# Stored data for newform 552.2.f.a, downloaded from the LMFDB on 13 March 2026.
{"Nk2": 2208, "analytic_conductor": 4.407742191574677, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 8, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 2, "char_parity": 1, "char_values": [552, 2, [415, 277, 185, 97], [2, 1, 2, 2]], "cm_discs": [], "conrey_index": 277, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[5, [4, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 343630938664, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "552.2.f.a", "level": 552, "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, 3, 23], "level_radical": 138, "minimal_twist": "552.2.f.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+(i+1)q^{2}+i q^{3}+2 i q^{4}+2 i q^{5}+\\cdots", "related_objects": ["ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-4761.1-d", "EllipticCurve/2.2.8.1/4761.1/d"], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "552.2.f", "trace_display": [2, 0, 0, 8], "trace_hash": 724920153552142593, "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "1.909", "prec": 17}, {"__RealLiteral__": 0, "data": "0.347", "prec": 17}, {"__RealLiteral__": 0, "data": "14.326", "prec": 20}, {"__RealLiteral__": 0, "data": "5.354", "prec": 17}, {"__RealLiteral__": 0, "data": "135.201", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.512", "prec": 17}, "traces": [0, 2, 2, 0, 0, 0, -2, 8, -4, -2, -4, 0, -4, 0, 8, -4, -8, 0, -2, 0, -8, 0, -4, 2, -4, 2, 8, 0, 0, 0, -4, -12, -8, -4, 0, 0, 0, 0, 8, 8, -8, 4, -8, 0, -8, 0, 2, -16, 0, 18, 2, 0, 16, 0, 2, -8, -16, 8, 4, 0, 0, 0, -12, -8, 0, 16, -4, 0, 0, 0, -16, 24, 4, 28, -12, 0, 16, 0, 8, 16, 0, 2, 4, 0, -16, 0, 16, 4, -8, 24, 4, 0, 0, 0, -16, 16, 8, -28, 18, 0, 0, 0, 0, 0, 16, -16, -12, 0, 4, 0, -8, -12, -32, -8, 8, 0, 8, 0, 8, 0, 8, 14, -12, 0, 0, 0, -8, -28, 16, 16, 16, 0, 0, 0, 8, 4, 0, -24, -2, 0, -32, 0, 24, 16, 8, 8, 28, 0, -24, 0, -2, -44, 16, 0, -16, 0, 0, 0, 16, -12, 16, 8, 2, 0, 0, 0, 28, 16, -16, -6, 0, 0, 32, 0, 4, 8, 0, 8, 24, 0, 8, 0, 32, -12, -4, -24, 12, 0, 0, 0, 16, -32, 16, 28, -28, 0, 0, 0, 4, -40, -4, 8, -36, 0, 0, 0, 0, -2, 0, 16, -16, 0, -24, 0, -4, 32, 4, -48, 4, 0, 0, 0, -12, 20, -32, -2, -8, 0, 0, 0, -4, -16, 8, -36, -8, 0, 16, 0, 0, -56, 16, 20, 14, 0, -24, 0, -4, -32, 24, 28, -24, 0, 0, 0, -28, 0, 32, -12, 16, 0, 0, 0, 0, 48, 8, -24, 32, 0, 16, 0, 4, -12, 0, 32, -24, 0, -4, 0, 8, 12, -32, -24, 16, 0, 0, 0, 16, 16, 8, -34, 8, 0, 0, 0, -18, 16, -24, 4, 20, 0, -4, 0, -44, -36, 0, -24, 0, 0, -32, 0, 24, -48, -16, -12, 44, 0, 0, 0, -12, 8, 32, -4, 8, 0, 0, 0, -40, 4, -8, -64, 8, 0, 56, 0, 16, 16, 0, 44, -6, 0, 0, 0, -8, 16, 32, -4, 12, 0, 0, 0, 8, -8, 16, -20, 8, 0, 0, 0, -32, -48, 8, 6, -4, 0, 64, 0, -12, 16, -8, -4, -24, 0, 24, 0, 0, -24, 32, -16, 8, 0, 0, 0, -32, 48, 16, -32, 28, 0, 0, 0, -16, 0, -36, 0, -36, 0, 8, 0, -40, 32, -8, -48, 8, 0, -72, 0, 16, -24, 0, 44, -8, 0, 0, 0, -2, 56, -32, 8, 16, 0, 0, 0, 24, 16, -24, 0, -24, 0, -8, 0, 32, 32, 0, -68, -48, 0, 8, 0, -28, 68, 16, -18, 0, 0, 0, 0, 20, 20, 