# Stored data for newform 640.2.l.b, downloaded from the LMFDB on 25 September 2025.
{"Nk2": 2560, "analytic_conductor": 5.110425729361944, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 16, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 12, "char_orbit_label": "l", "char_order": 4, "char_parity": 1, "char_values": [640, 4, [511, 261, 257], [4, 3, 4]], "cm_discs": [], "conrey_index": 161, "dim": 16, "field_disc": 110988513382355697664, "field_disc_factorization": [[2, 32], [160753, 2]], "field_poly": [256, -512, 256, 0, 112, -64, -112, 56, 17, 28, -28, -8, 7, 0, 4, -4, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [16, -64, 128, 1088, 5824, -2656, 1024, 2560, 2632, 176, 32, 80, 112, 8, 0, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504355575169664, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 4096, "hecke_ring_index_factorization": [[2, 12]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 16, 5, 1, 4, 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": false, "label": "640.2.l.b", "level": 640, "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, 5], "level_radical": 10, "minimal_twist": "80.2.l.a", "prim_orbit_index": 5, "qexp_display": "q+(-\\beta _{5}+\\beta _{7})q^{3}-\\beta _{1}q^{5}+(-\\beta _{1}+\\beta _{4}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "640.2.l", "trace_display": [0, 0, 0, 0], "trace_hash": 1121547374273482506, "trace_moments": [{"__RealLiteral__": 0, "data": "0.029", "prec": 17}, {"__RealLiteral__": 0, "data": "14.203", "prec": 20}, {"__RealLiteral__": 0, "data": "5.902", "prec": 17}, {"__RealLiteral__": 0, "data": "743.334", "prec": 24}, {"__RealLiteral__": 0, "data": "604.222", "prec": 24}, {"__RealLiteral__": 0, "data": "60420.117", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.272", "prec": 17}, "traces": [0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -24, 0, 16, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, -40, 0, -16, 0, 32, 0, -16, 0, 0, 0, 0, 0, 8, 0, -16, 0, 40, 0, 0, 0, -40, 0, -16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 16, 0, -16, 0, -40, 0, 16, 0, 0, 0, 0, 0, -32, 0, 48, 0, 32, 0, 0, 0, 8, 0, 48, 0, 0, 0, 0, 0, 32, 0, 0, 0, 80, 0, 0, 0, -8, 0, -48, 0, 0, 0, 0, 0, 72, 0, 0, 0, -40, 0, 32, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -32, 0, -80, 0, 0, 0, 40, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, -64, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 56, 0, -48, 0, -8, 0, -32, 0, -72, 0, 16, 0, 0, 0, 0, 0, -16, 0, -80, 0, -80, 0, -64, 0, 32, 0, -64, 0, 0, 0, 0, 0, -120, 0, 0, 0, 88, 0, -32, 0, 72, 0, 32, 0, 0, 0, 0, 0, -16, 0, 32, 0, 56, 0, 16, 0, -16, 0, 16, 0, 0, 0, 0, 0, -32, 0, 80, 0, 16, 0, 64, 0, -112, 0, -32, 0, 0, 0, 0, 0, -8, 0, -64, 0, 48, 0, 0, 0, -32, 0, -32, 0, 0, 0, 0, 0, 16, 0, 48, 0, 128, 0, 64, 0, -8, 0, 80, 0, 0, 0, 0, 0, 64, 0, -16, 0, 0, 0, 16, 0, -96, 0, 0, 0, 0, 0, 0, 0, -32, 0, 48, 0, -160, 0, 0, 0, 8, 0, 80, 0, 0, 0, 0, 0, 56, 0, 64, 0, -16, 0, -32, 0, 128, 0, 0, 0, 0, 0, 0, 0, 104, 0, 80, 0, -72, 0, 0, 0, 80, 0, -32, 0, 0, 0, 0, 0, -40, 0, 80, 0, -160, 0, 32, 0, 48, 0, 16, 0, 0, 0, 0, 0, -112, 0, 0, 0, 88, 0, 32, 0, 48, 0, -16, 0, 0, 0, 0, 0, -24, 0, -16, 0, 216, 0, 0, 0, -64, 0, -16, 0, 0, 0, 0, 0, -32, 0, -96, 0, -16, 0, 32, 0, -80, 0, 64, 0, 0, 0, 0, 0, -224, 0, 0, 0, 40, 0, -32, 0, 8, 0, -16, 0, 0, 0, 0, 0, 64, 0, -32, 0, 128, 0, 0, 0, -72, 0, -80, 0, 0, 0, 0, 0, 144, 0, 32, 0, -160, 0, -128, 0, -160, 0, 48, 0, 0, 0, 0, 0, 96, 0, -16, 0, -200, 0, 0, 0, 64, 0, -112, 0, 0, 0, 0, 0, 8, 0, -160, 0, 32, 0, -64, 0, 136, 0, 0, 0, 0, 0, 0, 0, 88, 0, -80, 0, -80, 0, 128, 0, 104, 0, 80, 0, 0, 0, 0, 0, -80, 0, -48, 0, -128, 0, 160, 0, 40, 0, 16, 0, 0, 0, 0, 0, -80, 0, 0, 0, -32, 0, 112, 0, 168, 0, -48, 0, 0, 0, 0, 0, 8, 0, -16, 0, 320, 0, -32, 0, 0, 0, -80, 0, 0, 0, 0, 0, -80, 0, 64, 0, 0, 0, -160, 0, -128, 0, -64, 0, 0, 0, 0, 0, -88, 0, -64, 0, 24, 0, 0, 0, -80, 0, -48, 0, 0, 0, 0, 0, 72, 0, 32, 0, 160, 0, -160, 0, -80, 0, 160, 0, 0, 0, 0, 0, 176, 0, -64, 0, -88, 0, -32, 0, -192, 0, -80, 0, 0, 0, 0, 0, 136, 0, 48, 0, -240, 0, -16, 0, 32, 0, 160, 0, 0, 0, 0, 0, 56, 0, 176, 0, 144, 0, 32, 0, 88, 0, 0, 0, 0, 0, 0, 0, 192, 0, 144, 0, -48, 0, -32, 0, -8, 0, -96, 0, 0, 0, 0, 0, 8, 0, 112, 0, -192, 0, -128, 0, 24, 0, 96, 0, 0, 0, 0, 0, -200, 0, 16, 0, 256, 0, -32, 0, 120, 0, 64, 0, 0, 0, 0, 0, -64, 0, 64, 0, 256, 0, 0, 0, -88, 0, 144, 0, 0, 0, 0, 0, -80, 0, -144, 0, 144, 0, 32, 0, -168, 0, 16, 0, 0, 0, 0, 0, -128, 0, 48, 0, 72, 0, 32, 0, -8, 