# Stored data for newform 513.2.a.e, downloaded from the LMFDB on 18 June 2024. {"Nk2": 2052, "analytic_conductor": 4.096325623691683, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [19, 1]], "atkin_lehner_string": "++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [513, 1, [191, 325], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 321, "field_disc_factorization": [[3, 1], [107, 1]], "field_poly": [1, -4, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-1, -4, 1, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014398543036929, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "513.2.a.e", "level": 513, "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": false, "level_primes": [3, 19], "level_radical": 57, "minimal_twist": "513.2.a.e", "nf_label": "3.3.321.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{1}+\\beta _{2})q^{4}+(-2+\\beta _{1}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "513.2.a", "trace_display": [-1, 0, -5, 1], "trace_hash": 522725262785344086, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.866", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.635", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "231.982", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "traces": [0, 3, -1, 0, 3, -5, 0, 1, -6, 0, -7, -8, 0, -1, -2, 0, 3, -7, 0, -3, 2, 0, 1, -9, 0, 2, 2, 0, -10, 6, 0, -2, -8, 0, 23, 0, 0, -11, 1, 0, 3, -5, 0, 9, -19, 0, -23, -27, 0, -8, 27, 0, 10, -2, 0, 15, 9, 0, -4, 1, 0, 7, -1, 0, -12, 0, 0, -12, 1, 0, 12, 0, 0, -3, 14, 0, -3, 10, 0, 7, 14, 0, -7, -5, 0, -9, 37, 0, 27, 4, 0, -13, 12, 0, 9, 5, 0, -23, 8, 0, -8, -17, 0, -22, -9, 0, 1, 4, 0, 5, 33, 0, 17, 8, 0, 41, 57, 0, -14, -31, 0, 1, -18, 0, -13, -6, 0, 3, 39, 0, -12, -12, 0, -1, 49, 0, 6, 27, 0, -5, 15, 0, 33, -10, 0, -8, -13, 0, -7, 33, 0, -1, 6, 0, 7, 5, 0, 23, -44, 0, 22, 2, 0, 40, 2, 0, 47, -35, 0, -26, -33, 0, -48, 23, 0, -17, 8, 0, -31, -4, 0, 17, -1, 0, -3, 8, 0, -10, -27, 0, 7, 6, 0, -3, -6, 0, -37, 5, 0, -4, 6, 0, 18, -47, 0, 17, -12, 0, -17, 8, 0, 10, -64, 0, -10, -55, 0, 12, -45, 0, 9, 31, 0, -13, -1, 0, 11, -24, 0, -11, 52, 0, -63, -38, 0, 45, -25, 0, -16, 3, 0, -40, 15, 0, 32, 8, 0, 1, 15, 0, -15, 49, 0, 29, -25, 0, -3, -9, 0, -18, -15, 0, -55, -25, 0, 3, 2, 0, -36, -14, 0, 0, -77, 0, 24, -23, 0, 3, 33, 0, -15, 57, 0, -32, -39, 0, -7, 0, 0, 64, -61, 0, 33, 57, 0, 12, 18, 0, -6, -2, 0, 20, -20, 0, -3, 4, 0, 39, 14, 0, 19, -2, 0, 11, -29, 0, 53, -19, 0, -65, 1, 0, 32, 7, 0, 17, -22, 0, 3, -9, 0, 38, -91, 0, -2, -25, 0, -1, 14, 0, -54, 18, 0, 14, 39, 0, 34, -43, 0, -58, -29, 0, 23, -15, 0, -33, 65, 0, 55, -28, 0, 3, 48, 0, 16, 19, 0, -58, 48, 0, 1, 61, 0, -28, -85, 0, 54, 47, 0, -8, -2, 0, 45, -44, 0, -27, -4, 0, -49, 9, 0, -41, 45, 0, -69, 30, 0, 26, -32, 0, -71, 68, 0, -12, -64, 0, -2, 15, 0, 60, 22, 0, 43, 40, 0, -37, 1, 0, -1, 21, 0, -57, -73, 0, 66, 86, 0, -7, 11, 0, -44, -40, 0, 32, 3, 0, 40, 9, 0, -5, -24, 0, 16, 16, 0, 23, 22, 0, -20, 52, 0, 15, 34, 0, -27, 27, 0, -11, 37, 0, 25, -30, 0, -33, -39, 0, -31, 11, 0, -25, 63, 0, 24, -7, 0, -2, 52, 0, 54, 10, 0, 18, 8, 0, 38, 52, 0, 15, -39, 0, 37, 46, 0, 80, -2, 0, 14, 6, 0, -29, -54, 0, 34, -20, 0, 16, 101, 0, -27, 