# Stored data for newform 800.4.c.k, downloaded from the LMFDB on 07 December 2025. {"Nk2": 12800, "analytic_conductor": 47.20152800459249, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [800, 2, [351, 101, 577], [2, 2, 1]], "cm_discs": [], "conrey_index": 449, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 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, [64, 0, 80, 0, 1]], [11, [160, -64, 1]]], "hecke_orbit": 11, "hecke_orbit_code": 45036133779768096, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 32, "hecke_ring_index_factorization": [[2, 5]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 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": false, "label": "800.4.c.k", "level": 800, "level_is_powerful": true, "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": "160.4.a.c", "nf_label": "4.0.2304.2", "prim_orbit_index": 2, "qexp_display": "q+(2\\beta _{1}-\\beta _{2})q^{3}+(-2\\beta _{1}-5\\beta _{2})q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "800.4.c", "trace_display": [0, 0, 0, 0], "trace_hash": 495555403285068165, "trace_moments": [{"__RealLiteral__": 0, "data": "0.087", "prec": 17}, {"__RealLiteral__": 0, "data": "3.847", "prec": 17}, {"__RealLiteral__": 0, "data": "0.977", "prec": 17}, {"__RealLiteral__": 0, "data": "77.641", "prec": 20}, {"__RealLiteral__": 0, "data": "15.265", "prec": 20}, {"__RealLiteral__": 0, "data": "2180.319", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -52, 0, 128, 0, 0, 0, 0, 0, 0, 0, -416, 0, -416, 0, 0, 0, 0, 0, 0, 0, 584, 0, 352, 0, 0, 0, 0, 0, 0, 0, -864, 0, 200, 0, 0, 0, 0, 0, 0, 0, -1092, 0, -2272, 0, 0, 0, 0, 0, 0, 0, -1440, 0, -2536, 0, 0, 0, 0, 0, 0, 0, 96, 0, -96, 0, 0, 0, 0, 0, 0, 0, -64, 0, 2500, 0, 0, 0, 0, 0, 0, 0, 1560, 0, -3744, 0, 0, 0, 0, 0, 0, 0, -6272, 0, 3032, 0, 0, 0, 0, 0, 0, 0, -88, 0, -1312, 0, 0, 0, 0, 0, 0, 0, -11552, 0, 2228, 0, 0, 0, 0, 0, 0, 0, -544, 0, 1792, 0, 0, 0, 0, 0, 0, 0, -5408, 0, -3488, 0, 0, 0, 0, 0, 0, 0, -5560, 0, -1120, 0, 0, 0, 0, 0, 0, 0, -4832, 0, 6240, 0, 0, 0, 0, 0, 0, 0, 2500, 0, -736, 0, 0, 0, 0, 0, 0, 0, -10080, 0, -4200, 0, 0, 0, 0, 0, 0, 0, 6464, 0, 1568, 0, 0, 0, 0, 0, 0, 0, 4672, 0, -1440, 0, 0, 0, 0, 0, 0, 0, -8704, 0, -2048, 0, 0, 0, 0, 0, 0, 0, 19040, 0, -18384, 0, 0, 0, 0, 0, 0, 0, 4072, 0, -22528, 0, 0, 0, 0, 0, 0, 0, 5696, 0, 18024, 0, 0, 0, 0, 0, 0, 0, 17248, 0, 10240, 0, 0, 0, 0, 0, 0, 0, 10528, 0, -19880, 0, 0, 0, 0, 0, 0, 0, 936, 0, 2464, 0, 0, 0, 0, 0, 0, 0, 32, 0, 4040, 0, 0, 0, 0, 0, 0, 0, -35660, 0, 5920, 0, 0, 0, 0, 0, 0, 0, 7008, 0, -20768, 0, 0, 0, 0, 0, 0, 0, 10720, 0, 16864, 0, 0, 0, 0, 0, 0, 0, 27904, 0, 28128, 0, 0, 0, 0, 0, 0, 0, -4000, 0, 39232, 0, 0, 0, 0, 0, 0, 0, 17376, 0, 7808, 0, 0, 0, 0, 0, 0, 0, 2888, 0, 17088, 0, 0, 0, 0, 0, 0, 0, -2752, 0, 21972, 0, 0, 0, 0, 0, 0, 0, 28120, 0, -8992, 0, 0, 0, 0, 0, 0, 0, 23712, 0, 32352, 0, 0, 0, 0, 0, 0, 0, 5512, 0, 25824, 0, 0, 0, 0, 0, 0, 0, 30976, 0, -27768, 0, 0, 0, 0, 0, 0, 0, -9032, 0, -23392, 0, 0, 0, 0, 0, 0, 0, -2400, 0, -14600, 0, 0, 0, 0, 0, 0, 0, -49536, 0, -17120, 0, 0, 0, 0, 0, 0, 0, 33472, 0, -16524, 0, 0, 0, 0, 0, 0, 0, -6376, 0, -16640, 0, 0, 0, 0, 0, 0, 0, 40384, 0, 28728, 0, 0, 0, 0, 0, 0, 0, 28512, 0, 12640, 0, 0, 0, 0, 0, 0, 0, 52032, 0, 8016, 0, 0, 0, 0, 0, 0, 0, 33504, 0, -49280, 0, 0, 0, 0, 0, 0, 0, -29600, 0, -2080, 0, 0, 0, 0, 0, 0, 0, -55608, 0, 50080, 0, 0, 0, 0, 0, 0, 0, -58464, 0, -11928, 0, 0, 0, 0, 0, 0, 0, 22652, 0, 