0, -52, -2, 0, 0, 0, 12, 64, -16, 76, 44, 0, -8, 0, -16, 12, 0, 24, -36, 0, -16, 0, 32, 44, 16, 32, -16, 0, 0, 0, -56, -48, 16, 48, 20, 0, 0, 0, -2, 76, -24, -40, -36, 0, -8, 0, -32, 8, 48, 96, 28, 0, -48, 0, 60, 16, 16, -72, -4, 0, 0, 0, 0, 112, 32, -8, -12, 0, 0, 0, -48, 12, -32, 24, -4, 0, 0, 0, 48, 0, 16, 2, -24, 0, 64, 0, -24, -8, 16, -32, -12, 0, 0, 0, -12, -4, 0, 8, 32, 0, 0, 0, -4, -16, -4, 64, -16, 0, 16, 0, 12, -64, 0, 0, -24, 0, 32, 0, -64, 8, -48, -16, -16, 0, 0, 0, 16, 2, 0, -68, -34, 0, 0, 0, 28, -24, -56, -16, 44, 0, -36, 0, 16, -36, 0, 68, 4, 0, 40, 0, 8, 64, -4, 52, 64, 0, 0, 0, -36, -44, -32, 16, -24, 0, 0, 0, 56, -8, -32, -24, 0, 0, 48, 0, -48, 96, -32, -38, -12, 0, 88, 0, 16, -88, -32, 24, -44, 0, 0, 0, 8, -24, 32, -32, -4, 0, 0, 0, 0, 24, -4, 16, 8, 0, -80, 0, 4, 0, -16, -28, -64, 0, 16, 0, -8, 0, 56, 64, 12, 0, 0, 0, 16, -24, 32, 60, 44, 0, 0, 0, 8, -112, 0, 12, 24, 0, -16, 0, 16, 44, 0, 48, -4, 0, 24, 0, 24, 16, -8, 0, -40, 0, 0, 0, -8, 48, 32, 32, -20, 0, 0, 0, -48, -16, -48, -12, 0, 0, -64, 0, -48, 72, 0, 0, 6, 0, -8, 0, -14, -24, 64, -2, -56, 0, 0, 0, 16, -36, -8, 16, -4, 0, 0, 0, -48, 32, 24, 40, -12, 0, 0, 0, -24, -64, 64, 60, -16, 0, 16, 0, 24, -4, -32, -4, 28, 0, 0, 0, 48, -32, 0, -100, -32, 0, 0, 0, -16, -12, 56, -48, 20, 0, -32, 0, 0, -4, -72, 88, 0, 0, -72, 0, -32, -32, 8, 48, 16, 0, 0, 0, 32, 0, -8, -24, -48, 0, 0, 0, -48, -12, -72, -52, -4, 0, 32, 0, -24, -80, 0, -64, 44, 0, -16, 0, 24, 28, 0, -4, 32, 0, 0, 0, 56, -16, -64, 0, 8, 0, 0, 0, -36, -48, 32, 50, -44, 0, 48, 0, 16, 56, 0, -64, 0, 0, -48, 0, -48, -16, -8, -44, -16, 0, 0, 0, 32, 32, -8, 24, -68, 0, 0, 0, -8, -32, 8, 28, 8, 0, -56, 0, 68, 44, 32, -104, -18, 0, 0, 0, 48, 56, 24, -112, -48, 0, 0, 0, 20, -64, 64, 8, -52, 0, 0, 0, -8, 64, 16, -8, 44, 0, 24, 0, 64, 0, -32, 56, 76, 0, 88, 0, 0, -16, -8, 56, -20, 0, 0, 0, 12, 0, -16, -100, 24, 0, 0, 0, 36, 0, -16, -36, 32, 0, 64, 0, 44, 4, 0, 16, 32, 0, -32, 0, 8, -44, 0, -96, 12, 0, 0, 0, -48, -96, 0, 10, 48, 0, 0, 0, -8, -12, -28, 0, 56, 0, -4, 0, 76, 8, 0, 56, -40, 0, -72, 0, 80, -64, -8, -72, 0, 0, 0, 0, 8, 20, 48, -8, 96, 0, 0, 0, -40, 12, -48], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [1, 1], [0, 1], [0, 2], [0, 2], [-1, 1], [4, 0], [-2, 2], [-1, 0], [-2, 2], [0, 2], [-2, 0], [0, -4], [4, 4], [-2, 0], [-4, 0], [0, 0], [-1, -1], [0, -4], [-4, 0], [0, 4], [-2, 2], [1, 0], [-2, -2], [1, 0], [4, -4], [0, -1], [0, 8], [0, -2], [-2, -2], [-6, 0], [-4, -4], [-2, 0], [0, 0], [0, 8], [0, -2], [0, 6], [4, -4], [4, 0], [-4, -4], [2, 0], [-4, 4], [0, -8], [-4, 0], [0, -2], [1, 1], [-8, 0], [0, -4], [9, 0], [1, 1], [0, 0], [8, 0], [0, 6], [1, -1], [-4, 0], [-8, 8], [4, 0], [2, -2], [0, -4], [0, -4], [0, 6], [-6, -6], [-4, 0], [0, -8], [8, 0], [-2, -2], [0, -4], [0, 0], [0, 1], [-8, 8], [12, 0], [2, -2], [14, 0], [-6, 6], [0, 1], [8, 0], [0, 8], [4, 4], [8, 0], [0, -8], [1, 0], [2, 2], [0, -14], [-8, 0], [0, 0], [8, -8], [2, 0], [-4, -4], [12, 0], [2, -2], [0, -16], [0, 2], [0, -6], [-8, -8], [8, 0], [4, -4], [-14, 0], [9, 9], [0, -2], [0, 2]]}