, -20, 80, 4, 20, 12, 48, -56, 76, 112, -100, -8, 56, 12, 124, 112, 0, -48, 336, 64, 164, 16, -28, -32, -36, 36, -192, 124, 0, 36, -24, 60, -4, 16, 24, -160, -64, 0, 156, 192, -28, 28, 128, -80, 92, -48, -48, 120, 252, 0, 96, 0, 8, 24, 136, -8, -160, -24, 32, -20, 128, -12, 44, 0, -8, 32, -288, -48, -68, 40, -168, -64, -216, -8, 256, -24, 4, 8], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 35, 11, 1, 12, 0]], "char_orbit_index": 21, "prim_orbit_index": 11, "minimal_twist": "210.2.u.a", "char_is_minimal": true, "conrey_index": 73, "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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [-1, 1, 0, 0, -1, -1, 1, 0, -1, 0, 0, -1, 0, 1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, -1, 0, -1, 0, 0, 2, 0, 1, 1, -1, 1, 2, -1, 1, 1], [-2, 2, 0, 1, 2, 1, 0, -2, -1, -2, 0, 0, 2, 0, -1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, 0, -2, -1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1], [0, 0, 1, -1, -1, 0, 1, 0, 0, -1, -1, 0, 0, -2, -1, 1], [1, 0, -1, -1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [-4, 1, 2, 0, -1, -2, 2, -1, 2, -1, -1, 1, 3, -2, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [3, 0, -2, 1, 1, 3, 1, -1, -2, 1, 3, 1, 0, 2, 3, 1], [0, 0, 0, 1, 1, 2, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, -1, -1, -1, 0, 1, 1, -1, 0, 0, 0, 0, 0, -1, -1, 1], [3, -2, -1, -2, -1, 0, 2, 1, 1, 2, 0, 1, 0, -1, 3, 0], [2, 2, 1, 2, 1, 0, 0, -1, -1, -2, 2, 0, 1, -1, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [-2, 0, 1, 1, 0, -2, -1, 0, 1, 2, 0, -1, 0, 2, 0, -1], [-3, 1, 1, 0, 2, -1, -1, -1, 0, -2, 0, 0, 0, 1, -1, 1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1], [0, 0, 1, 0, -1, 0, -2, 0, -1, -1, 1, -1, -5, -1, -1, -4], [0, 0, 0, 0, 0, 0, -1, 1, -1, 0, -1, -1, -1, 1, 0, -1], [0, -2, -4, 2, 2, 6, -3, -2, 2, 2, 1, 1, -2, 0, 2, 1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 0, -1, 1, 1, 0, 0, 2, 2, 1, 0, 1, 2, 0], [1, -1, -2, -1, 2, 1, -2, -1, 0, -1, 0, 1, -1, -1, 1, 2], [2, -2, -1, -1, -2, -2, 2, 3, 0, 2, -1, -2, -2, -2, 0, -4], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -3, -4, 4, -4, -3, -3, -4, -5, 2, -2, -2], [-1, -1, 1, 0, -2, -1, 0, 3, 1, 1, -1, -2, -2, -1, 0, -2], [0, -1, 0, 0, 1, -1, -1, 1, 0, -1, 0, 0, -1, 0, 1, 0], [1, 0, 1, 0, -1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, -1], [-2, -1, -3, -3, 1, -3, 6, 1, 4, 2, -4, 1, 4, -2, 1, 3], [1, -1, 0, 1, 0, 1, -3, 0, -1, 0, 1, -1, -2, 0, 0, -2], [-1, 0, 0, -1, -3, -1, 0, 2, -3, -1, -1, -2, -3, -2, -2, -1], [-1, 1, 0, 2, 1, 1, -2, 0, -2, -1, 0, -2, -1, 1, -2, -2], [0, 0, 0, -1, -1, -2, 0, 1, 0, 0, -1, -1, -1, 1, 0, 0], [0, -1, -4, -2, -1, -1, 3, 1, 2, 1, 0, 0, 3, -2, 1, 2], [-1, 2, 0, 2, 2, 3, -2, 0, 0, -1, 1, 2, 1, 0, 2, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [3, -1, 2, -1, 0, -4, -5, 