# Stored data for newform 243.5.b.d, downloaded from the LMFDB on 27 June 2026. {"Nk2": 6075, "analytic_conductor": 25.11890102937417, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": -1, "char_values": [243, 2, [2], [1]], "cm_discs": [], "conrey_index": 242, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[2, [27, 0, 1]], [7, [-50, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510867685474547, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 6, "hecke_ring_index_factorization": [[2, 1], [3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 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": true, "label": "243.5.b.d", "level": 243, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "243.5.b.d", "nf_label": "2.0.3.1", "prim_orbit_index": 2, "qexp_display": "q-\\beta q^{2}-11 q^{4}-5\\beta q^{5}+50 q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "4.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "243.5.b", "trace_display": [0, 0, 0, 100], "trace_hash": 1212510843446919765, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.882", "prec": 17}, {"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "15.143", "prec": 20}, {"__RealLiteral__": 0, "data": "0.188", "prec": 17}, {"__RealLiteral__": 0, "data": "153.294", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 2, 0, 0, -22, 0, 0, 100, 0, 0, -270, 0, 0, 508, 0, 0, -622, 0, 0, 502, 0, 0, -216, 0, 0, -100, 0, 0, -1100, 0, 0, 760, 0, 0, -3564, 0, 0, -2648, 0, 0, -1350, 0, 0, -7172, 0, 0, -3510, 0, 0, 198, 0, 0, -5588, 0, 0, -1080, 0, 0, 11286, 0, 0, 3652, 0, 0, 2522, 0, 0, 10450, 0, 0, -13500, 0, 0, -6062, 0, 0, -5522, 0, 0, -8720, 0, 0, -32184, 0, 0, -17820, 0, 0, -1080, 0, 0, 25400, 0, 0, 14526, 0, 0, -638, 0, 0, 1100, 0, 0, -5408, 0, 0, 52326, 0, 0, 35728, 0, 0, -31100, 0, 0, -17550, 0, 0, 18684, 0, 0, 28418, 0, 0, -8360, 0, 0, -12512, 0, 0, -68580, 0, 0, 25100, 0, 0, -17820, 0, 0, 54868, 0, 0, 97686, 0, 0, 56430, 0, 0, 29128, 0, 0, 28132, 0, 0, -10800, 0, 0, -22748, 0, 0, 62370, 0, 0, -57098, 0, 0, -70200, 0, 0, 71910, 0, 0, 78892, 0, 0, -5000, 0, 0, -108540, 0, 0, 100888, 0, 0, -17550, 0, 0, -14256, 0, 0, -67770, 0, 0, 41212, 0, 0, -2178, 0, 0, 108592, 0, 0, 48870, 0, 0, -160920, 0, 0, -157988, 0, 0, -49532, 0, 0, 79380, 0, 0, 38000, 0, 0, 11880, 0, 0, -21284, 0, 0, -202284, 0, 0, -2840, 0, 0, 56430, 0, 0, 72630, 0, 0, -178200, 0, 0, -100628, 0, 0, -40172, 0, 0, 127508, 0, 0, -155250, 0, 0, -14040, 0, 0, 171842, 0, 0, -132400, 0, 0, -106380, 0, 0, 261630, 0, 0, -114950, 0, 0, -34448, 0, 0, 36720, 0, 0, -106820, 0, 0, -67500, 0, 0, 94090, 0, 0, -54864, 0, 0, -68182, 0, 0, 66682, 0, 0, 93420, 0, 0, -77544, 0, 0, -358600, 0, 0, -156122, 0, 0, 281578, 0, 0, -102600, 0, 0, 102502, 0, 0, 95920, 0, 0, 45144, 0, 0, -175500, 0, 0, -25400, 0, 0, -160920, 0, 0, 169930, 0, 0, -167130, 0, 0, -231422, 0, 0, 196020, 0, 0, -230200, 0, 0, 81270, 0, 0, -326348, 0, 0, 49896, 0, 0, 488430, 0, 0, 186624, 0, 0, -134640, 0, 0, -279400, 0, 0, 347380, 0, 0, 357480, 0, 0, 22828, 0, 0, 72630, 0, 0, 518542, 0, 0, 3186, 0, 0, -54000, 0, 0, 7018, 0, 0, -231660, 0, 0, 515160, 0, 0, 111364, 0, 0, 31100, 0, 0, 193040, 0, 0, 564300, 0, 0, 183658, 0, 0, 59488, 0, 0, -351000, 0, 0, -54216, 0, 0, 255052, 0, 0, 261630, 0, 0, 182600, 0, 0, 968220, 0, 0, -77942, 0, 0, -393008, 0, 0, 187792, 0, 0, -905256, 0, 0, -542700, 0, 0, 126100, 0, 0, -128736, 0, 0, 683424, 0, 0, -588572, 0, 0, 193050, 0, 0, -238460, 0, 0, -677160, 0, 0, 522500, 0, 0, 93420, 0, 0, -25100, 0, 0, 912114, 0, 0, -672592, 0, 0, -312598, 0, 0, -572528, 0, 0, -26730, 