# Stored data for newform 162.7.d.d, downloaded from the LMFDB on 25 April 2024.
{"label": "162.7.d.d", "space_label": "162.7.d", "level": 162, "weight": 7, "hecke_orbit": 4, "hecke_orbit_code": 13511005157982370, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 1052669183102337372, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [915546564, 0, -30258, 0, 1]]], "qexp_display": "q+(-4\\beta _{1}+4\\beta _{3})q^{2}+(2^{5}-2^{5}\\beta _{2})q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "d", "char_is_real": false, "Nk2": 7938, "analytic_conductor": 37.26876154641586, "hecke_ring_index": 1, "level_radical": 6, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [162, 6, [83], [5]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [53, 107], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "3.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "91.783", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3281.121", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "6.2.3.c6", "trace_display": [0, 0, 0, 968], "traces": [0, 4, 0, 0, 64, 0, 0, 968, 0, 0, -3936, 0, 0, -6736, 0, 0, -2048, 0, 0, 22976, 0, 0, 15168, 0, 0, 29266, 0, 0, 61952, 0, 0, 79592, 0, 0, 144, 0, 0, 210104, 0, 0, -62976, 0, 0, -7600, 0, 0, 76416, 0, 0, -233214, 0, 0, 215552, 0, 0, -932832, 0, 0, 332112, 0, 0, -26500, 0, 0, -131072, 0, 0, -337936, 0, 0, -952512, 0, 0, 944576, 0, 0, 367616, 0, 0, 70232, 0, 0, 838176, 0, 0, 4428, 0, 0, -485376, 0, 0, -6520448, 0, 0, 868800, 0, 0, 642848, 0, 0, 1873024, 0, 0, -3986824, 0, 0, 2701008, 0, 0, 777824, 0, 0, 991232, 0, 0, -1174896, 0, 0, 5653248, 0, 0, 51694, 0, 0, -2546944, 0, 0, 12228848, 0, 0, 6628224, 0, 0, 5560192, 0, 0, 9216, 0, 0, 2184656, 0, 0, -6012864, 0, 0, -20424888, 0, 0, 3361664, 0, 0, 8157416, 0, 0, 14682624, 0, 0, -12311356, 0, 0, 2015232, 0, 0, 3202784, 0, 0, -124224, 0, 0, -13033230, 0, 0, -486400, 0, 0, -14164744, 0, 0, -1463184, 0, 0, -41524768, 0, 0, 1222656, 0, 0, 34128, 0, 0, -22608384, 0, 0, 7863908, 0, 0, 7462848, 0, 0, -2263600, 0, 0, 7566384, 0, 0, -12886956, 0, 0, 13795328, 0, 0, 27033008, 0, 0, -2949120, 0, 0, 77045056, 0, 0, -14925312, 0, 0, 10709672, 0, 0, 18597408, 0, 0, -8692816, 0, 0, -10627584, 0, 0, -53431200, 0, 0, -69696, 0, 0, 6241856, 0, 0, -1696000, 0, 0, -38691584, 0, 0, 1952256, 0, 0, 18110592, 0, 0, -2097152, 0, 0, 50845168, 0, 0, -69553920, 0, 0, 83055996, 0, 0, 10813952, 0, 0, 118559600, 0, 0, -50732016, 0, 0, -26442544, 0, 0, -60960768, 0, 0, 13486496, 0, 0, 51085824, 0, 0, 96549628, 0, 0, 15113216, 0, 0, -86918688, 0, 0, 50252640, 0, 0, 3678400, 0, 0, -11763712, 0, 0, -20922400, 0, 0, -78318528, 0, 0, -44955652, 0, 0, 4494848, 0, 0, 78710544, 0, 0, 18492672, 0, 0, -197135776, 0, 0, 13410816, 0, 0, 11522768, 0, 0, -108717312, 0, 0, 80210336, 0, 0, -141696, 0, 0, 2017312, 0, 0, -40389072, 0, 0, 84127676, 0, 0, -31064064, 0, 0, -184895568, 