# Stored data for newform 1911.4.a.ba, downloaded from the LMFDB on 15 September 2025.
{"Nk2": 30576, "analytic_conductor": 112.75265002097031, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, -1], [13, 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": [1911, 1, [638, 1522, 1471], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 13, "field_disc": 1743903178583423288739943508060027001235200, "field_disc_factorization": [[2, 8], [3, 3], [5, 2], [7, 1], [78852461, 1], [18283752711769035469927635767, 1]], "field_poly": [-201600, 485568, 80232, -613272, -22526, 217075, 7442, -32595, -1043, 2342, 56, -79, -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, [201600, 485568, -80232, -613272, 22526, 217075, -7442, -32595, 1043, 2342, -56, -79, 1, 1]], [5, [-189323197920, -1386101264256, 221880013500, 110857867992, -16667771284, -3037380386, 450645527, 32093319, -5141446, -91896, 24835, -275, -39, 1]]], "hecke_orbit": 27, "hecke_orbit_code": 117093590378743671, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 588, "hecke_ring_index_factorization": [[2, 2], [3, 1], [7, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1911.4.a.ba", "level": 1911, "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, 7, 13], "level_radical": 273, "minimal_twist": "273.4.i.f", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{2}+3q^{3}+(4+\\beta _{2})q^{4}+(3+\\beta _{2}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 13, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1911.4.a", "trace_display": [-1, 39, 39, 0], "trace_hash": 1483957636059314405, "trace_moments": [{"__RealLiteral__": 0, "data": "0.224", "prec": 17}, {"__RealLiteral__": 0, "data": "10.892", "prec": 20}, {"__RealLiteral__": 0, "data": "7.713", "prec": 17}, {"__RealLiteral__": 0, "data": "372.837", "prec": 24}, {"__RealLiteral__": 0, "data": "658.912", "prec": 24}, {"__RealLiteral__": 0, "data": "21905.348", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 13, -1, 39, 55, 39, -3, 0, -54, 117, 5, -49, 165, -169, 0, 117, 223, 82, -9, -26, 898, 0, 578, -162, -162, 446, 13, 351, 0, 185, 15, 299, -658, -147, 395, 0, 495, -116, -198, -507, -606, 986, 0, 398, -828, 351, 1809, -190, 669, 0, 575, 246, -715, 697, -27, -415, 0, -78, 65, 2551, 2694, 102, 1869, 0, 2494, 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