# Stored data for newform 201.2.a.d, downloaded from the LMFDB on 19 April 2024.
{"label": "201.2.a.d", "space_label": "201.2.a", "level": 201, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666121, "dim": 3, "is_polredabs": true, "nf_label": "3.3.148.1", "trace_hash": 221836007696320923, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [5, -1, -3, 1]]], "qexp_display": "q+(1+\\beta _{2})q^{2}-q^{3}+(2-\\beta _{1}+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 804, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 1.6049930806277357, "hecke_ring_index": 1, "level_radical": 201, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [201, 1, [68, 136], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 67], "conrey_indexes": [1], "field_disc": 148, "field_disc_factorization": [[2, 2], [37, 1]], "field_poly": [1, -3, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "2.866", "prec": 17}, {"__RealLiteral__": 0, "data": "0.640", "prec": 17}, {"__RealLiteral__": 0, "data": "21.674", "prec": 20}, {"__RealLiteral__": 0, "data": "4.756", "prec": 17}, {"__RealLiteral__": 0, "data": "239.994", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [67, -1]], "trace_display": [3, -3, 1, 1], "traces": [0, 3, 3, -3, 5, 1, -3, 1, 9, 3, -1, 10, -5, -8, 7, -1, 5, 0, 3, -2, -7, -1, 0, 3, -9, -8, -18, -3, 3, 4, 1, 11, 11, -10, -2, 5, 5, -9, -28, 8, -17, 1, -7, -3, -2, 1, -7, 18, -5, -10, -2, 0, -32, 7, -3, 12, -11, 2, -4, 15, 7, -2, 3, 1, 33, 6, 0, 3, 16, -3, 9, 18, 9, -19, 5, 8, -42, 2, 18, 28, -29, 3, 29, -7, -3, -18, -3, -4, 4, -6, -1, -4, 11, -11, 36, 12, -11, -8, -14, 10, -12, 16, 2, 4, -50, -5, -29, -2, -5, 2, 14, 9, -5, -4, 28, -15, -28, -8, 55, -20, 17, 19, 0, -1, 33, -3, 7, 16, 25, 3, 20, -11, 2, -14, 3, -1, 54, -3, 7, 3, 1, -18, 4, -8, 5, 28, -39, 10, 21, 20, 2, 10, -44, 0, 32, -19, 32, -47, 32, -7, -29, -25, 3, -44, 49, -12, 13, -27, 11, 1, -36, -2, -5, -12, 4, 8, -38, -15, -52, 4, -7, -11, -10, 2, 57, -25, -3, -16, 34, -1, 26, 0, -33, 19, 34, -6, -34, -15, 0, -24, -38, -3, -2, 20, -16, -19, -26, 3, -68, 32, -9, 30, -21, -18, -12, -1, -9, -27, -36, 19, 4, -16, -5, -26, 3, -8, 26, -33, 42, -14, -33, -2, -68, 51, -18, 20, 75, -28, -18, 38, 29, -7, -37, -3, 30, 10, -29, 44, 101, 7, 17, -4, 3, 4, 26, 18, 5, 32, 3, -11, 46, 4, 19, -21, -4, -1, 8, 6, 5, -20, 1, 44, 68, 4, -39, -28, -11, -17, 65, 11, -19, -16, -36, 26, -6, -12, -4, 9, 11, 5, 52, 8, -69, 54, 14, -5, 39, -10, 64, -14, 12, -1, 68, -16, -106, -32, -2, -12, 10, -4, -49, -20, 50, 22, -39, 5, 64, 20, 29, 48, -11, 2, -9, -12, 5, 20, -40, -2, 61, 38, -14, -13, 1, -9, -69, 1, 5, 14, 65, 4, -34, 22, -28, -1, -9, 15, 18, 8, 28, -7, -14, 8, -28, -43, -55, 28, -86, 20, -22, -1, -17, 35, -17, -19, -8, 11, 0, 24, 49, 1, -41, -37, -33, -18, -60, 3, 12, 24, -7, 27, 56, -16, 4, 36, -25, 24, -5, -3, -4, 38, -20, 58, -70, 11, -7, -4, -2, -30, -40, 14, -20, 47, -3, -44, 72, 1, 36, -66, -54, -16, -39, 3, 0, 35, -7, 5, -94, -3, -40, -21, -1, 17, 110, 18, 31, -20, -4, -30, -22, 8, 1, 43, -5, -4, 3, -28, -38, 12, 39, -28, -18, -10, -48, -64, -21, 28, -42, -20, 3, -38, -2, -44, 0, -10, -45, -6, 44, 18, -6, 0, -29, 20, -32, 27, -116, 19, 77, -26, -32, 1, 22, 47, 75, -10, -32, -8, 0, 7, -2, 25, 29, -12, -93, 25, -63, 30, -3, 55, 88, 44, 30, -75, -49, -72, 128, 12, 93, 14, -13, -12, 57, 27, -28, -30, -11, -58, -78, -1, -4, -4, 36, -9, -1, 2, 16, -22, 5, 56, -43, 12, 84, -16, -4, 16, 