# Stored data for newform 2352.2.b.k, downloaded from the LMFDB on 19 April 2024.
{"label": "2352.2.b.k", "space_label": "2352.2.b", "level": 2352, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036065026738480, "dim": 8, "is_polredabs": true, "nf_label": "8.0.339738624.1", "trace_hash": 1319685262854001540, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [196, 0, 640, 0, 284, 0, 32, 0, 1]], [11, [16, 0, 608, 0, 392, 0, 40, 0, 1]], [13, [98, 0, 20, 0, 1]], [19, [-56, -96, -40, 0, 1]], [31, [-824, 160, 56, -16, 1]]], "qexp_display": "q-q^{3}+(-\\beta _{4}+\\beta _{6})q^{5}+q^{9}+(\\beta _{2}+\\beta _{4}+\\cdots)q^{11}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 28, "char_orbit_label": "b", "char_is_real": true, "Nk2": 9408, "analytic_conductor": 18.780814555405147, "hecke_ring_index": 64, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.534", "prec": 17}, "analytic_rank_proved": true, "char_values": [2352, 2, [1471, 1765, 785, 2257], [1, 2, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [1567], "field_disc": 339738624, "field_disc_factorization": [[2, 22], [3, 4]], "field_poly": [4, 0, -8, 0, 14, 0, -4, 0, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.824", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "246.554", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13401.464", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -8, 0, 0], "traces": [0, 8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -8, 0, 16, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 16, 0, 64, 0, 0, 0, -48, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 8, 0, 0, 0, -64, 0, -16, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 48, 0, 0, 0, -16, 0, 48, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -64, 0, 80, 0, 24, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -16, 0, 16, 0, 32, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 48, 0, -32, 0, -24, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -80, 0, 48, 0, 64, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -32, 0, 32, 0, 112, 0, -96, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -80, 0, -128, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 32, 0, -32, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, -80, 0, 32, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 112, 0, 0, 0, -64, 0, 64, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 16, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, -32, 0, 16, 0, 0, 0, -32, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 64, 0, 32, 0, 16, 0, 80, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -80, 0, -128, 0, -144, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -48, 0, -32, 0, 32, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 32, 0, -32, 0, -32, 0, -112, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -16, 0, -80, 0, 64, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -48, 0, -48, 0, 144, 0, 96, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -48, 0, -64, 0, 96, 0, -16, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 32, 0, 80, 0, 48, 0, 24, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 80, 0, -16, 0, 144, 0, 160, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -32, 0, 128, 0, 8, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, -224, 0, 16, 0, -48, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, -48, 0, -16, 0, -128, 0, 96, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, -80, 0, 64, 0, -32, 0, 160, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -32, 0, 80, 0, -88, 0, -112, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -64, 0, -8, 0, -128, 0, -32, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 64, 0, 128, 0, 16, 0, 96, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 128, 0, 144, 0, -16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, -48, 0, 0, 0, 16, 0, -192, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 16, 0, 0, 0, 16, 0, -160, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, -64, 0, 96, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 144, 0, -32, 0, -80, 0, 64, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 176, 0, 32, 0, 0, 0, -176, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 64, 0, -96, 0, 80, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -32, 0, 96, 0, -128, 0, -32, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, -352, 0, -32, 0, -64, 0, -64, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 176, 0, 48, 0, 64, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 144, 0, 112, 0, -32, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, -48, 0, -256, 0, 48, 0, 288, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 224, 0, 176, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, -48, 0, 48, 0, 32, 0, -128, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -96, 0, 128, 0, 96, 0, 80, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -16, 0, -64, 0, 16, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 104, 0, 64, 0, 80, 0, -288, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -64, 0, -32, 0, 80, 0, 80, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -32, 0, -96, 0, 288, 0, -16, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 144, 0, -80, 0, 32, 0, 128, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368, 0, 0, 0, 0, 0, -320, 0, -128, 0, -64, 0, 32, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 128, 0, 0, 0, -96, 0, 144, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, -256, 0, -288, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 48, 0, 192, 0, -160, 0, 32, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, -32, 0, -48, 0, 208, 0, 32, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, -112, 0, 96, 0, 64, 0, -320, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 32, 0, -336, 0, 168, 0, 32, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 384, 0, 112, 0, -240, 0, 128, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, -16, 0, -32, 0, -16, 0, -32, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 80, 0, 128, 0, -16, 0, -64, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, -64, 0, 288, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 96, 0, 192, 0, 32, 0, -288, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 48, 0, 64, 0, -392, 0, -144, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -176, 0, -152, 0, -384, 0, 224, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 80, 0, -96, 0, -32, 0, 224, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 64, 0, -144, 0, -48, 0, -96, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, -80, 0, 32, 0, 160, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 432, 0, 192, 0, 48, 0, 112, 0, 0, 0, 0, 0, 304, 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, 28, 4, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "2352.2.b.k", "char_is_minimal": true, "conrey_index": 1567, "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, 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, -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, 1, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, -1, 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, 2, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 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, -1, 0, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, 0, 0, 2, 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], [2, -1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, -2, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 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], [0, 1, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, -6, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -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, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [8, 2, 0, -1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -2, 0, -2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -3, 0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 1, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, 0, 0, -2, 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, 4, 0, 4, 0, 0, 1], [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, 2, 0, 3, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 1, 0, -2, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 7, 0, 3, 2], [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, 2, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 2, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, -1, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}