# Stored data for newform 525.2.b.j, downloaded from the LMFDB on 19 March 2024. {"label": "525.2.b.j", "space_label": "525.2.b", "level": 525, "weight": 2, "hecke_orbit": 10, "hecke_orbit_code": 40532465399366157, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 991529726738975592, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 0, 1]], [11, [8, 0, 1]], [17, [-8, 0, 1]], [37, [0, 1]]], "qexp_display": "q-\\zeta_{24}q^{2}-\\zeta_{24}^{3}q^{3}-q^{4}+(\\zeta_{24}^{2}+\\cdots)q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 21, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2100, "analytic_conductor": 4.19214610611722, "hecke_ring_index": 256, "level_radical": 105, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.889", "prec": 17}, "analytic_rank_proved": true, "char_values": [525, 2, [176, 127, 451], [1, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 8, "level_primes": [3, 5, 7], "conrey_indexes": [251], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "6.280", "prec": 17}, {"__RealLiteral__": 0, "data": "5.835", "prec": 17}, {"__RealLiteral__": 0, "data": "753.833", "prec": 24}, {"__RealLiteral__": 0, "data": "1297.140", "prec": 27}, {"__RealLiteral__": 0, "data": "114083.892", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -32, 0, 0, 0, 0, 0, 0, 48, 0, 0, 40, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, -56, 0, 0, 8, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, -40, 0, 0, 0, 0, 0, 0, 64, 0, 0, -96, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, -192, 0, 0, -40, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, -32, 0, 0, 144, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, -32, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, -64, 0, 0, 96, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 64, 0, 0, -128, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, -96, 0, 0, 0, 0, 0, 0, 152, 0, 0, 32, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 288, 0, 0, -96, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, -160, 0, 0, 96, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, -48, 0, 0, 88, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, -32, 0, 0, 0, 0, 0, 0, -32, 0, 0, -48, 0, -8, 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, 0, -64, 0, -240, 0, 0, 64, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 64, 0, 0, 192, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 24, 0, 0, -64, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -304, 0, -64, 0, 0, 96, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, -184, 0, 0, 0, 0, 0, 0, -144, 0, 0, -160, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, -192, 0, 0, 0, 0, 0, 0, -64, 0, 0, -200, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, -32, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, -24, 0, 0, 32, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, -32, 0, 0, 0, 0, 0, 0, 240, 0, 0, 288, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 80, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 192, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -520, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, -48, 0, 0, 0, 0, 0, 0, 64, 0, 0, -96, 0, 32, 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, 3, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 15, 4, -1, 2, 0], [1, 1, 21, 3, 1, 2, 0], [1, 1, 35, 3, -1, 2, 0], [1, 1, 105, 7, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 3, "minimal_twist": "105.2.g.a", "char_is_minimal": true, "conrey_index": 251, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, -2, 0, -2, 0, 0], [0, 0, 0, 0, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 1, 0, 0], [0, -1, 0, 1, 0, 1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 1, 0, -1, 0], [0, 0, 0, -1, 0, -1, 0, -2], [0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, -2, 0], [0, 0, 0, -2, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 2, 0, 2, 0], [0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 3, 0, 0], [0, 0, 2, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, 0], [0, 1, 0, 2, 0, 5, 0, 1], [0, 0, 0, -1, 0, -1, 0, -2], [0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 1, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0], [5, 0, -2, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 2, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 2, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, -2, 0, -4], [0, 0, 0, 0, -2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, -2, 0, -2, 0], [0, 0, 0, 6, 0, -6, 0, 0], [0, 4, 0, 1, 0, -1, 0, 1], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, -1, 0, 3, 0], [0, 0, 0, -1, 0, -1, 0, -2], [0, 0, 0, 1, 0, -1, 0, 0], [0, 0, -2, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 0], [0, -1, 0, 1, 0, 1, 0, 2], [0, 0, 0, 4, 0, 4, 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], [0, -4, 0, -1, 0, 1, 0, 0], [0, 4, 0, 2, 0, 2, 0, 4], [-8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, -3, 0, -3, 0, 0], [0, 0, 0, 1, 0, -1, 0, 0], [1, 0, 1, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0], [0, 0, 0, 2, 0, 6, 0, 0], [0, 0, 0, -1, 0, -1, 0, -2], [0, 0, 0, 0, -3, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -4, 0, -2, 0, -2, 0], [0, -2, 0, 0, 0, 0, 0, 0], [0, -8, 0, 2, 0, 2, 0, 4], [0, 0, 2, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, -3, 0, 0, 0], [0, 0, 0, -4, 0, -4, 0, 0], [0, -5, 0, -3, 0, 3, 0, 0], [8, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}