3, -1, 0, -1, -2, -6, 2, -2, -3], [-3, 0, 0, 0, 1, 1, 2, -2, 1, 0, -2, 1, 1, -1, -3, 3], [3, -2, -3, 0, 1, 1, -2, 1, -1, 1, 1, 0, -4, 1, 1, -2], [1, -1, -2, -1, 0, -1, 0, 0, 0, 2, 1, 0, -2, 1, 1, 1], [6, -2, -1, 1, 0, 4, -5, 1, -1, 1, 2, 0, -8, -2, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-4, 0, 2, 0, 0, -1, -1, -1, 2, 0, -1, 0, 4, -3, 2, 0], [1, 0, -1, 0, -1, 0, -1, 1, 0, 0, 1, -1, -2, 1, 0, 0], [0, 0, 2, -1, -3, 0, 4, 1, 3, 1, -1, 1, 3, -2, 2, 2], [2, 0, -1, 0, -1, -4, -1, 0, 0, -1, 1, -1, -1, 1, -2, 0], [0, -2, -1, -2, -2, 0, -2, -1, 2, -1, 1, -1, 0, -4, 0, 4], [0, 1, 2, 0, -1, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0], [-1, 2, 3, 0, 3, -3, -2, -1, 1, -3, 1, 0, -2, 3, 1, 2], [3, -2, 3, 2, 2, -1, 0, -1, 2, 2, 0, 1, 0, 2, 4, -4], [1, -1, 0, 1, 0, 1, -2, 0, 0, 1, 0, -1, -2, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 2, -2, 1, -3, -1, -1, 3, -2, -1, 1, -1, 0, 4, -3, 3], [-2, 0, 1, 0, 0, -1, -1, 1, 0, -1, -2, -2, 0, 0, -2, -1], [0, -1, 2, 0, 1, 2, 2, -1, 0, 1, -1, 1, 1, 4, -5, -1], [3, -1, -2, 1, 0, -1, -2, 1, -1, 2, 2, -1, -2, 4, 3, -2], [1, 0, -1, 0, -1, 2, 0, 0, 2, 1, 2, 2, 3, -1, 2, -1], [-1, 3, -1, 2, 0, 2, 0, -2, -1, -2, 0, 0, 2, -3, -3, 1], [-2, -4, -2, 0, 4, 0, -2, -4, 0, 0, 0, 0, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [-5, 0, 4, -2, 2, 7, 2, -4, -2, -2, 0, 2, 2, -4, -3, 0], [0, 4, 2, 0, -4, -1, 5, 0, 0, 0, 3, 3, 2, 0, 2, 3], [-3, 0, -2, -2, 2, -1, 4, -1, 0, 0, -2, 1, 2, 0, 0, 2], [-4, 3, 1, 1, 1, 1, 2, -3, 0, -2, 0, 1, 2, -2, -3, 1], [-2, -3, 1, -4, -4, -4, 3, 5, 3, 2, -4, 0, 2, -5, 0, -1], [0, 1, -2, 1, 0, 0, 0, 0, 0, 1, 2, 0, -1, 1, 1, 1], [0, 3, 2, 2, 1, 0, 1, 2, -3, -1, -1, -2, 0, 2, -1, -5], [-1, 1, 1, 0, 1, -1, 0, 0, 0, -1, -1, 0, 1, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [2, 1, -2, 1, 4, 4, 0, -3, -3, 1, -1, 1, 1, -2, 3, 0], [4, -2, -1, -3, 3, 2, 0, 1, -3, 3, -1, 1, -3, 2, 6, 1], [0, 0, 0, 1, -1, 0, 0, 0, 1, 0, 1, 0, 0, 1, -1, 0], [-5, 1, 0, -1, -4, -5, 0, 3, 4, -1, -2, -1, 3, -3, -7, 4], [-1, 2, 1, 0, -3, -1, 0, 1, -1, -3, 1, 0, -2, -1, -1, 0], [-1, -1, 0, 1, 0, 0, -1, -1, 1, 0, 1, 0, 0, -3, -4, -1], [1, 0, 1, -1, -2, 0, 3, 0, 2, 1, 0, 2, 2, -2, 1, 1], [0, 2, 2, 2, 0, 4, 2, -2, 0, 0, 2, 2, 4, 2, 2, 2], [-1, 1, 1, 0, 0, 0, 1, -1, -1, -1, 0, 0, 1, 0, -1, 1], [2, -1, -1, 5, 3, 5, -2, -3, -2, 0, 4, -1, 2, 4, -1, 3], [0, 1, -2, 1, 2, 4, -2, -2, -2, -1, 0, -2, -1, -1, 1, -1], [4, 0, 4, 0, 1, -2, 4, 1, 1, 2, -2, 2, 3, -1, 3, 0], [2, 0, 0, -2, 0, -3, 3, 2, 2, 2, -1, 1, 0, 2, 4, -1], [-1, -3, 2, -1, 2, -1, 2, -2, -2, -2, -1, 0, 2, 3, 3, -5], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 3, -1, -1, -1, 4, 4, -3, -1, -1, 2, 3, 3, 0, -2, 5], [-3, 3, -1, 1, -1, -3, -1, -1, -1, 0, 1, 0, 3, 4, -4, 3], [-1, -1, 1, -2, -1, -2, 1, 1, 2, 0, -2, 0, 1, -1, 0, 1], [2, -2, 1, 0, 1, 0, -2, 0, 0, 1, 0, 2, -1, -1, 3, -1]]}