# Stored data for newform 400.6.c.n, downloaded from the LMFDB on 24 April 2024. {"label": "400.6.c.n", "space_label": "400.6.c", "level": 400, "weight": 6, "hecke_orbit": 14, "hecke_orbit_code": 58546932695433616, "dim": 4, "is_polredabs": true, "nf_label": "4.0.929296.1", "trace_hash": 330904822114389240, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [19881, 0, 682, 0, 1]]], "qexp_display": "q+(\\beta _{1}-2\\beta _{2})q^{3}+(-2\\beta _{1}+20\\beta _{2})q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 14400, "analytic_conductor": 64.15352792519225, "hecke_ring_index": 100, "level_radical": 10, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [400, 2, [351, 101, 177], [2, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [49], "field_disc": 929296, "field_disc_factorization": [[2, 4], [241, 2]], "field_poly": [3600, 0, 121, 0, 1], "hecke_ring_index_factorization": [[2, 2], [5, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "3.625", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "68.390", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1797.811", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -392, 0, 392, 0, 0, 0, 0, 0, 0, 0, -6360, 0, 5928, 0, 0, 0, 0, 0, 0, 0, 7840, 0, 2192, 0, 0, 0, 0, 0, 0, 0, 8224, 0, 55508, 0, 0, 0, 0, 0, 0, 0, 23372, 0, 35752, 0, 0, 0, 0, 0, 0, 0, 23920, 0, -48792, 0, 0, 0, 0, 0, 0, 0, -36984, 0, 174592, 0, 0, 0, 0, 0, 0, 0, 130960, 0, 92564, 0, 0, 0, 0, 0, 0, 0, 145620, 0, 41152, 0, 0, 0, 0, 0, 0, 0, 443584, 0, 146808, 0, 0, 0, 0, 0, 0, 0, 459880, 0, -225488, 0, 0, 0, 0, 0, 0, 0, 166896, 0, -3288, 0, 0, 0, 0, 0, 0, 0, 1085696, 0, 622992, 0, 0, 0, 0, 0, 0, 0, -122920, 0, 1259408, 0, 0, 0, 0, 0, 0, 0, -975200, 0, 306192, 0, 0, 0, 0, 0, 0, 0, -177136, 0, 323568, 0, 0, 0, 0, 0, 0, 0, 1108788, 0, 1298080, 0, 0, 0, 0, 0, 0, 0, 1705960, 0, 1173608, 0, 0, 0, 0, 0, 0, 0, -1454040, 0, 1037392, 0, 0, 0, 0, 0, 0, 0, -290400, 0, -1565652, 0, 0, 0, 0, 0, 0, 0, 220220, 0, -900008, 0, 0, 0, 0, 0, 0, 0, -869816, 0, -1585232, 0, 0, 0, 0, 0, 0, 0, 133040, 0, -2311056, 0, 0, 0, 0, 0, 0, 0, 422080, 0, -907692, 0, 0, 0, 0, 0, 0, 0, -1438044, 0, 865992, 0, 0, 0, 0, 0, 0, 0, 774176, 0, -1539520, 0, 0, 0, 0, 0, 0, 0, -617440, 0, -6526608, 0, 0, 0, 0, 0, 0, 0, -10818816, 0, -1053192, 0, 0, 0, 0, 0, 0, 0, -998208, 0, -2752208, 0, 0, 0, 0, 0, 0, 0, -469056, 0, -2651392, 0, 0, 0, 0, 0, 0, 0, -365264, 0, -7227408, 0, 0, 0, 0, 0, 0, 0, -195680, 0, 3947028, 0, 0, 0, 0, 0, 0, 0, -6640416, 0, 6026792, 0, 0, 0, 0, 0, 0, 0, 5352824, 0, -13040184, 0, 0, 0, 0, 0, 0, 0, 2166600, 0, 1578080, 0, 0, 0, 0, 0, 0, 0, -3640080, 0, 1388904, 0, 0, 0, 0, 0, 0, 0, -9295784, 0, 4671072, 0, 0, 0, 0, 0, 0, 0, 1407960, 0, 8293768, 0, 0, 0, 0, 0, 0, 0, 1846920, 0, -1931088, 0, 0, 0, 0, 0, 0, 0, -13474320, 0, -7612092, 0, 0, 0, 0, 0, 0, 0, 199180, 0, 18211512, 0, 0, 0, 0, 0, 0, 0, 15700040, 0, 12838608, 0, 0, 0, 0, 0, 0, 0, 1287952, 0, -12193008, 0, 0, 0, 0, 0, 0, 0, -2339520, 0, 5421544, 0, 0, 0, 0, 0, 0, 0, 1311500, 0, 619784, 0, 0, 0, 0, 0, 0, 0, 6437240, 0, -1906992, 0, 0, 0, 0, 0, 0, 0, 9540904, 0, -21332528, 0, 0, 0, 0, 0, 0, 0, -9861840, 0, 2234208, 0, 0, 0, 0, 0, 0, 0, 17699476, 0, 10236592, 0, 0, 0, 0, 0, 0, 0, 23938800, 0, 3523248, 0, 0, 0, 0, 0, 0, 0, 31079480, 0, 12986032, 0, 0, 0, 0, 0, 0, 0, 15381984, 0, 8501108, 0, 0, 0, 0, 0, 0, 0, 23277068, 0, 16550240, 0, 0, 0, 0, 0, 0, 0, 11930456, 0, -2741792, 0, 0, 0, 0, 0, 0, 0, -14498384, 0, -13815200, 0, 0, 0, 0, 0, 0, 0, -15331136, 0, 5070196, 0, 0, 0, 0, 0, 0, 0, -39974340, 0, 25946992, 0, 0, 0, 0, 0, 0, 0, 12140504, 0, 17688888, 0, 0, 0, 0, 0, 0, 0, -22042280, 0, 31287792, 