# Stored data for newform 224.2.x.b, downloaded from the LMFDB on 19 April 2024.
{"label": "224.2.x.b", "space_label": "224.2.x", "level": 224, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505180208890080, "dim": 112, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [50535568838414565376, 0, 273966215644558917632, 0, 742620386391555571712, 0, -33834839909995542216704, 0, 7281245948548920507367424, 0, 27686199663285679740157952, 0, 54422655699555162295107584, 0, -416171679547803050883153920, 0, 1142073556442771485340729344, 0, -745488373057344880530423808, 0, 530734986167718450017861632, 0, -1930402290616671739572649984, 0, 6114447344540783748171317248, 0, -4792025443305755413952757760, 0, 1322992865772413986319400960, 0, 1320044116244881586243387392, 0, 1998758853571717278634782720, 0, -722340778483101040113401856, 0, 188152123779874503393165312, 0, 227606914529997069565763584, 0, 206769208185609729681681408, 0, -33735770562958407657809920, 0, 8034752948122201458083840, 0, 10404431021351394894332928, 0, 8363536676177922874863872, 0, -662714450008310901927936, 0, 123728416699458035924992, 0, 169002049327126558115840, 0, 139589255327675933822976, 0, -7193941535671964485632, 0, 699488419209010104320, 0, 930425358330308742144, 0, 882241325181364838656, 0, -55732659290538316800, 0, 3724252891028670464, 0, 2997096502792282624, 0, 2033334431668531584, 0, -113389294247033600, 0, 7048647399174912, 0, 4509285243496832, 0, 2137448428667744, 0, -86165525740800, 0, 5164885847040, 0, 2983920960384, 0, 1088136536128, 0, -26342232576, 0, 1505246720, 0, 826311552, 0, 258527648, 0, -3442432, 0, 182592, 0, 96192, 0, 27036, 0, -168, 0, 8, 0, 4, 0, 1]]], "char_order": 8, "char_parity": 1, "char_degree": 4, "char_conductor": 224, "char_orbit_label": "x", "char_is_real": false, "Nk2": 896, "analytic_conductor": 1.7886490052766806, "level_radical": 14, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [224, 8, [127, 197, 129], [4, 1, 4]], "inner_twist_count": 4, "level_primes": [2, 7], "conrey_indexes": [27, 83, 139, 195], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 28, "sato_tate_group": "1.2.3.c8", "trace_display": [-8, 0, 0, -4], "traces": [112, -8, 0, -8, 0, 0, -4, -8, -8, 0, -8, 0, 0, -20, -16, 16, 0, -16, 0, 0, -4, 32, -48, 0, -8, 0, 0, -24, -8, 16, 0, -8, 0, 0, 20, 32, -8, 0, -8, 0, 0, 16, 32, -144, 0, -8, 0, 0, 0, 16, -32, 0, -32, 0, 0, 64, -8, -72, 0, -88, 0, 0, 0, 112, -16, 0, -64, 0, 0, -40, 56, -8, 0, -168, 0, 0, 52, 192, -16, 0, 0, 0, 0, -24, -48, -8, 0, -96, 0, 0, -52, -8, -32, 0, 0, 0, 0, 88, 16, 112, 0, 40, 0, 0, -32, 56, 64, 0, 80, 0, 0, 120, 0, 48, 0, 216, 0, 0, 8, -8, 0, 0, 72, 0, 0, 204, 0, -64, 0, 112, 0, 0, 44, 8, -160, 0, 0, 0, 0, 120, 16, -80, 0, 48, 0, 0, 88, -56, -112, 0, -96, 0, 0, -96, -48, 72, 0, -32, 0, 0, -8, -248, -168, 0, -56, 0, 0, -32, -8, 40, 0, 160, 0, 0, 120, -320, 0, 0, 152, 0, 0, 32, -184, 56, 0, 280, 0, 0, -96, -296, 0, 0, -16, 0, 0, 112, 152, -48, 0, 280, 0, 0, 124, -368, -8, 0, 304, 0, 0, -192, -128, -72, 0, -80, 0, 0, -32, -112, 216, 0, -112, 0, 0, -240, -128, 144, 0, -368, 0, 0, 88, -24, 112, 0, 176, 0, 0, -280, 224, -96, 0, -256, 0, 0, -88, -24, 168, 0, -8, 0, 0, -200, 80, 64, 0, -32, 0, 0, -212, 176, 48, 0, 72, 0, 0, -48, -88, -48, 0, -296, 0, 0, 0, 416, -32, 0, -8, 0, 0, -80, -80, -136, 0, -320, 