# Stored data for newform 1274.2.a.j, downloaded from the LMFDB on 11 July 2026.
{"Nk2": 5096, "analytic_conductor": 10.172941217511122, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -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": [1274, 1, [885, 197], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [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": 0, "hecke_cutters": [[3, [1, 1]], [5, [0, 1]], [11, [3, 1]], [17, [0, 1]]], "hecke_orbit": 10, "hecke_orbit_code": 40532396679890170, "hecke_ring_generator_nbound": 1, "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": "1274.2.a.j", "level": 1274, "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, 13], "level_radical": 182, "minimal_twist": "182.2.a.d", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\\cdots", "related_objects": ["EllipticCurve/Q/1274/j"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1274.2.a", "trace_display": [1, -1, 0, 0], "trace_hash": 266863015665973946, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "2.086", "prec": 17}, {"__RealLiteral__": 0, "data": "0.115", "prec": 17}, {"__RealLiteral__": 0, "data": "5.339", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "traces": [0, 1, 1, -1, 1, 0, -1, 0, 1, -2, 0, -3, -1, -1, 0, 0, 1, 0, -2, -2, 0, 0, -3, -3, -1, -5, -1, 5, 0, 0, 0, -5, 1, 3, 0, 0, -2, -7, -2, 1, 0, -3, 0, 8, -3, 0, -3, 3, -1, 0, -5, 0, -1, -12, 5, 0, 0, 2, 0, -6, 0, 1, -5, 0, 1, 0, 3, 5, 0, 3, 0, 12, -2, -11, -7, 5, -2, 0, 1, -1, 0, 1, -3, -12, 0, 0, 8, 0, -3, 18, 0, 0, -3, 5, 3, 0, -1, -17, 0, 6, -5, 3, 0, -14, -1, 0, -12, 0, 5, 2, 0, 7, 0, 9, 2, 0, 0, 2, -6, 0, 0, -2, 1, 3, -5, 0, 0, -7, 1, -8, 0, 0, 3, 0, 5, 0, 0, -6, 3, 4, 0, -3, 12, 3, -2, 0, -11, 0, -7, -15, 5, 8, -2, 0, 0, 0, 1, 13, -1, 12, 0, 0, 1, 20, -3, 0, -12, 24, 0, 1, 0, 4, 8, 18, 0, 0, -3, 6, 18, -6, 0, 7, 0, -1, -3, 0, 5, 0, 3, 0, 0, 0, -1, -4, -17, 0, 0, -3, 6, 16, -5, -5, 3, 0, 0, 0, -14, 6, -1, 6, 0, -22, -12, -12, 0, 0, 5, 0, 2, 11, 0, 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