0, -96, 0, 0, 0, 0, 0, 0, 0, -192, 0, 48, 0, -32, 0, -48, 0, -144, 0, 0, 0, 0, 0, 144, 0, 64, 0, -48, 0, 192, 0, -96, 0, 80, 0, 0, 0, 0, 0, -96, 0, -32, 0, -336, 0, 0, 0, 72, 0, -256, 0, 0, 0, 0, 0, 96, 0, -240, 0, -64, 0, 160, 0, 224, 0, 0, 0, 0, 0, 0, 0, 120, 0, -48, 0, -120, 0, -128, 0, 32, 0, 32, 0, 0, 0, 0, 0, -72, 0, -80, 0, -400, 0, -64, 0, 72, 0, 32, 0, 0, 0, 0, 0, -184, 0, -32, 0, 296, 0, -160, 0, 80, 0, -64, 0, 0, 0, 0, 0, -136, 0, -48, 0, 152, 0, 32, 0, 48, 0, 32, 0, 0, 0, 0, 0, 0, 0, 128, 0, 48, 0, 64, 0, -256, 0, -112, 0, 0, 0, 0, 0, -184, 0, 64, 0, 64, 0, 0, 0, 64, 0, 64, 0, 0, 0, 0, 0, -32, 0, 96, 0, 224, 0, 64, 0, -112, 0, 192, 0, 0, 0, 0, 0, 224, 0, -16, 0, -136, 0, 32, 0, -152, 0, -112, 0, 0, 0, 0, 0, 48, 0, -80, 0, -176, 0, 32, 0, 200, 0, 192, 0, 0, 0, 0, 0, 80, 0, 304, 0, -176, 0, -112, 0, 264, 0, 0, 0, 0, 0, 0, 0, 72, 0, 16, 0, 0, 0, 128, 0, -48, 0, -96, 0, 0, 0, 0, 0, 8, 0, 96, 0, -336, 0, 192, 0, 32, 0, -48, 0, 0, 0], "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 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, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 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, 0, 0, 0], [0, -1, 0, 0, 1, 0, 0, 1, -1, 0, -1, 1, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, -1, 1, 1, 0, 1, -1, 0, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 1, -1, 0, -1, -1, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 1, -1, 1, 0, 0, 0, 0, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 2, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -2, 0, 1, -1, -1, 1, -1, 1, -1, 0, -2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, -1, 0, 1, -3, 0, 0, 1, -1, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -4, 0, 0, 0, -1, 1, 1, -2, 1, -1, 0, -2, 2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 1, -1, 1, -2, -1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, -1, 0, 1, -1, 0, 0, -2, 1, 0, 1, -2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 1, 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], [1, 2, 1, 2, -1, 0, 0, 0, 1, 0, 0, 1, 2, -2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 2, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 0, -2, 0, 1, -1, -1, 0, -1, 1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 1, 0, 0, -3, 1, 0, 0, 1, 0, 0, -1, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 4, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, -2, 3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, -1, 3, 1, -1, -3, -1, 1, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 1, 2, -1, -1, 1, 1, 0, 1, -1, -2, 0, 1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, -1, 1, 0, -1, 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, 1, -1, -1, 1, -1, -1, 0, 0, 3, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -3, -1, -1, 1, 0, 0, 0, -1, 0, 0, 2, -1, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, -1, -2, 2, 0, 3, 0, 2, -3, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -3, 1, 2, 0, 4, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, -1, 0, -1, 1, 0, 0, 0, 1, 0, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 2, 0, 2, -2, -3, 0, 0, -1, -1, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 1, 0, -1, 1, -1, -1, 0, -1, 1, 0, 2, -2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 2, -2, 2, 2, -2, 2, 0, 2, -2, 4, -2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 1, 1, -1, 0, 1, 0, -1, -1, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, 0, 1, -1, -1, 4, 0, 1, -2, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, 0, 1, 0, -2, -1, 1, 0, 0, 0, 0, 1, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -8, -3, -2, 0, 4, 2, -4, 0, 0, 2, 0, -2, 4, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 2, 1, 0, 4, 1, -1, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 0, 1, -1, 1, 1, 0, 1, -1, 0, -2, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, -2, 0, -3, -2, 0, 2, 0, -1, -2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 2, -4, 0, -2, 4, -2, 2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 1, 2, -1, 1, -1, -1, 1, -1, 1, -4, 4, -4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -1, 0, -1, 0, 0, -2, -1, 2, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, -1, 0, 0, 0, 1, 0, 0, 1, -1, 0, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 3, 0, 1, -1, 0, 0, 2, -3, 0, 1, 2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 0, -1, -4, -1, -1, 1, 0, 0, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}