2, 0, -23, 29, 0, -52, 56, 0, 72, -3, 0, 15, 44, 0, -39, 48, 0, 41, -24, 0, 36, 66, 0, 10, 0, 0, 2, 48, 0, -77, 45, 0, -29, -90, 0, -2, 35, 0, 30, -12, 0, -110, -6, 0, -2, -64, 0, -55, 13, 0, -20, -51, 0, -43, 14, 0, -27, 66, 0, 39, 9, 0, 19, -14, 0, 12, -89, 0, -24, 0, 0, -43, 39, 0, 67, -30, 0, -50, -69, 0, 2, 51, 0, -46, -21, 0, 78, 66, 0, -32, 21, 0, -55, -46, 0, -71, -17, 0, -1, 8, 0, -10, 9, 0, -66, -75, 0, -24, -40, 0, 50, 13, 0, 2, -30, 0, 17, -87, 0, 139, 75, 0, 32, -60, 0, 65, 19, 0, -21, 10, 0, -51, -10, 0, -81, 25, 0, -23, -60, 0, 37, 29, 0, 47, -4, 0, 79, 14, 0, 18, -13, 0, -12, -28, 0, 96, 0, 0, -12, -61, 0, -38, -28, 0, -5, -135, 0, -55, -18, 0, 32, 63, 0, 6, 18, 0, -78, 14, 0, -54, -61, 0, 21, -23, 0, 89, -23, 0, -9, 61, 0, 11, -49, 0, 11, 16, 0, 41, 29, 0, -71, -27, 0, -69, 11, 0, 27, -35, 0, 108, -20, 0, -53, -1, 0, -14, 47, 0, 38, -3, 0, -1, 25, 0, 63, -45, 0, 50, 11, 0, -23, -32, 0, 1, -5, 0, -60, 75, 0, 49, 3, 0, -1, -27, 0, 2, 22, 0, -19, 22, 0, -3, -67, 0, 10, -69, 0, 18, -40, 0, -22, -48, 0, -36, -55, 0, -19, 72, 0, -138, 5, 0, 6, -53, 0, 5, -17, 0, -22, 10, 0, 21, -37, 0, 7, -126, 0, 97, -44, 0, 63, -33, 0, 7, -14, 0, -36, -3, 0, 81, 31, 0, 38, 29, 0, -45, -58, 0, -9, 86, 0, 7, -6, 0, -51, -21, 0, 13, 17, 0, -34, 7, 0, 20, -18, 0, 72, 19, 0, -10, -33, 0, 123, 10, 0, 128, 38, 0, -52, 59, 0, 23, 2, 0, 42, 11, 0, -15, 49, 0, -44, -17, 0, -19, -21, 0, -80, -20, 0, -6, -23, 0, 25, -45, 0, 23, 63, 0, -41, -9, 0, -93, -48, 0, -13, -52, 0, -41, -67, 0, 55, -11, 0, -89, 27, 0, -47, -9, 0, 113, -53, 0, -118, 33, 0, -42, -82, 0, 42, 66, 0, 12, 26, 0, 54, 76, 0, -112, -5, 0, 57, -66, 0, -9, -6, 0, 38, 94, 0, -14, -61, 0, 8, 59, 0, -84, 105, 0, 64, -37, 0, -18, -13, 0, 41, 68, 0, -157, -33, 0, 23, -27, 0, -21, 63, 0, -57, 45, 0, -48, 15, 0, -79, 3, 0, -11, 10, 0, -15, -39, 0, 107, -21, 0, 17, 118, 0, 29, 6, 0, -42, 13, 0, -22, -133, 0, 59, 146, 0, -10, -147, 0, 40, 7, 0, -33, 40, 0, 5, -27, 0, 60], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, -1, 0], [0, 0, 0], [1, 1, 1], [-2, 1, 0], [0, 0, 0], [0, 0, -1], [-2, -1, -1], [0, 0, 0], [-3, 1, -1], [-3, 0, -1], [0, 0, 0], [0, 0, 1], [-1, 1, 0], [0, 0, 0], [0, 2, -1], [-1, -2, 2], [0, 0, 0], [-1, 0, 0], [0, 1, -1], [0, 0, 0], [-1, 4, 0], [-4, 3, 0], [0, 0, 0], [2, -3, 1], [1, -1, 0], [0, 0, 0], [-3, 0, 1], [3, 1, 4], [0, 0, 0], [-1, 0, -1], [-3, 1, 0], [0, 0, 0], [8, 1, 2], [1, -1, 2], [0, 0, 0], [-3, -1, 1], [0, 1, 0], [0, 0, 0], [2, -2, 1], [-2, 1, 0], [0, 0, 0], [4, -5, -2], [-6, -3, -2], [0, 0, 0], [-9, 1, -3], [-9, 0, 0], [0, 0, 0], [-3, -1, -2], [10, 0, 3], [0, 0, 0], [3, 0, -1], [-2, -1, -5], [0, 0, 0], [7, -4, 2], [3, 0, 0], [0, 0, 0], [1, -8, -1], [-1, 1, -3], [0, 0, 0], [2, 2, 1], [-1, 2, 0], [0, 0, 0], [-3, -2, 1], [-1, 1, -2], [0, 0, 0], [-2, -5, 1], [1, -7, -5], [0, 0, 0], [5, -2, 1], [1, -4, -1], [0, 0, 0], [-1, 2, 2], [4, 3, 1], [0, 0, 0], [-1, -1, -1], [4, -1, 1], [0, 0, 0], [1, 5, 1], [7, -3, 4], [0, 0, 0], [-3, 1, -1], [-1, -6, -4], [0, 0, 0], [-6, 3, -6], [13, 3, 5], [0, 0, 0], [9, 3, 3], [1, 4, 3], [0, 0, 0], [-4, 1, 2], [2, 5, -1], [0, 0, 0], [0, 9, 0], [2, -1, 0], [0, 0, 0], [-9, 1, -3], [1, 6, 1], [0, 0, 0], [-1, -7, -2]]}