# Stored data for newform 210.2.t.f, downloaded from the LMFDB on 21 September 2025. {"Nk2": 840, "analytic_conductor": 1.676858442446888, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 105, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 20, "char_orbit_label": "t", "char_order": 6, "char_parity": 1, "char_values": [210, 6, [71, 127, 31], [3, 3, 1]], "cm_discs": [], "conrey_index": 59, "dim": 8, "field_disc": 3317760000, "field_disc_factorization": [[2, 16], [3, 4], [5, 4]], "field_poly": [81, 0, -36, 0, 7, 0, -4, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[11, [1, 0, -22, 0, 483, 0, -22, 0, 1]], [13, [49, 0, -46, 0, 1]], [23, [841, -58, 33, 2, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22519303840465106, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 4, -1, 6, 0], [1, 1, 15, 4, -1, 2, 0], [1, 1, 105, 16, 1, 6, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "210.2.t.f", "level": 210, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [2, 3, 5, 7], "level_radical": 210, "minimal_twist": "210.2.t.e", "nf_label": "8.0.3317760000.3", "prim_orbit_index": 16, "qexp_display": "q+\\beta _{4}q^{2}+(\\beta _{5}-\\beta _{6})q^{3}+(-1+\\beta _{4}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "210.2.t", "trace_display": [4, 0, -12, 0], "trace_hash": 671092773544834431, "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "7.061", "prec": 17}, {"__RealLiteral__": 0, "data": "1.245", "prec": 17}, {"__RealLiteral__": 0, "data": "352.081", "prec": 24}, {"__RealLiteral__": 0, "data": "110.403", "prec": 24}, {"__RealLiteral__": 0, "data": "25210.646", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.598", "prec": 17}, "traces": [0, 8, 4, 0, -4, -12, 0, 0, -8, 8, -12, 0, 0, 0, 0, 8, -4, 0, -8, 12, 0, 4, 0, -4, 0, 4, 0, 0, 0, 0, 4, -24, 4, 12, 0, 8, -16, 0, 12, -8, 12, 0, 8, 0, 0, -24, 4, 12, 0, -24, 8, 20, 0, 20, 0, 0, 0, 40, 0, 0, -4, 24, 0, -20, 8, -16, 12, 0, 0, 0, -8, 0, -8, 0, 0, -24, 0, 4, -16, -24, 12, 4, 0, 0, 4, 0, 0, -12, 0, 0, 0, -32, 8, 20, 12, -12, 0, 0, -12, -40, 4, 0, -20, 0, 0, 40, 40, 0, 0, 16, -24, 0, 0, -96, 20, 12, 0, -60, 0, 0, -8, 0, 24, -8, 24, 0, 20, 0, 4, 12, 16, 0, 0, 0, 0, 28, 0, 8, 60, 0, -16, -120, 0, 12, 8, 24, 0, 40, 0, 0, -24, 8, -12, 0, -40, 48, -8, 0, 24, 0, 0, 0, 8, 0, 0, 8, -72, 0, -4, 80, 0, 24, 0, 36, 0, -48, 0, -8, 0, 0, 24, 0, -76, 0, 4, 48, -20, 0, 0, 56, -24, 0, 0, 0, 0, 0, 12, -72, -20, -24, -4, 48, 0, 80, -40, -16, 0, 8, 0, 0, 8, 152, 20, 12, 0, -24, 0, 0, 32, 12, -24, 0, 24, 0, 0, 16, -48, -72, -20, -72, 0, 40, 0, -16, -60, -12, 0, 0, 0, 0, -4, -60, 0, 0, 0, 36, -16, 0, 24, -40, 36, 0, 40, 0, 0, -60, -4, 120, 0, 28, 32, 40, 0, -8, -12, 0, 0, -16, 0, 0, -28, 0, 0, -100, 16, -48, 60, 0, -96, 0, -8, 0, -60, 0, 0, -48, 0, -32, 16, -28, 24, -12, 0, 0, 80, 32, 0, 84, 0, 0, 0, -80, 