# Stored data for newform 400.6.c.f, downloaded from the LMFDB on 19 April 2024.
{"label": "400.6.c.f", "space_label": "400.6.c", "level": 400, "weight": 6, "hecke_orbit": 6, "hecke_orbit_code": 22518135676469648, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 377648659395224301, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [144, 0, 1]]], "qexp_display": "q+6iq^{3}-44iq^{7}+99q^{9}-540q^{11}+\\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": 2, "level_radical": 10, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": 13, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [49], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "1.935", "prec": 17}, {"__RealLiteral__": 0, "data": "0.659", "prec": 17}, {"__RealLiteral__": 0, "data": "15.648", "prec": 20}, {"__RealLiteral__": 0, "data": "7.378", "prec": 17}, {"__RealLiteral__": 0, "data": "157.318", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, 198, 0, -1080, 0, 0, 0, 0, 0, 0, 0, 1672, 0, 2112, 0, 0, 0, 0, 0, 0, 0, 1188, 0, -8512, 0, 0, 0, 0, 0, 0, 0, 10032, 0, 34452, 0, 0, 0, 0, 0, 0, 0, 18126, 0, 14256, 0, 0, 0, 0, 0, 0, 0, -15336, 0, -69476, 0, 0, 0, 0, 0, 0, 0, -98496, 0, 93744, 0, 0, 0, 0, 0, 0, 0, -153824, 0, -50382, 0, 0, 0, 0, 0, 0, 0, -59508, 0, -73568, 0, 0, 0, 0, 0, 0, 0, -106920, 0, 22572, 0, 0, 0, 0, 0, 0, 0, -199804, 0, -7152, 0, 0, 0, 0, 0, 0, 0, -104544, 0, 261098, 0, 0, 0, 0, 0, 0, 0, -290400, 0, -201960, 0, 0, 0, 0, 0, 0, 0, -296648, 0, 31104, 0, 0, 0, 0, 0, 0, 0, -393228, 0, -148720, 0, 0, 0, 0, 0, 0, 0, -467856, 0, 722304, 0, 0, 0, 0, 0, 0, 0, 393138, 0, 165528, 0, 0, 0, 0, 0, 0, 0, 987336, 0, -1118900, 0, 0, 0, 0, 0, 0, 0, 722304, 0, 1448064, 0, 0, 0, 0, 0, 0, 0, 112336, 0, -523488, 0, 0, 0, 0, 0, 0, 0, -902880, 0, 678392, 0, 0, 0, 0, 0, 0, 0, -1621488, 0, -496584, 0, 0, 0, 0, 0, 0, 0, 545492, 0, -1140480, 0, 0, 0, 0, 0, 0, 0, 2309472, 0, 1314148, 0, 0, 0, 0, 0, 0, 0, 1625184, 0, -2683800, 0, 0, 0, 0, 0, 0, 0, 52448, 0, 117612, 0, 0, 0, 0, 0, 0, 0, -1935036, 0, 1036640, 0, 0, 0, 0, 0, 0, 0, -842688, 0, -393228, 0, 0, 0, 0, 0, 0, 0, 2134042, 0, -2937552, 0, 0, 0, 0, 0, 0, 0, 3430944, 0, 2129600, 0, 0, 0, 0, 0, 0, 0, -654144, 0, 1461456, 0, 0, 0, 0, 0, 0, 0, -641520, 0, -2936736, 0, 0, 0, 0, 0, 0, 0, -228096, 0, -755896, 0, 0, 0, 0, 0, 0, 0, 711504, 0, 4596480, 0, 0, 0, 0, 0, 0, 0, 7983140, 0, 3430944, 0, 0, 0, 0, 0, 0, 0, 2323728, 0, -3554406, 0, 0, 0, 0, 0, 0, 0, 3410748, 0, 3430944, 0, 0, 0, 0, 0, 0, 0, 8087704, 0, -8076288, 0, 0, 0, 0, 0, 0, 0, 1900692, 0, 4875552, 0, 0, 0, 0, 0, 0, 0, 1765632, 0, 1528740, 0, 0, 0, 0, 0, 0, 0, -5281012, 0, -7611408, 0, 0, 0, 0, 0, 0, 0, -9960408, 0, -475988, 0, 0, 0, 0, 0, 0, 0, -5417280, 0, 7764768, 0, 0, 0, 0, 0, 0, 0, -13002704, 0, 1794474, 0, 0, 0, 0, 0, 0, 0, -7553412, 0, -18604080, 0, 0, 0, 0, 0, 0, 0, 4875552, 0, 13370940, 0, 0, 0, 0, 0, 0, 0, 3838912, 0, 2901072, 0, 0, 0, 0, 0, 0, 0, 6443712, 0, 249128, 0, 0, 0, 0, 0, 0, 0, -2672160, 0, -5643000, 0, 0, 0, 0, 0, 0, 0, -8272568, 0, 11803968, 0, 0, 0, 0, 0, 0, 0, -8682012, 0, 11890912, 0, 0, 0, 0, 0, 0, 0, -16978896, 0, -13483692, 0, 0, 0, 0, 0, 0, 0, -20812946, 0, -1518264, 0, 