3360, 0, 0, 0, 0, 0, 0, 0, -11904, 0, 14456, 0, 0, 0, 0, 0, 0, 0, 57544, 0, -48448, 0, 0, 0, 0, 0, 0, 0, -23904, 0, -126848, 0, 0, 0, 0, 0, 0, 0, 34104, 0, 62272, 0, 0, 0, 0, 0, 0, 0, -53792, 0, 9824, 0, 0, 0, 0, 0, 0, 0, -41216, 0, -18208, 0, 0, 0, 0, 0, 0, 0, -1152, 0, -11192, 0, 0, 0, 0, 0, 0, 0, -85312, 0, -13344, 0, 0, 0, 0, 0, 0, 0, -43616, 0, 13632, 0, 0, 0, 0, 0, 0, 0, 38288, 0, 63648, 0, 0, 0, 0, 0, 0, 0, -166176, 0, 55464, 0, 0, 0, 0, 0, 0, 0, -34560, 0, -27392, 0, 0, 0, 0, 0, 0, 0, -50528, 0, -23240, 0, 0, 0, 0, 0, 0, 0, 5344, 0, -99584, 0, 0, 0, 0, 0, 0, 0, -28960, 0, 43872, 0, 0, 0, 0, 0, 0, 0, -22224, 0, 50496, 0, 0, 0, 0, 0, 0, 0, -74912, 0, 22296, 0, 0, 0, 0, 0, 0, 0, 44008, 0, -131264, 0, 0, 0, 0, 0, 0, 0, -2240, 0, -61984, 0, 0, 0, 0, 0, 0, 0, 79052, 0, -86752, 0, 0, 0, 0, 0, 0, 0, 84128, 0, 60672, 0, 0, 0, 0, 0, 0, 0, 28896, 0, 107872, 0, 0, 0, 0, 0, 0, 0, -6144, 0, -74456, 0, 0, 0, 0, 0, 0, 0, -7752, 0, -16096, 0, 0, 0, 0, 0, 0, 0, -51520, 0, 122496, 0, 0, 0, 0, 0, 0, 0, -33440, 0, -45024, 0, 0, 0, 0, 0, 0, 0, -28832, 0, 16584, 0, 0, 0, 0, 0, 0, 0, -31464, 0, 58240, 0, 0, 0, 0, 0, 0, 0, 47136, 0, 69304, 0, 0, 0, 0, 0, 0, 0, -154136, 0, -156448, 0, 0, 0, 0, 0, 0, 0, -16128, 0, 12284, 0, 0, 0, 0, 0, 0, 0, 14816, 0, -59616, 0, 0, 0, 0, 0, 0, 0, -63008, 0, 40640, 0, 0, 0, 0, 0, 0, 0, 97024, 0, 27168, 0, 0, 0, 0, 0, 0, 0, -62688, 0, -25432, 0, 0, 0, 0, 0, 0, 0, 135264, 0, 75392, 0, 0, 0, 0, 0, 0, 0, 42176, 0, -54032, 0, 0, 0, 0, 0, 0, 0, -199160, 0, 10976, 0, 0, 0, 0, 0, 0, 0, 99328, 0, -128416, 0, 0, 0, 0, 0, 0, 0, -156648, 0, 144288, 0, 0, 0, 0, 0, 0, 0, -42144, 0, -69448, 0, 0, 0, 0, 0, 0, 0, 103440, 0, 88928, 0, 0, 0, 0, 0, 0, 0, -13472, 0, -84732, 0, 0, 0, 0, 0, 0, 0, 164096, 0, -82752, 0, 0, 0, 0, 0, 0, 0, 22272, 0, 136312, 0, 0, 0, 0, 0, 0, 0, 84192, 0, 49888, 0, 0, 0, 0, 0, 0, 0, 69184, 0], "weight": 4, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 2, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, -5, 0], [0, 0, 0, 0], [-13, 0, 0, 4], [0, 0, 0, 0], [32, 0, 0, -3], [0, 0, 0, 0], [0, 3, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, -24, 0], [0, 0, 0, 0], [-104, 0, 0, -4], [0, 0, 0, 0], [-104, 0, 0, 8], [0, 0, 0, 0], [0, 30, 11, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -68, 18, 0], [0, 0, 0, 0], [146, 0, 0, -8], [0, 0, 0, 0], [88, 0, 0, 3], [0, 0, 0, 0], [0, 136, -56, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 89, 16, 0], [0, 0, 0, 0], [-216, 0, 0, 19], [0, 0, 0, 0], [50, 0, 0, 20], [0, 0, 0, 0], [0, -94, -37, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 70, -13, 0], [0, 0, 0, 0], [-273, 0, 0, -20], [0, 0, 0, 0], [-568, 0, 0, 47], [0, 0, 0, 0], [0, 79, -24, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -112, 72, 0], [0, 0, 0, 0], [-360, 0, 0, -10], [0, 0, 0, 0], [-634, 0, 0, 16], [0, 0, 0, 0], [0, -454, 33, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 186, 47, 0], [0, 0, 0, 0], [24, 0, 0, 8], [0, 0, 0, 0], [-24, 0, 0, -109], [0, 0, 0, 0], [0, -235, 120, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 296, -136, 0], [0, 0, 0, 0], [-16, 0, 0, -86], [0, 0, 0, 0], [625, 0, 0, 4], [0, 0, 0, 0], [0, -398, 47, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 484, -210, 0], [0, 0, 0, 0], [390, 0, 0, 24], [0, 0, 0, 0], [-936, 0, 0, -1], [0, 0, 0, 0], [0, 104, -64, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -305, -40, 0], [0, 0, 0, 0], [-1568, 0, 0, 167], [0, 0, 0, 0]]}