# Stored data for newform 1232.4.a.w, downloaded from the LMFDB on 02 January 2025.
{"Nk2": 19712, "analytic_conductor": 72.69035312707244, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [7, -1], [11, 1]], "atkin_lehner_string": "--+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [1232, 1, [463, 309, 353, 673], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 509800, "field_disc_factorization": [[2, 3], [5, 2], [2549, 1]], "field_poly": [15, 5, -10, -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": [[3, [-60, 370, -15, -12, 1]], [5, [-10852, -2960, -107, 18, 1]]], "hecke_orbit": 23, "hecke_orbit_code": 99079191869261008, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 8, "hecke_ring_index_factorization": [[2, 3]], "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": "1232.4.a.w", "level": 1232, "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": [2, 7, 11], "level_radical": 154, "minimal_twist": "77.4.a.c", "nf_label": "4.4.509800.1", "prim_orbit_index": 1, "qexp_display": "q+(3-\\beta _{2})q^{3}+(-5+\\beta _{1}-\\beta _{2}-\\beta _{3})q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1232.4.a", "trace_display": [0, 12, -18, 28], "trace_hash": 478481341518981283, "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "3.731", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "38.125", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "583.633", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 4, 0, 12, 0, -18, 0, 28, 0, 66, 0, -44, 0, -134, 0, 62, 0, -74, 0, 164, 0, 84, 0, -194, 0, 38, 0, 510, 0, -108, 0, 412, 0, -132, 0, -126, 0, 286, 0, 256, 0, -18, 0, 496, 0, 580, 0, -62, 0, 196, 0, 508, 0, -828, 0, 198, 0, 700, 0, 1224, 0, -350, 0, 462, 0, -396, 0, 1498, 0, -386, 0, -2326, 0, -1630, 0, 1362, 0, -308, 0, 1020, 0, 1128, 0, 1920, 0, 2008, 0, -1640, 0, 1550, 0, -938, 0, 6046, 0, -2332, 0, -2202, 0, -726, 0, -46, 0, 1954, 0, 434, 0, 1060, 0, 2488, 0, 918, 0, 3598, 0, 2430, 0, -1150, 0, -518, 0, 484, 0, 2164, 0, 1770, 0, 2188, 0, 6304, 0, -792, 0, 1148, 0, 3470, 0, 450, 0, 4, 0, 4092, 0, 1474, 0, -1676, 0, 588, 0, 1360, 0, 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