# Stored data for newform 675.4.a.m, downloaded from the LMFDB on 07 December 2025.
{"Nk2": 10800, "analytic_conductor": 39.82628925387491, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [5, 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": [675, 1, [326, 352], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -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": 1, "hecke_cutters": [[2, [-13, 0, 1]], [7, [-9, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043195595555491, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "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": true, "label": "675.4.a.m", "level": 675, "level_is_powerful": true, "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], "level_radical": 15, "minimal_twist": "675.4.a.l", "nf_label": "2.2.13.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta q^{2}+5q^{4}+9q^{7}+3\\beta q^{8}+4\\beta q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "675.4.a", "trace_display": [0, 0, 0, 18], "trace_hash": 754351161961575410, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.887", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.300", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "137.153", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 2, 0, 0, 10, 0, 0, 18, 0, 0, 0, 0, 0, -68, 0, 0, -158, 0, 0, -202, 0, 0, -104, 0, 0, 0, 0, 0, 90, 0, 0, -6, 0, 0, -52, 0, 0, 134, 0, 0, 0, 0, 0, 274, 0, 0, -780, 0, 0, -524, 0, 0, -340, 0, 0, 0, 0, 0, 1196, 0, 0, -1126, 0, 0, -166, 0, 0, -2088, 0, 0, 0, 0, 0, 1006, 0, 0, -1010, 0, 0, 1230, 0, 0, -1456, 0, 0, 0, 0, 0, 312, 0, 0, -612, 0, 0, -832, 0, 0, 38, 0, 0, 0, 0, 0, -298, 0, 0, -4888, 0, 0, -2354, 0, 0, -1422, 0, 0, 0, 0, 0, 6292, 0, 0, -2246, 0, 0, -30, 0, 0, 592, 0, 0, 0, 0, 0, -1818, 0, 0, 156, 0, 0, -3746, 0, 0, -5668, 0, 0, 0, 0, 0, 670, 0, 0, -2062, 0, 0, -936, 0, 0, 4886, 0, 0, 0, 0, 0, -376, 0, 0, 1716, 0, 0, -2082, 0, 0, 1370, 0, 0, 0, 0, 0, -7020, 0, 0, -572, 0, 0, 2340, 0, 0, 208, 0, 0, 0, 0, 0, 6002, 0, 0, -2620, 0, 0, -3088, 0, 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