# Stored data for newform 1323.4.a.bm, downloaded from the LMFDB on 09 September 2024.
{"Nk2": 21168, "analytic_conductor": 78.05952693759484, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [7, 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": [1323, 1, [785, 1081], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 8, "field_disc": 24940747816960000, "field_disc_factorization": [[2, 20], [5, 4], [31, 2], [199, 2]], "field_poly": [3136, 0, -4176, 0, 887, 0, -54, 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, [3136, 0, -4176, 0, 887, 0, -54, 0, 1]], [5, [86285521, 0, -7017984, 0, 108362, 0, -576, 0, 1]], [13, [-932864, -100608, 8328, -168, 1]]], "hecke_orbit": 39, "hecke_orbit_code": 171136785907189035, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 7, "hecke_ring_index_factorization": [[7, 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": "1323.4.a.bm", "level": 1323, "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, 7], "level_radical": 21, "minimal_twist": "1323.4.a.bl", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(6-\\beta _{2}+\\beta _{4})q^{4}+(\\beta _{1}+\\beta _{3}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1323.4.a", "trace_display": [0, 0, 0, 0], "trace_hash": 249542934621247216, "trace_moments": [{"__RealLiteral__": 0, "data": "0.073", "prec": 17}, {"__RealLiteral__": 0, "data": "7.130", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "274.131", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15731.975", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.511", "prec": 17}, "traces": [0, 8, 0, 0, 44, 0, 0, 0, 0, 0, 132, 0, 0, 336, 0, 0, 204, 0, 0, -288, 0, 0, 484, 0, 0, 152, 0, 0, 0, 0, 0, 120, 0, 0, 1008, 0, 0, 592, 0, 0, 1620, 0, 0, -1872, 0, 0, -1644, 0, 0, 0, 0, 0, 2400, 0, 0, 1344, 0, 0, -1200, 0, 0, 2400, 0, 0, -1388, 0, 0, 0, 0, 0, 0, 0, 0, 1824, 0, 0, 2844, 0, 0, 2368, 0, 0, 2436, 0, 0, 3512, 0, 0, 3780, 0, 0, 0, 0, 0, 4368, 0, 0, 5712, 0, 0, -528, 0, 0, -5400, 0, 0, 4840, 0, 0, -1656, 0, 0, 0, 0, 0, 6888, 0, 0, 1752, 0, 0, -920, 0, 0, -6804, 0, 0, -6640, 0, 0, 2624, 0, 0, 0, 0, 0, 20616, 0, 0, 3888, 0, 0, 372, 0, 0, 5568, 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