# Stored data for newform 252.4.b.c, downloaded from the LMFDB on 19 April 2024. {"label": "252.4.b.c", "space_label": "252.4.b", "level": 252, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007268041326844, "dim": 4, "is_polredabs": true, "nf_label": "4.0.784.1", "trace_hash": 1125741813109780124, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [0, 1]], [11, [4624, 0, 1]], [19, [0, 1]]], "qexp_display": "q-\\beta _{3}q^{2}+(-2-5\\beta _{2})q^{4}+(-7+14\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 28, "char_orbit_label": "b", "char_is_real": true, "Nk2": 4032, "analytic_conductor": 14.868481321446636, "hecke_ring_index": 4, "level_radical": 42, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.887", "prec": 17}, "analytic_rank_proved": true, "char_values": [252, 2, [127, 29, 73], [1, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 8, "level_primes": [2, 3, 7], "conrey_indexes": [55], "field_disc": 784, "field_disc_factorization": [[2, 4], [7, 2]], "field_poly": [4, 0, -3, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.305", "prec": 17}, {"__RealLiteral__": 0, "data": "0.198", "prec": 17}, {"__RealLiteral__": 0, "data": "153.938", "prec": 24}, {"__RealLiteral__": 0, "data": "27.596", "prec": 20}, {"__RealLiteral__": 0, "data": "8036.966", "prec": 27}], "related_objects": [], "self_twist_discs": [-7], "cm_discs": [-7], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, 680, 0, 0, 500, 0, 0, 490, 0, 0, 0, 0, 0, 0, 0, 0, 1800, 0, 0, 0, 0, 0, 0, 0, 0, 400, 0, 0, -1372, 0, 0, 0, 0, 0, 0, 0, 0, -1400, 0, 0, 0, 0, 0, 1998, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2250, 0, 0, 0, 0, 0, -2632, 0, 0, -216, 0, 0, -4410, 0, 0, 0, 0, 0, 0, 0, 0, -13172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6880, 0, 0, 0, 0, 0, -8100, 0, 0, 0, 0, 0, -6664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8788, 0, 0, 14140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -400, 0, 0, 0, 0, 0, 0, 0, 0, 18360, 0, 0, 6174, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12208, 0, 0, 0, 0, 0, 23800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10880, 0, 0, -11966, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21420, 0, 0, 0, 0, 0, 4144, 0, 0, 29240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19652, 0, 0, 0, 0, 0, 0, 0, 0, 18760, 0, 0, -39592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6300, 0, 0, 0, 0, 0, -3920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -37400, 0, 0, 0, 0, 0, -20840, 0, 0, -27436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -55880, 0, 0, 0, 0, 0, 0, 0, 0, -40720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26824, 0, 0, 0, 0, 0, -11750, 0, 0, 0, 0, 0, -49000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 61048, 0, 0, 44744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8330, 0, 0, 0, 0, 0, 0, 0, 0, -32040, 0, 0, 0, 0, 0, 0, 0, 0, 28112, 0, 0, 59976, 0, 0, 0, 0, 0, 0, 0, 0, 73760, 0, 0, 0, 0, 0, 59274, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -54180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -75200, 0, 0, 42268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63512, 0, 0, 0, 0, 0, 0, 0, 0, 85000, 0, 0, -17640, 0, 0, 0, 0, 0, 0, 0, 0, 44240, 0, 0, 0, 0, 0, -6880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -59500, 0, 0, 0, 0, 0, 0, 0, 0, -60040, 0, 0, 113288, 0, 0, 0, 0, 0, 0, 0, 0, 62500, 0, 0, 0, 0, 0, 0, 0, 0, -46984, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -134280, 0, 0, -39546, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -127260, 0, 0, 0, 0, 0, -41000, 0, 0, 0, 0, 0, 61250, 0, 0, 0, 0, 0, 0, 0, 0, 50184, 0, 0, 0, 0, 0, 0, 0, 0, -81040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22000, 0, 0, 0, 0, 0, -92120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -139320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -82620, 0, 0, 0, 0, 0, -59080, 0, 0, -187136, 0, 0, 32242, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 306000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 182444, 0, 0, -46900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15800, 0, 0, 0, 0, 0, -86080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26200, 0, 0, 0, 0, 0, 0, 0, 0, 185800, 0, 0, 151704, 0, 0, 0, 0, 0, 0, 0, 0, 99680, 0, 0, 0, 0, 0, 207536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 225000, 0, 0, -124600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -119164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -67424, 0, 0, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 28, 4, 1, 2, 0], [1, 1, 21, 3, 1, 2, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0], [1, 1, 84, 8, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "252.4.b.c", "char_is_minimal": true, "conrey_index": 55, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [-2, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-7, 0, 14, 0], [0, 10, 0, 7], [0, 0, 0, 0], [0, 0, 0, 0], [0, -17, 0, 17], [0, 0, 0, 0], [0, 0, 0, 0], [0, -28, 0, -7], [0, 0, 0, 0], [-46, 0, 45, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [136, 0, 68, 0], [0, -10, 0, 10], [0, 0, 0, 0], [125, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [154, 0, -63, 0], [0, 125, 0, 75], [0, 0, 0, 0], [0, 0, 0, 0], [0, -90, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [450, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-202, 0, 404, 0], [0, -136, 0, -204], [0, 0, 0, 0], [80, 0, 40, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-343, 0, 0, 0], [0, 0, 0, -125], [0, 0, 0, 0], [0, 0, 0, 0], [0, 235, 0, 141], [0, 0, 0, 0], [0, 0, 0, 0], [0, 126, 0, -91], [0, 0, 0, 0], [-600, 0, 500, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [542, 0, -85, 0], [0, 0, 0, 0], [0, 0, 0, 0], [306, 0, -612, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -172, 0, 172], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -450], [0, 0, 0, 0], [0, 0, 0, 0], [0, 595, 0, 357], [0, 0, 0, 0], [-90, 0, 180, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -808, 0, -202], [0, 0, 0, 0], [408, 0, -1156, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -80, 0, -120], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 343], [0, 0, 0, 0], [-250, 0, -625, 0]]}