# Stored data for newform 1682.2.a.m, downloaded from the LMFDB on 17 November 2024.
{"Nk2": 6728, "analytic_conductor": 13.43083761997936, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [29, 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": [1682, 1, [843], [1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 14, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-1, -1, 2, 1]], [5, [-1, 6, -5, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043195562002066, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "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": "1682.2.a.m", "level": 1682, "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, 29], "level_radical": 58, "minimal_twist": "58.2.d.a", "nf_label": "3.3.49.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}+(-1-\\beta _{2})q^{3}+q^{4}+(1+\\beta _{1}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1682.2.a", "trace_display": [-3, -2, 5, 1], "trace_hash": 272693551646666031, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.934", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "24.114", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "298.502", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "traces": [0, 3, -3, -2, 3, 5, 2, 1, -3, -3, -5, -3, -2, 2, -1, -1, 3, -5, 3, -10, 5, -10, 3, 0, 2, -2, -2, 1, 1, 0, 1, -5, -3, -12, 5, -3, -3, -3, 10, 8, -5, -6, 10, -21, -3, -5, 0, -2, -2, -2, 2, 15, 2, 24, -1, -12, -1, 9, 0, -19, -1, -2, 5, 13, 3, 1, 12, -33, -5, 7, 3, 1, 3, -8, 3, 13, -10, 27, -8, 14, 5, -1, 6, -14, -10, 1, 21, 0, 3, -25, 5, -18, 0, 1, 2, -26, 2, -4, 2, 24, -2, 24, -15, -11, -2, -19, -24, 1, 1, 17, 12, -19, 1, 26, -9, -14, 0, -23, 19, -25, 1, 12, 2, -10, -5, -12, -13, -3, -3, 28, -1, -13, -12, -8, 33, -10, 5, -18, -7, -7, -3, -1, -1, -30, -3, 0, 8, -8, -3, -12, -13, -19, 10, -9, -27, 8, 8, -4, -14, -2, -5, -14, 1, -41, -6, -27, 14, -24, 10, -5, -1, -4, -21, 21, 0, -24, -3, 1, 25, -14, -5, -25, 18, 13, 0, -12, -1, -30, -2, 19, 26, 14, -2, 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