# Stored data for newform 7168.2.a.ba, downloaded from the LMFDB on 28 March 2024. {"label": "7168.2.a.ba", "space_label": "7168.2.a", "level": 7168, "weight": 2, "hecke_orbit": 27, "hecke_orbit_code": 117093590345194496, "dim": 8, "is_polredabs": true, "nf_label": "8.8.9433055232.1", "trace_hash": 1406821671300308544, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [16, 32, -152, -24, 94, 4, -18, 0, 1]], [5, [-128, 128, 512, 176, -162, -84, 6, 8, 1]], [11, [64, -128, -192, 640, -492, 88, 32, -12, 1]], [13, [4096, 0, -6784, -4960, -882, 284, 138, 20, 1]], [17, [116608, 15872, -46272, -4992, 3528, 272, -100, -4, 1]], [23, [-70592, -56064, 12800, 15680, 1428, -688, -84, 8, 1]], [31, [-251648, 366848, -59584, -25792, 5304, 576, -132, -4, 1]]], "qexp_display": "q-\\beta _{5}q^{3}+(-1-\\beta _{2})q^{5}-q^{7}+(2+\\beta _{1}+\\cdots)q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 28672, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 57.23676816885378, "hecke_ring_index": 4, "level_radical": 14, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [7168, 1, [1023, 5125, 1025], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 7], "conrey_indexes": [1], "field_disc": 9433055232, "field_disc_factorization": [[2, 16], [3, 4], [1777, 1]], "field_poly": [-8, 48, -4, -76, 9, 32, -6, -4, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.217", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", 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