16, 32, -12, -24, 0, 0, -44, 16, 24, 0, 8, 0, 0, 44, 48, 48, 0, 64, -12, 0, 0, 80, 4, 96, 0, -180, 0, 0, 16, -20, -72, 20, 36, 0, -8, 0, 40, 60, 0, 0, 0, 0, 0, 56, 36, -48, 12, 0, 0, -112, 0, -48, 8, -24, 0, -20, 0, 0, 24, -24, 0, 0, -44, -48, 0, 0, -4, -60, 0, 0, -40, 0, 0, 28, -12, 0, 28, -120, -12, 12, 0, -60, 0, -48, 0, -40, 0, 0, 84, 0, 24, 56, -36, 72, 20, 0, 0, -40, -8, 0, 48, 0, 0, 0, 64, 56, -20, -24, 16, 60, 0, 136, 16, -72, 0, 40, 0, 0, -32, 64, 76, 24, -20, 0, 0, 0, 0, -20, -24, 0, 0, 0, 0, -56, 16, -132, -12, 48, 0, -24, 0, -104, 24, 16, 0, 0, 0, 0, 8, 12, 48, 0, 0, -12, -40, 0, -72, -20, -12, 0, 80, 0, 0, -84, 16, 216, 0, 56, -24, -8, 0, -64, -60, 0, 0, 80, 0, 0, 4, -156, 0, -8, 0, -24, 0, 0, -24, 0, 36, 0, -8, 0, 0, 12, 0, -80, -80, 80, 36, 60, 0, 0, 20, -128, 0, 240, 0, 0, 0, 96, -8, 20, 120, -16, -12, 0, 68, 80, 16, 0, -40, 0, 0, -124, -16, 40, -12, -32, -60, 0, 0, 184, -8, 0, 0, -84, 0, 0, -56, -56, 0, 20, 0, 0, -80, 0, 8, 48, 48, 0, 0, 0, 0, 44, -96, -20, 48, 0, 8, -40, 0, -72, 60, 144, 0, 80, 0, 0, -48, -16, -12, 0, -76, -8, 8, 0, 28, 36, 0, 0, -24, 0, 0, 92, 12, 0, 40, 32, 16, 0, 0, -120, 0, 80, 0, -120, 0, 0, 24, 0, -64, -80, 8, 0, -32, 0, 0, -100, -48, 0, 0, 0, 0, 0, -4, -160, 8, 12, -24, 60, 0, -136, 16, 92, 0, -8, 0, 0, -32, -16, 24, -60, -48, -24, 0, 0, 128, -40, -12, 0, -60, 0, 0, 56, 40, 12, -4, 168, 0, -44, 0, 28, -180, -56, 0, 0, 0, 0, 8, 48, 20, -60, 0, 64, 40, 0, 36, -40, -96, 0, -4, 0, 0, -168, -40, 228, 0, -48, 0, 0, 0, -32, -24, 0, 0, 40, 0, 0, -56, 24, 0, -80, -96, -96, 12, 0, -72, 0, 48, 0, -56, 0, 0, 192, 0, -64, 16, 24, -24, 48, 0, 0, 20, -24, 0, 0, 0, 0, 0, 136, -48, 80, 0, -48, 120, 0, 32, 176, -24, 0, 0, 0, 0, -24, -8, 136, -60, -4, -48, 0, 0, 24, -20, 24, 0, -144, 0, 0, 56, 128, -12, 36, 72, 0, -28, 0, -60, 48, 12, 0, 0, 0, 0, 40, -60, 88, 0, 0, 36, 80, 0, 156, 40, -24, 0, 40, 0, 0, 84, -64, 120, 0, 12, 32, 28, 0, 36, 0, 0, 0, 40, 0, 0, 20, 24, 0, -8, -240, -4, -120, 0, 48, 0, -112, 0, -16, 0, 0, -12, 0, -16, 80, 28, 144, 20, 0, 0, -152, 32, 0, 60, 0, 0, 0, 32, -144, 8, -240, 72, -48, 0, 80, 80, 36, 0, -20, 0, 0, -40, 24, 32, -24, -76, -120, 0, 0, -40, -48, 0, 0, -12, 0, 0, 32, 0, -192, 20, -168, 0, -100, 0, -84, 0, -36, 0, 0, 0, 0, -28, -72, -16, 120, 0, 112, -24, 0, 48, -40, 24, 0, 24, 0, 0, -96, 104, -24, 0, 200, 32, -80, 0, -108, 12, 0, 0, 136, 0, 0, -8, 0, 0, 100, 96, 0, 0, 0, 72, 0, 108, 0, -20, 0, 0, 24, 0, -4, -40, 64, -12, 12, 0, 0, 40, -192, 0, 120, 0, 0, 0, -116, 32, -16, 216, 40, 60, 0, -80, 0, -12, 0, 8, 0, 0, -64, -128, 0, -60, 168, 12, 0, 0, -288, 40, 72, 0, -180, 0, 0, 8, -36, -156, 0, 60, 0, -64, 0, 0, 60, 24, 0, 0, 0, 0, 128, -24, -72, 72, 0, 0, 64, 0, 300, 8, 108, 0, 120, 0, 0, 12, -64, -24, 0, -64, 48, -40, 0, -80, 168, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, -1, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [-2, 