0, 0, 744876, 0, 0, -236360, 0, 0, -383318, 0, 0, 53460, 0, 0, 244350, 0, 0, 137632, 0, 0, -303100, 0, 0, 878580, 0, 0, 58104, 0, 0, -342900, 0, 0, -425282, 0, 0, 544104, 0, 0, 331532, 0, 0, -276100, 0, 0, 396900, 0, 0, -620136, 0, 0, -494660, 0, 0, 823284, 0, 0, 394558, 0, 0, 10800, 0, 0, -436000, 0, 0, -603548, 0, 0, -1821688, 0, 0, 375300, 0, 0, -1011420, 0, 0, 488430, 0, 0, 727114, 0, 0, -1609200, 0, 0, 139882, 0, 0, -620730, 0, 0, 209304, 0, 0, -112050, 0, 0, 190760, 0, 0, 823528, 0, 0, -891000, 0, 0, -891540, 0, 0, -538982, 0, 0, -309452, 0, 0, 977908, 0, 0, -493020, 0, 0, -572792, 0, 0, -54000, 0, 0, 463228, 0, 0, -380970, 0, 0, -838750, 0, 0, 250228, 0, 0, 867292, 0, 0, 1250424, 0, 0, 50292, 0, 0, 657450, 0, 0, 1187830, 0, 0, -894564, 0, 0, 74736, 0, 0, 628078, 0, 0, -531900, 0, 0, 726300, 0, 0, -1406348, 0, 0, -351000, 0, 0, 733590, 0, 0, -1410750, 0, 0, -120230, 0, 0, -791010, 0, 0, -31900, 0, 0, -82080, 0, 0, 183600, 0, 0, 2230492, 0, 0, -1587698, 0, 0, -32184, 0, 0, -2124144, 0, 0, 55000, 0, 0, -664648, 0, 0, -1259280, 0, 0, 1698292, 0, 0, -542700, 0, 0, -274320, 0, 0, -204930, 0, 0, -270400, 0, 0, -1109768, 0, 0, 1533292, 0, 0, 818370, 0, 0, 273892, 0, 0, 810810, 0, 0, -622028, 0, 0, 2616300, 0, 0, -387720, 0, 0, 156816, 0, 0, 832612, 0, 0, 2866644, 0, 0, 240628, 0, 0, -338850, 0, 0, 1786400, 0, 0, 1998810, 0, 0, -1570082, 0, 0, -453332, 0, 0, -38000, 0, 0, -605610, 0, 0, 390744, 0, 0, -61578, 0, 0, 2407438, 0, 0, 1177200, 0, 0, 927608, 0, 0, -1194512, 0, 0, 958716, 0, 0, 1312740, 0, 0, -877500, 0, 0, 244350, 0, 0, 166030, 0, 0, 285984, 0, 0, -1800172, 0, 0, 1770120, 0, 0, -601268, 0, 0, 934200, 0, 0, -1858880, 0, 0, 640588, 0, 0, -835650, 0, 0, -1963224, 0, 0, -944212, 0, 0, 544852, 0, 0, 1420900, 0, 0, 178200, 0, 0, -2464940, 0, 0, 396900, 0, 0, 300982, 0, 0, 2434050, 0, 0, 406350, 0, 0, -418000, 0, 0, 2654300, 0, 0, -881010, 0, 0, 2095600, 0, 0, 335880, 0, 0, 1956652, 0, 0, -3852900, 0, 0, -625600, 0, 0, 234124, 0, 0, 933120, 0, 0, -239436, 0, 0, 3453516, 0, 0, -1011420, 0, 0, 2420830, 0, 0, -3429000, 0, 0, -280800, 0, 0, 31240, 0, 0, -2509808, 0, 0, -1758240, 0, 0, 132400, 0, 0, -2607066, 0, 0, 49698, 0, 0, -3832596, 0, 0, 511180, 0, 0, -798930, 0, 0, -2091960, 0, 0, 774576, 0, 0, -1539748, 0, 0, -891000, 0, 0, 15930, 0, 0, 3215160, 0, 0, -1558242, 0, 0, 1106908, 0, 0, 1991512, 0, 0, 86130, 0, 0, 2743400, 0, 0, -1135772, 0, 0, -434160, 0, 0, -3495744, 0, 0, 2575800, 0, 0, -1402588, 0, 0, 124888, 0, 0, 4884300, 0, 0, -992720, 0, 0, -776250], "weight": 5, "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], [1, 0], [0, -1], [0, 0], [-11, 0], [0, -5], [0, 0], [50, 0], [0, -5], [0, 0], [-135, 0], [0, -4], [0, 0], [254, 0], [0, -50], [0, 0], [-311, 0], [0, -66], [0, 0], [251, 0], [0, 55], [0, 0], [-108, 0], [0, -65], [0, 0], [-50, 0], [0, -254], [0, 0], [-550, 0], [0, 209], [0, 0], [380, 0], [0, 231], [0, 0], [-1782, 0], [0, -250], [0, 0], [-1324, 0], [0, -251], [0, 0], [-675, 0], [0, -596], [0, 0], [-3586, 0], [0, 44], [0, 0], [-1755, 0], [0, 269], [0, 0], [99, 0], [0, 50], [0, 0], [-2794, 0], [0, 969], [0, 0], [-540, 0], [0, -250], [0, 0], [5643, 0], [0, 346], [0, 0], [1826, 0], [0, -380], [0, 0], [1261, 0], [0, -1270], [0, 0], [5225, 0], [0, 726], [0, 0], [-6750, 0], [0, 1809], [0, 0], [-3031, 0], [0, 1324], [0, 0], [-2761, 0], [0, -200], [0, 0], [-4360, 0], [0, 1555], [0, 0], [-16092, 0], [0, -1300], [0, 0], [-8910, 0], [0, 3586], [0, 0], [-540, 0], [0, -2010], [0, 0], [12700, 0], [0, 715], [0, 0], [7263, 0], [0, -1255], [0, 0], [-319, 0], [0, -99], [0, 0], [550, 0]]}