0, 0, -84139776, 0, 0, -56209380, 0, 0, -104327168, 0, 0, 53170952, 0, 0, -206742336, 0, 0, -35765860, 0, 0, -27801600, 0, 0, 288391040, 0, 0, 147010944, 0, 0, -225745344, 0, 0, 41142272, 0, 0, -85968, 0, 0, 60864048, 0, 0, 62764424, 0, 0, 29968384, 0, 0, 268065856, 0, 0, 321484416, 0, 0, 231023264, 0, 0, 127578368, 0, 0, 7639776, 0, 0, 87124992, 0, 0, -278477680, 0, 0, 172864512, 0, 0, 12826000, 0, 0, 7478400, 0, 0, -160252552, 0, 0, 12445184, 0, 0, 277183688, 0, 0, -969984, 0, 0, -44992908, 0, 0, -31719424, 0, 0, 198647712, 0, 0, -153938112, 0, 0, -71332960, 0, 0, -75193344, 0, 0, -229956232, 0, 0, -228913776, 0, 0, -327122048, 0, 0, 90451968, 0, 0, 168103904, 0, 0, 461478912, 0, 0, -353815136, 0, 0, -1654208, 0, 0, -300675376, 0, 0, 229482576, 0, 0, 747252, 0, 0, -163004416, 0, 0, -183091648, 0, 0, 57645504, 0, 0, -465332616, 0, 0, 195661568, 0, 0, 228587392, 0, 0, -326680608, 0, 0, 205905600, 0, 0, -212103168, 0, 0, -151076224, 0, 0, 353629056, 0, 0, -273261602, 0, 0, 355852288, 0, 0, -90685440, 0, 0, 2843568, 0, 0, 101919968, 0, 0, 147456, 0, 0, -410431792, 0, 0, 443906688, 0, 0, -33992288, 0, 0, -69908992, 0, 0, 51193600, 0, 0, -69280656, 0, 0, -285935148, 0, 0, -384823296, 0, 0, -483003616, 0, 0, 202838592, 0, 0, -197591608, 0, 0, -326798208, 0, 0, 640138896, 0, 0, 226815072, 0, 0, 457176448, 0, 0, -107573248, 0, 0, 4286304, 0, 0, -128684544, 0, 0, 862180484, 0, 0, 522074624, 0, 0, -33398104, 0, 0, 26076000, 0, 0, -769283128, 0, 0, 234921984, 0, 0, -509746432, 0, 0, -706476288, 0, 0, 517313122, 0, 0, 393963392, 0, 0, 369440720, 0, 0, -312497232, 0, 0, -785464752, 0, 0, 128974848, 0, 0, -751892656, 0, 0, 827136, 0, 0, 1339819776, 0, 0, 51244544, 0, 0, 1069391520, 0, 0, 840998400, 0, 0, 945089636, 0, 0, 3975168, 0, 0, 396541728, 0, 0, 332529024, 0, 0, -1097666500, 0, 0, -834126720, 0, 0, -311138432, 0, 0, -603625728, 0, 0, 3120018984, 0, 0, -7782400, 0, 0, 745624400, 0, 0, -1534426752, 0, 0, -942948, 0, 0, 453271808, 0, 0, 1206837376, 0, 0, -199093776, 0, 0, 493020464, 0, 0, -93643776, 0, 0, 1570889088, 0, 0, -158301504, 0, 0, -3859245632, 0, 0, -664396288, 0, 0, -782741704, 0, 0, -929462784, 0, 0, -69815632, 0, 0, -39124992, 0, 0, -1211997376, 0, 0, -1307287872, 0, 0, -772634340, 0, 0, 2184192, 0, 0, 164654024, 0, 0, 1118553216, 0, 0, -2414314720, 0, 0, -361734144, 0, 0, 188233408, 0, 0, -196552704, 0, 0, -1631591140, 0, 0, -251645056, 0, 0, 2329339472, 0, 0, -559362480, 0, 0, -1425048768, 0, 0, 477622272, 0, 0, 804924320, 0, 0, -69108288, 0, 0, 178504000, 0, 0, -36217600, 0, 0, 1954800, 0, 0, 1073702112, 0, 0, 568649664, 0, 0, -242124288, 0, 0, 902084480, 0, 0, 796714368, 0, 0, -43654400, 0, 0, -824765184, 0, 0, 1414671656, 0, 0, 1368086016, 0, 0, 2015305568, 0, 0, 220725248, 0, 0, 1671528672, 0, 0, -3319287168, 0, 0, 533765554, 0, 0, -865056256, 0, 0, 50039792, 0, 0, -2107152, 0, 0, 37597028, 0, 