0, 0, -1, 1, -1, 0, 0], [0, -1, 0, 0, 0, 1, -1, 0], [0, 0, -1, -1, 0, 0, 0, 1], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 2, 0, 0, 0], [-1, 0, 0, 0, -1, -1, 0, 0], [0, 0, 0, -2, 0, -1, 0, 1], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 0, 0, 0, 1], [0, 0, -1, -1, 0, -1, 0, 0], [1, -1, 1, 0, 0, -1, 1, -1], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, -2, 0], [-2, 0, 0, 0, 2, 0, 0, -1], [2, 2, 0, -1, -1, -1, 0, 0], [1, 0, 0, 1, -2, 0, 0, 0], [1, 0, 0, 0, -1, 2, 1, -1], [0, 0, -1, -1, 0, -2, 0, 1], [0, 2, 0, -1, -1, -3, 4, 0], [0, 0, 0, 0, 0, -1, 1, 0], [1, 0, 0, 4, -1, 2, 0, 0], [0, 0, -1, 2, 0, 2, 0, 2], [0, -1, 0, -3, 0, 1, -1, 0], [0, 0, 0, 0, 0, -1, 0, -1], [0, 0, 2, 1, 0, 2, 0, -2], [0, 1, 1, 0, 1, -2, 2, 0], [-2, 0, 0, 0, -2, 1, -2, 0], [1, 0, 0, 0, -1, 0, 0, 0], [2, -1, 1, 3, -1, 3, 0, -2], [0, -2, 0, 1, 0, 2, -2, 0], [0, 2, 1, 0, 2, -2, 0, -2], [-2, 0, 1, 0, 0, 0, 0, -1], [0, 0, -1, -2, 0, 2, 0, 0], [1, 0, 0, 0, 1, 1, -2, 0], [-2, -2, 0, 6, 2, 4, -1, 2], [2, 0, 0, 1, -1, 1, 0, 0], [0, 0, 1, 2, 0, 0, 0, 1], [1, 1, 1, -3, 0, -1, 1, -1], [0, 0, -2, -1, 0, -2, 0, 2], [0, 0, -1, 1, 0, -1, 0, 0], [-2, 0, 2, 0, -2, -1, -2, -1], [1, 4, 0, -2, -1, -3, 2, 0], [2, -6, 0, 3, -1, 3, 0, 0], [0, 1, 0, 0, 0, -1, 1, 0], [-3, 4, 0, -2, 0, -4, 4, 0], [1, 0, 0, 2, 0, 4, 0, 0], [0, 0, -1, 0, 5, 0, 0, 0], [0, 0, -2, 0, 0, 2, 0, 1], [5, 0, 0, 0, -5, 0, 0, 0], [0, -1, 0, -3, 0, -3, 0, 0], [-2, 2, -1, 2, 4, -2, 2, -1], [0, 0, 1, 1, 0, 0, 0, -1], [5, 1, -1, 0, 0, 1, -1, 1], [0, 0, 2, -1, 0, 1, 0, 0], [0, 0, 4, 0, 0, 2, 0, -2], [-1, 2, 0, 0, 1, -1, 1, 1], [4, 0, 0, 0, -2, 0, 0, 0], [2, -2, 0, 1, -4, 2, -2, 0], [0, 2, -2, -3, -5, -3, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 2, -3, -3, -4, -1, 4, 0], [1, 0, 2, 0, 1, 2, 1, -1], [0, 0, 0, -8, 0, -4, 0, 2], [0, -2, 0, 1, 0, 1, 0, 0], [5, 1, 1, 0, -10, -1, 1, 1], [-2, 0, 2, 2, 2, 2, -2, -1], [0, 0, -2, -1, 0, -2, 0, 2], [0, 0, 1, 0, -2, 0, 0, 0], [0, 0, 4, 0, 0, -3, 0, -2], [0, 0, 0, -4, 0, -2, 0, -1], [-4, 1, -2, 0, 2, 0, 0, 4], [-1, -2, 0, 1, 2, 2, -2, 0], [-3, 4, 0, -2, 7, -4, 4, 0], [-2, -1, -2, 3, 0, 5, 1, 2], [0, -2, 0, 1, -6, 3, -4, 0], [1, 0, 0, 0, 1, 1, 0, 0], [1, 0, 0, 0, -1, 0, 0, -4], [0, 0, -1, 2, 0, 2, 0, 2], [-6, -4, 0, 2, 12, 4, -4, 0], [0, 1, 1, -3, 1, -3, 0, 0], [0, -2, 2, 1, 0, 0, 2, -2], [0, 0, -2, 1, 0, -1, 0, 0], [-1, 0, -2, 0, -1, -4, -2, 1], [0, 0, 0, 2, 0, 1, 0, -1], [0, 0, -2, 2, 0, 2, 0, 4], [2, -2, 1, 3, -4, 2, -2, 1], [-9, -6, 0, 3, 10, 4, -2, 0], [1, 2, 0, -1, 0, 0, -2, 0], [0, 2, -1, 0, 5, -4, 4, 0], [1, 0, 0, 0, 1, -3, 6, 0], [-3, -4, 0, 0, 3, 2, -2, -2], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, -2, 3, 0, 0, 0, -2], [0, 4, 0, -2, -3, -2, 0, 0], [-5, 2, -2, -3, 0, -4, -2, 2], [0, 0, 0, -2, 1, 2, 0, 0]]}