# Stored data for newform 2025.4.a.be, downloaded from the LMFDB on 19 April 2024.
{"label": "2025.4.a.be", "space_label": "2025.4.a", "level": 2025, "weight": 4, "hecke_orbit": 31, "hecke_orbit_code": 135107988888225769, "dim": 12, "is_polredabs": true, "trace_hash": 871007245730613904, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [73008, -143136, -96816, 144610, 52669, -45247, -13834, 5130, 1452, -241, -64, 4, 1]], [7, [284111126595504, -49069079780724, -12328245550998, 857927085426, 159370316127, -5001274746, -849150162, 12946194, 2090268, -14914, -2373, 6, 1]], [11, [27256136074433856, -12280529942857944, -3157793940816144, 34317620761625, 18363263926723, -190920855323, -33136722397, 337214331, 25135263, -189035, -8485, 29, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(4+\\beta _{2})q^{4}+(-1+\\beta _{6})q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32400, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 119.47886776162474, "hecke_ring_index": 13122, "level_radical": 15, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [2025, 1, [326, 1702], [1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 263261020407121666698427219578165144, "field_disc_factorization": [[2, 3], [3, 5], [3370173259633, 1], [40182603435384874897, 1]], "field_poly": [73008, 143136, -96816, -144610, 52669, 45247, -13834, -5130, 1452, 241, -64, -4, 1], "hecke_ring_index_factorization": [[2, 1], [3, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.341", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "296.998", "prec": 24}, {"__RealLiteral__": 0, "data": "57.577", "prec": 20}, {"__RealLiteral__": 0, "data": "12691.710", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1]], "trace_display": [-4, 0, 0, -6], "traces": [0, 12, -4, 0, 48, 0, 0, -6, -45, 0, 0, -29, 0, -24, 69, 0, 192, -79, 0, -75, 0, 0, 18, -318, 0, 0, 154, 0, -96, -106, 0, 60, -914, 0, -108, 0, 0, 84, -640, 0, 0, 353, 0, 426, -571, 0, 270, -1210, 0, 666, 0, 0, 75, -448, 0, 0, 570, 0, -594, -482, 0, 402, -2544, 0, 975, 0, 0, 201, -3437, 0, 0, 944, 0, 453, -10, 0, -462, -2652, 0, 258, 0, 0, -873, -3012, 0, 0, -1952, 0, 216, 738, 0, -618, -5232, 0, 63, 0, 0, 318, -7511, 0, 0, -2448, 0, 462, 3420, 0, -477, -3891, 0, 96, 0, 0, -3570, -6154, 0, 0, -6281, 0, 2727, 3186, 0, 1839, -2899, 0, 3507, 0, 0, -2184, -12783, 0, 0, -1776, 0, 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