0, -188743680, 0, 0, -1103863216, 0, 0, -1135801152, 0, 0, 2483927928, 0, 0, 1232720896, 0, 0, -1138168448, 0, 0, 438933504, 0, 0, 1170774140, 0, 0, 477609984, 0, 0, 880339616, 0, 0, -1260829248, 0, 0, 2959381216, 0, 0, 685419008, 0, 0, -2587298112, 0, 0, -691455888, 0, 0, -12154536, 0, 0, 297558528, 0, 0, -1463228464, 0, 0, 6416120832, 0, 0, -29441088, 0, 0, 278170112, 0, 0, -863946640, 0, 0, 1719488208, 0, 0, 1537225916, 0, 0, -680165376, 0, 0, -1339581216, 0, 0, 997535808, 0, 0, -2969793352, 0, 0, -854899200, 0, 0, 250195536, 0, 0, -115276800, 0, 0, -1590665984, 0, 0, 2230272, 0, 0, -9041173056, 0, 0, -1011884352, 0, 0, -1392435870, 0, 0, 399478784, 0, 0, 2188219640, 0, 0, -632562432, 0, 0, 2114747008, 0, 0, -27136000, 0, 0, -346774608, 0, 0, -1020094464, 0, 0, 1871569476, 0, 0, 1238130688, 0, 0, 2038409072, 0, 0, 2910226176, 0, 0, 1981560092, 0, 0, 124944384], "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, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "18.7.b.a", "char_is_minimal": false, "conrey_index": 53, "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, -4, 0, 4], [0, 0, 0, 0], [32, 0, -32, 0], [0, 123, 0, 0], [0, 0, 0, 0], [0, 0, 484, 0], [0, 0, 0, 128], [0, 0, 0, 0], [-984, 0, 0, 0], [0, -948, 0, 948], [0, 0, 0, 0], [-3368, 0, 3368, 0], [0, -1936, 0, 0], [0, 0, 0, 0], [0, 0, -1024, 0], [0, 0, 0, -9], [0, 0, 0, 0], [5744, 0, 0, 0], [0, 3936, 0, -3936], [0, 0, 0, 0], [7584, 0, -7584, 0], [0, -2388, 0, 0], [0, 0, 0, 0], [0, 0, 14633, 0], [0, 0, 0, -13472], [0, 0, 0, 0], [15488, 0, 0, 0], [0, -20757, 0, 20757], [0, 0, 0, 0], [39796, 0, -39796, 0], [0, 4096, 0, 0], [0, 0, 0, 0], [0, 0, 72, 0], [0, 0, 0, 59532], [0, 0, 0, 0], [52526, 0, 0, 0], [0, -22976, 0, 22976], [0, 0, 0, 0], [-31488, 0, 31488, 0], [0, -26193, 0, 0], [0, 0, 0, 0], [0, 0, -3800, 0], [0, 0, 0, 30336], [0, 0, 0, 0], [19104, 0, 0, 0], [0, -54300, 0, 54300], [0, 0, 0, 0], [-116607, 0, 116607, 0], [0, -58532, 0, 0], [0, 0, 0, 0], [0, 0, 107776, 0], [0, 0, 0, -168813], [0, 0, 0, 0], [-233208, 0, 0, 0], [0, -61952, 0, 61952], [0, 0, 0, 0], [166056, 0, -166056, 0], [0, -176664, 0, 0], [0, 0, 0, 0], [0, 0, -13250, 0], [0, 0, 0, 159184], [0, 0, 0, 0], [-32768, 0, 0, 0], [0, -414264, 0, 414264], [0, 0, 0, 0], [-168968, 0, 168968, 0], [0, -288, 0, 0], [0, 0, 0, 0], [0, 0, -476256, 0], [0, 0, 0, 375804], [0, 0, 0, 0], [236144, 0, 0, 0], [0, -210104, 0, 210104], [0, 0, 0, 0], [183808, 0, -183808, 0], [0, -458832, 0, 0], [0, 0, 0, 0], [0, 0, 35116, 0], [0, 0, 0, -125952], [0, 0, 0, 0], [209544, 0, 0, 0], [0, 7764, 0, -7764], [0, 0, 0, 0], [2214, 0, -2214, 0], [0, 15200, 0, 0], [0, 0, 0, 0], [0, 0, -242688, 0], [0, 0, 0, 91449], [0, 0, 0, 0], [-1630112, 0, 0, 0], [0, -76416, 0, 76416], [0, 0, 0, 0], [434400, 0, -434400, 0], [0, 706512, 0, 0], [0, 0, 0, 0], [0, 0, 321424, 0], [0, 0, 0, -466428], [0, 0, 0, 0], [468256, 0, 0, 0]]}