# Stored data for newform 675.4.a.t, downloaded from the LMFDB on 07 December 2025.
{"Nk2": 10800, "analytic_conductor": 39.82628925387491, "analytic_rank": 0, "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": 4, "field_disc": 467024, "field_disc_factorization": [[2, 4], [17, 2], [101, 1]], "field_poly": [101, 0, -26, 0, 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, [-2, 3, 1]], [7, [32724, 0, -927, 0, 1]]], "hecke_orbit": 20, "hecke_orbit_code": 85568392987148963, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 18, "hecke_ring_index_factorization": [[2, 1], [3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 15, 4, -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": false, "label": "675.4.a.t", "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": "135.4.b.b", "nf_label": "4.4.467024.1", "prim_orbit_index": 1, "qexp_display": "q+(-2-\\beta _{3})q^{2}+3\\beta _{3}q^{4}-\\beta _{2}q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "675.4.a", "trace_display": [-6, 0, 0, 0], "trace_hash": 1932966629805160839, "trace_moments": [{"__RealLiteral__": 0, "data": "0.068", "prec": 17}, {"__RealLiteral__": 0, "data": "4.026", "prec": 17}, {"__RealLiteral__": 0, "data": "2.907", "prec": 17}, {"__RealLiteral__": 0, "data": "78.075", "prec": 20}, {"__RealLiteral__": 0, "data": "106.438", "prec": 24}, {"__RealLiteral__": 0, "data": "2058.562", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 4, -6, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -46, 66, 0, -110, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -268, 582, 0, -388, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -944, 1116, 0, 482, 0, 0, 0, 1824, 0, 0, 0, 0, 0, 0, 0, -1798, 1830, 0, -862, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, 1236, 4086, 0, 682, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, -360, 2796, 0, -76, 0, 0, 0, 2796, 0, 0, 0, 0, 0, 0, 0, -1682, 6210, 0, 358, 0, 0, 0, 3096, 0, 0, 0, 0, 0, 0, 0, 8482, 2748, 0, -3882, 0, 0, 0, -4842, 0, 0, 0, 0, 0, 0, 0, 1544, 2802, 0, 5536, 0, 0, 0, 6408, 0, 0, 0, 0, 0, 0, 0, -3070, 1620, 0, -774, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, 8434, 534, 0, 2084, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 722, -3744, 0, 4684, 0, 0, 0, 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