0, 0, 0, 0, 0, 0, -9788040, 0, -1364132, 0, 0, 0, 0, 0, 0, 0, -6878124, 0, 993168, 0, 0, 0, 0, 0, 0, 0, 10115600, 0, -7698240, 0, 0, 0, 0, 0, 0, 0, 25844940, 0, 12167144, 0, 0, 0, 0, 0, 0, 0, -170544, 0, -11918016, 0, 0, 0, 0, 0, 0, 0, -7116032, 0, -12730608, 0, 0, 0, 0, 0, 0, 0, -15964560, 0, 20348020, 0, 0, 0, 0, 0, 0, 0, 1254528, 0, -1083456, 0, 0, 0, 0, 0, 0, 0, 12914680, 0, -33685632, 0, 0, 0, 0, 0, 0, 0, 354024, 0, 28102736, 0, 0, 0, 0, 0, 0, 0, 9280656, 0, 16943364, 0, 0, 0, 0, 0, 0, 0, 8281440, 0, -8988672, 0, 0, 0, 0, 0, 0, 0, 9449352, 0, -12348404, 0, 0, 0, 0, 0, 0, 0, 18704640, 0, 37517040, 0, 0, 0, 0, 0, 0, 0, 21542048, 0, 17877024, 0, 0, 0, 0, 0, 0, 0, 16296984, 0, -45311176, 0, 0, 0, 0, 0, 0, 0, 3692304, 0, 38033820, 0, 0, 0, 0, 0, 0, 0, -30262252, 0, -15228576, 0, 0, 0, 0, 0, 0, 0, -30064608, 0, 4797056, 0, 0, 0, 0, 0, 0, 0, -28922346, 0, 14374800, 0, 0, 0, 0, 0, 0, 0, -24209240, 0, 8386752, 0, 0, 0, 0, 0, 0, 0, 21536064, 0, -57692512, 0, 0, 0, 0, 0, 0, 0, 53187840, 0, 9091764, 0, 0, 0, 0, 0, 0, 0, 43184636, 0, 3176496, 0, 0, 0, 0, 0, 0, 0, 28801872, 0, -50621760, 0, 0, 0, 0, 0, 0, 0, 22638528, 0, -5217696, 0, 0, 0, 0, 0, 0, 0, -1539648, 0, -5891292, 0, 0, 0, 0, 0, 0, 0, 6200172, 0, -3743608, 0, 0, 0, 0, 0, 0, 0, -7283232, 0, -40036788, 0, 0, 0, 0, 0, 0, 0, -50441884, 0, 53345424, 0, 0, 0, 0, 0, 0, 0, -35524656, 0, -40316626, 0, 0, 0, 0, 0, 0, 0, -37254624, 0, -2445984, 0, 0, 0, 0, 0, 0, 0, 44707672, 0, 36381312, 0, 0, 0, 0, 0, 0, 0, 83064960, 0, 18234832, 0, 0, 0, 0, 0, 0, 0, 25732080, 0, -6293916, 0, 0, 0, 0, 0, 0, 0, 59226112, 0, 27206280, 0, 0, 0, 0, 0, 0, 0, -5056128, 0, 23158872, 0, 0, 0, 0, 0, 0, 0, 2234628, 0, 5191776, 0, 0, 0, 0, 0, 0, 0, -35282192, 0, -38061408, 0, 0, 0, 0, 0, 0, 0, -79356996, 0, 15153336, 0, 0, 0, 0, 0, 0, 0, -14036592, 0, 92501244, 0, 0, 0, 0, 0, 0, 0, 56481832, 0, -59588784, 0, 0, 0, 0, 0, 0, 0, 55816992, 0, -21031230, 0, 0, 0, 0, 0, 0, 0, 11918016, 0, 54406728, 0, 0, 0, 0, 0, 0, 0, 32134320, 0, -19780596, 0, 0, 0, 0, 0, 0, 0, -99316800, 0, -58386112, 0, 0, 0, 0, 0, 0, 0, -2445984, 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": "4.6.a.a", "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], [1, 0], [0, 0], [0, 6], [0, 0], [0, 0], [0, 0], [0, -44], [0, 0], [99, 0], [0, 0], [-540, 0], [0, 0], [0, -209], [0, 0], [0, 0], [0, 0], [0, -297], [0, 0], [836, 0], [0, 0], [1056, 0], [0, 0], [0, 2052], [0, 0], [0, 0], [0, 0], [0, 2052], [0, 0], [594, 0], [0, 0], [-4256, 0], [0, 0], [0, -3240], [0, 0], [0, 0], [0, 0], [0, 149], [0, 0], [5016, 0], [0, 0], [17226, 0], [0, 0], [0, 6050], [0, 0], [0, 0], [0, 0], [0, -648], [0, 0], [9063, 0], [0, 0], [7128, 0], [0, 0], [0, 9747], [0, 0], [0, 0], [0, 0], [0, 5016], [0, 0], [-7668, 0], [0, 0], [-34738, 0], [0, 0], [0, -4356], [0, 0], [0, 0], [0, 0], [0, 10906], [0, 0], [-49248, 0], [0, 0], [46872, 0], [0, 0], [0, 33781], [0, 0], [0, 0], [0, 0], [0, 23760], [0, 0], [-76912, 0], [0, 0], [-25191, 0], [0, 0], [0, -33858], [0, 0], [0, 0], [0, 0], [0, 3564], [0, 0], [-29754, 0], [0, 0], [-36784, 0], [0, 0], [0, -25536], [0, 0], [0, 0], [0, 0], [0, 61199], [0, 0], [-53460, 0], [0, 0]]}