0, 0, 0, 0, 0, 0, 0, -12307600, 0, -8155492, 0, 0, 0, 0, 0, 0, 0, 16246080, 0, -2633728, 0, 0, 0, 0, 0, 0, 0, 45807440, 0, 10832520, 0, 0, 0, 0, 0, 0, 0, 9576184, 0, -35475408, 0, 0, 0, 0, 0, 0, 0, -7470016, 0, 30253608, 0, 0, 0, 0, 0, 0, 0, 25962160, 0, 66872544, 0, 0, 0, 0, 0, 0, 0, -45057080, 0, -21302592, 0, 0, 0, 0, 0, 0, 0, -18741584, 0, -28881616, 0, 0, 0, 0, 0, 0, 0, -14677984, 0, -22641632, 0, 0, 0, 0, 0, 0, 0, -15512224, 0, 22066392, 0, 0, 0, 0, 0, 0, 0, 43869744, 0, -25903792, 0, 0, 0, 0, 0, 0, 0, -12058320, 0, -61226880, 0, 0, 0, 0, 0, 0, 0, -75693360, 0, 38541728, 0, 0, 0, 0, 0, 0, 0, 54692188, 0, -65277328, 0, 0, 0, 0, 0, 0, 0, 858480, 0, -12401360, 0, 0, 0, 0, 0, 0, 0, -33478056, 0, 21729792, 0, 0, 0, 0, 0, 0, 0, 16619568, 0, -36720492, 0, 0, 0, 0, 0, 0, 0, -16951940, 0, -105281328, 0, 0, 0, 0, 0, 0, 0, -95005720, 0, 29160016, 0, 0, 0, 0, 0, 0, 0, -70537624, 0, -11760048, 0, 0, 0, 0, 0, 0, 0, -12223744, 0, -114912360, 0, 0, 0, 0, 0, 0, 0, -54011720, 0, 17870192, 0, 0, 0, 0, 0, 0, 0, 19874304, 0, -51240792, 0, 0, 0, 0, 0, 0, 0, 7378640, 0, 1208832, 0, 0, 0, 0, 0, 0, 0, 19458080, 0, -65135796, 0, 0, 0, 0, 0, 0, 0, 53701956, 0, -4261728, 0, 0, 0, 0, 0, 0, 0, -20613480, 0, 105398856, 0, 0, 0, 0, 0, 0, 0, -47656920, 0, -2190368, 0, 0, 0, 0, 0, 0, 0, 11674704, 0, -34805192, 0, 0, 0, 0, 0, 0, 0, -73976336, 0, 31725272, 0, 0, 0, 0, 0, 0, 0, 25504320, 0, -64847752, 0, 0, 0, 0, 0, 0, 0, 124428816, 0, 10323392, 0, 0, 0, 0, 0, 0, 0, 92028240, 0, 18418228, 0, 0, 0, 0, 0, 0, 0, -36727160, 0, -23665480, 0, 0, 0, 0, 0, 0, 0, -33968176, 0, -70027792, 0, 0, 0, 0, 0, 0, 0, -33880144, 0, 76885952, 0, 0, 0, 0, 0, 0, 0, -44779824, 0, 178294612, 0, 0, 0, 0, 0, 0, 0, -54652580, 0, -69158808, 0, 0, 0, 0, 0, 0, 0, -111531240, 0, 84493360, 0, 0, 0, 0, 0, 0, 0, 10834176, 0, 88013392, 0, 0, 0, 0, 0, 0, 0, 23794640, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "25.6.a.b", "char_is_minimal": false, "conrey_index": 49, "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, 0], [0, 1, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 20, 0], [0, 0, 0, 0], [-98, 0, 0, -4], [0, 0, 0, 0], [98, 0, 0, -5], [0, 0, 0, 0], [0, -16, -36, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -68, -149, 0], [0, 0, 0, 0], [-1590, 0, 0, -7], [0, 0, 0, 0], [1482, 0, 0, 24], [0, 0, 0, 0], [0, 6, -156, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -55, 674, 0], [0, 0, 0, 0], [1960, 0, 0, 8], [0, 0, 0, 0], [548, 0, 0, 110], [0, 0, 0, 0], [0, -152, 1009, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 192, -202, 0], [0, 0, 0, 0], [2056, 0, 0, -4], [0, 0, 0, 0], [13877, 0, 0, 40], [0, 0, 0, 0], [0, -1064, 300, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -772, 2576, 0], [0, 0, 0, 0], [5843, 0, 0, -80], [0, 0, 0, 0], [8938, 0, 0, -13], [0, 0, 0, 0], [0, -376, -2698, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1940, 4867, 0], [0, 0, 0, 0], [5980, 0, 0, -196], [0, 0, 0, 0], [-12198, 0, 0, 200], [0, 0, 0, 0], [0, 2196, -3888, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 793, -4006, 0], [0, 0, 0, 0], [-9246, 0, 0, -168], [0, 0, 0, 0], [43648, 0, 0, -100], [0, 0, 0, 0], [0, -556, -7029, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2304, -450, 0], [0, 0, 0, 0], [32740, 0, 0, 502], [0, 0, 0, 0], [23141, 0, 0, -188], [0, 0, 0, 0], [0, -429, -9258, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2360, -5848, 0], [0, 0, 0, 0], [36405, 0, 0, 1044], [0, 0, 0, 0], [10288, 0, 0, -248], [0, 0, 0, 0], [0, 6048, -27606, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5472, 12614, 0], [0, 0, 0, 0], [110896, 0, 0, 98], [0, 0, 0, 0]]}