0, 0, 0, 408, 112, 0, 128, 0, 0, 56, -248, -136, 0, -304, 0, 0, -68, 392, -16, 0, 0, 0, 0, 96, -8, 72, 0, -24, 0, 0, 68, 368, -8, 0, 0, 0, 0, 24, -144, 344, 0, 224, 0, 0, 24, 272, 88, 0, 16, 0, 0, 424, 0, 200, 0, 208, 0, 0, -28, 0, -128, 0, -144, 0, 0, 308, 0, 144, 0, 392, 0, 0, -152, -40, 368, 0, -8, 0, 0, 176, -8, 184, 0, 176, 0, 0, -236, -384, 184, 0, -224, 0, 0, 136, 56, 248, 0, 200, 0, 0, -8, -312, 472, 0, -8, 0, 0, 16, -8, 280, 0, 496, 0, 0, -296, -544, 0, 0, -256, 0, 0, -120, 368, 32, 0, 264, 0, 0, -36, -632, 0, 0, -16, 0, 0, -272, -32, -232, 0, -56, 0, 0, -212, -432, 312, 0, -304, 0, 0, -232, 8, -168, 0, -176, 0, 0, 32, -360, -328, 0, 248, 0, 0, -432, -16, -184, 0, -64, 0, 0, -32, -40, -8, 0, -384, 0, 0, -456, -272, 32, 0, -384, 0, 0, 260, 248, -360, 0, 112, 0, 0, -368, 328, -128, 0, -672, 0, 0, 128, 224, 128, 0, -128, 0, 0, -264, -128, 48, 0, -376, 0, 0, 0, 856, -136, 0, -168, 0, 0, -120, 184, 160, 0, -168, 0, 0, 0, 640, -16, 0, -120, 0, 0, -136, 248, -104, 0, -264, 0, 0, -52, 544, -288, 0, 0, 0, 0, 264, 152, 144, 0, -256, 0, 0, -72, 880, -64, 0, 0, 0, 0, 376, 104, -128, 0, 128, 0, 0, -200, 288, -248, 0, -368, 0, 0, 392, 0, 40, 0, 496, 0, 0, 236, 192, -8, 0, 144, 0, 0, 472, 0, 208, 0, 440, 0, 0, -164, -24, -416, 0, -200, 0, 0, 264, -160, 160, 0, 544, 0, 0, 280, -520, 152, 0, 296, 0, 0, 360, -248, -72, 0, 616, 0, 0, -8, -824, -224, 0, 320, 0, 0, 240, 184, 312, 0, 432, 0, 0, 328, -960, 0, 0, 632, 0, 0, -304, -232, -16, 0, 384, 0, 0, 104, -704, 0, 0, -16, 0, 0, -264, -408, -264, 0, 128, 0, 0, 368, -576, -224, 0, 688, 0, 0, -240, 144, -96, 0, -72, 0, 0, -72, -648, 512, 0, 224, 0, 0, -480, -16, -496, 0, -368, 0, 0, 160, -464, -8, 0, 304, 0, 0, -92, 80, -336, 0, -808, 0, 0, 300, 360, 552, 0, -144, 0, 0, -272, -128, -472, 0, -528, 0, 0, 20, 592, -96, 0, 264, 0, 0, -408, -136, -336, 0, -696, 0, 0, 0, 416, 224, 0, -48, 0, 0, 104, 64, -160, 0, -488, 0, 0, 0, 944, -16, 0, 248, 0, 0, 272, -256, -336, 0, 16, 0, 0, 236, 1160, -288, 0, 0, 0, 0, 344, 192, -552, 0, 152, 0, 0, 180, 544, -288, 0, 0, 0, 0, 680, -208, -48, 0, 72, 0, 0, 184, 568, 216, 0, -8, 0, 0, 512, 0, 88, 0, -88, 0, 0, 200, 480, -8, 0, -424, 0, 0, 664, 0, 280, 0, 168, 0, 0, 304, -296, 504, 0, -8, 0, 0, 512, 16, 432, 0, 960, 0, 0, -572, -560, -296, 0, -392, 0, 0, 264, 328, 88, 0, 896, 0, 0, -144, -968, 552, 0, -224, 0, 0, 256, -192, -304, 0, 480, 0, 0, -568, -880, 0, 0, -480, 0, 0, 96, 312, -16, 0, 544, 0, 0, -16, -912, 0, 0, -16, 0, 0, -416, -104, -152, 0, 72, 0, 0, -408, -1024, -488, 0, -976, 0, 0, -712, 208, -96, 0, 344, 0, 0, 152, -768, -448, 0, -80, 0, 0, -96, -16, -56, 0, -616, 0, 0, -184, 104, 248, 0, -696, 0, 0, -576, 256, -592, 0, -368, 0, 0, -148, 272, -376, 0, 312, 0, 0, -568, -560, 56, 0, -768, 0, 0, -8, 752, -328, 0, -624, 0, 0, -424, 232, 48, 0, -1488, 0, 0, 0, 432, -192, 0, 56, 0, 0, -256, 256, -200, 0, -376, 0, 0, 0, 1248, 112, 0, 8, 0, 0, 352, 432, 624, 0, -24, 0, 0, 92, 1176, -512, 0, 0, 0, 0, 504, -456, 104, 0, -32, 0, 0, 40, 1000, 16, 0, 0, 0, 0, 464, 472, 32, 0, 336, 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, 7, 2, -1, 2, 0], [1, 1, 32, 8, -1, 8, 0], [1, 1, 224, 24, 1, 8, 0]], "char_orbit_index": 24, "prim_orbit_index": 24, "minimal_twist": "224.2.x.b", "char_is_minimal": true, "conrey_index": 27, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}