13, -8, -109, 76, 38, 2, -9, 15, -2, -50, 52, 8, 9, -4, 26, -16, 7, 42, 8, 11, 66, 4, 10, 57, -87, -2, 32, 48, -57, 0, 83, 25, 101, 12, 3, 8, -29, 16, -6, -42, -34, 22, -8, 1, -12, -10, -26, 22, 4, 0, -17, -34, 33, -42, 37, -19, 52, 25, -34, 56, -109, 6, 106, -36, 34, -6, -25, 15, 101, -41, 0, -38, 76, 24, -36, -30, 38, 38, -7, 3, 46, 45, 2, 26, -136, -20, -62, -52, 16, -73, 60, 19, -64, -72, 26, -28, -63, -3, 2, -18, 68, -3, -4, -32, -93, 52, 9, -64, 124, -30, 26, 46, 21, 44, 56, 18, 3, -57, 12, -24, 3, 1, -88, -54, 9, 0, 44, 27, -56, 7, 36, -5, 135, -19, 56, -27, -4, -38, 15, 16, -43, -4, 5, -60, -79, 26, -1, -40, -3, 20, 32, 8, 131, 75, -26, 72, -12, 33, -92, -64, -42, 45, -59, 14, -5, 14, 33, 42, 36, 2, -84, -33, 68, 30, 95, -51, -8, 35, 18, -58, 74, -20, -41, -76, -75, 27, 38, 28, -108, 95, 18, -16, -32, -38, 97, 15, -29, -52, 51, 7, -69, 8, 37, -9, 2, 3, 41, 0, -30, -82, 80, -10, 45, 10, 29, -17, -37, -44, 13, 23, -101, 8, -68, -7, -20, -2, -17, -50, 10, 4, 80, 32, -3, 10, -59, -4, 102, -2, -26, -34, -32, -18, 80, -90, -5, 32, 46, -32, -23, -28, -3, -60, -122, 11, -72, -104, -46, 96, 68, -4, -78, 7, -19, -39, -15, 21, -36, 52, 4, -28, 30, 1, -60, 82, -8, -60, -30, -6, 79, -26, -5, -37, -110, 20, 238, -1, -1, -3, 4, -44, -24, -28, -68, 2, 84, -4, -69, 24, 39, -34, 82, 28, 25, 66, 11, -38, 17, 17, -124, -36, -65, -17, -12, -11, 109, 46, 19, 25, 69, 16, 150, -65, 36, -11, -47, -26, -12, 29, 6, -50, -36, 12, -32, 93, 4, -14, 7, -9, 27, 19, -11, -30, -20, -5, 11, 76, -52, -8, -4, -8, -98, -23, 69, 34, 24, -54, -48, -88, -14, -29, -116, 5, -6, 41, -39, 56, 62, 10, -14, -52, -64, 14, 49, 14, -20, -76, -12, 46, 26, 1, -82, 41, -68, -52, -33, 16, -8, 66, 106, -36, -86, 32, -38, 25, 2, -15, -3, 12, 52, -12, -10, 16, -7, 4, -116, -28, 49, 32, 99, 20, -16, -56, -50, 130, 7, -22, -32, -8, 39, 3, 145, -5, 0, -9, -64, 88, 92, -20, 34, 20, -29, 36, 38, -48, 53, 9, 11, 54, -54, -2, -113, 37, 9, 14, -59, 12, 68, 78, -5, 29, -21, -20, 126, 6, 40, 56, 54, 2, -67, -4, -61, -7, -144, -38, 240, -3, 14, -51, 107, 13, 64, -4, -1, 53, 44, 9, 117], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "201.2.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [1, 0, 1], [-1, 0, 0], [2, -1, 1], [0, 1, 0], [-1, 0, -1], [0, 1, 1], [4, -3, 0], [1, 0, 0], [-1, 2, 0], [3, 1, -1], [-2, 1, -1], [-3, 1, -1], [2, 1, 0], [0, -1, 0], [3, -4, 2], [1, -3, -1], [1, 0, 1], [-1, 1, -3], [-3, 2, -1], [0, -1, -1], [-1, 3, 3], [2, -3, -2], [-4, 3, 0], [-3, 1, 1], [-7, 3, -3], [-1, 0, 0], [1, 0, 0], [0, 4, 0], [1, -2, 0], [5, -4, -2], [5, -4, 3], [-3, -1, 1], [1, -5, 1], [1, 2, 1], [2, -1, 1], [-2, -3, 1], [-11, 5, -1], [3, -1, 1], [-6, 1, -3], [1, -2, 3], [-2, -1, 0], [-1, 0, 0], [-1, 1, 1], [0, 1, 0], [-1, -4, 2], [5, 3, 3], [-3, 4, -2], [-4, 2, 0], [-1, 1, -3], [-1, 3, 1], [-13, 7, -5], [3, -2, -5], [-1, 0, -1], [3, 3, 1], [-3, -2, 1], [1, -1, 3], [-4, 8, 0], [5, 0, 5], [3, -2, 1], [1, -5, -1], [3, -6, 5], [0, 1, 1], [12, -3, 1], [3, -3, 1], [1, -3, -3], [1, 0, 0], [7, -5, 3], [-2, 3, 2], [2, 3, 1], [5, 3, -1], [4, -3, 0], [-7, 2, -2], [4, -7, -2], [3, -1, -1], [-17, 9, -5], [-1, 5, 5], [7, -3, 3], [10, -2, 0], [-10, 1, -4], [1, 0, 0], [12, -7, 1], [-3, 2, 3], [-1, 0, 0], [-5, -3, -3], [-1, 0, -1], [0, -4, 0], [3, -5, -7], [-3, 3, -5], [-1, 2, 0], [-1, -1, -1], [5, -4, 3], [-5, 4, 2], [11, 3, 5], [5, -3, 1], [-5, 4, -3], [-5, 7, 7], [-6, 4, -4], [3, 1, -1], [-5, 3, -3]]}