# Stored data for newform 1275.4.a.l, downloaded from the LMFDB on 10 February 2025.
{"Nk2": 20400, "analytic_conductor": 75.22743525731929, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [5, 1], [17, 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": [1275, 1, [851, 52, 751], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 33, "field_disc_factorization": [[3, 1], [11, 1]], "field_poly": [-8, -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, [-6, 3, 1]], [7, [-200, -5, 1]]], "hecke_orbit": 12, "hecke_orbit_code": 49539595968185595, "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": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1275.4.a.l", "level": 1275, "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, 5, 17], "level_radical": 255, "minimal_twist": "255.4.a.f", "nf_label": "2.2.33.1", "prim_orbit_index": 1, "qexp_display": "q+(-1-\\beta )q^{2}+3q^{3}+(1+3\\beta )q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1275.4.a", "trace_display": [-3, 6, 0, 5], "trace_hash": 304164660543020196, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.619", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.192", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, -3, 6, 5, 0, -9, 5, -33, 18, 0, -21, 15, 50, -90, 0, -7, -34, -27, 67, 0, 15, 246, 132, -99, 0, -174, 54, 260, -195, 0, -212, 423, -63, 51, 0, 45, -61, -282, 150, 0, -363, -270, -316, -696, 0, 396, -387, -21, -261, 0, -102, 422, 111, -81, 0, 0, 201, 408, -906, 0, 70, 252, 45, -727, 0, 738, -286, -85, 396, 0, 264, -297, -331, -288, 0, 712, -1125, -522, -986, 0, 162, 660, -60, 780, 0, 936, -585, 132, -2076, 0, 620, -1452, -636, 366, 0, 1269, -1492, -21, -189, 0, 240, 153, -1468, -726, 0, 972, 504, 135, -188, 0, -183, -760, 4170, -846, 0, -834, 450, -60, -85, 0, 347, -666, -1089, -332, 0, -810, -628, 231, -948, 0, -3312, -2088, 1075, 924, 0, 561, 3057, 1188, 1570, 0, -1161, -4224, -1812, -63, 0, -1632, -783, 986, -1638, 0, 511, -924, -306, 3090, 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