# Stored data for newform 680.2.cg.b, downloaded from the LMFDB on 17 September 2025. {"Nk2": 2720, "analytic_conductor": 5.429827337447066, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 85, "char_degree": 8, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 59, "char_orbit_label": "cg", "char_order": 16, "char_parity": 1, "char_values": [680, 16, [511, 341, 137, 241], [16, 16, 4, 15]], "cm_discs": [], "conrey_index": 57, "dim": 112, "has_non_self_twist": 1, "hecke_cutters": [[3, [592973922304, -618963843153920, 160480313305202688, 4162037303650287616, 49338572478793908224, 349744358212446978048, 1810145231153859919872, 7602530667251792478208, 27273084092151813120000, 83875933692917971845120, 222380637238280023228416, 511816772235359394357248, 1009017621550892223489024, 1527441036305315256123392, 1036750073978585443012096, -2652653801618086754455040, -12017279917467608028458944, -26349484100727694802119168, -34499474670400377884039424, -14064659118476127972529664, 65764982082393345525874944, 240767881410987145971114240, 526131737405854650247021824, 922307859236748065906999808, 1403744830976932329677072896, 1884144327525492803218872832, 2289814192601321154886264704, 2544169804751055257310185984, 2586755373456005389476166144, 2415093044111997259158466432, 2223547406743480677430392064, 1865624650915189551517059072, 1685555440674276978335570208, 1352405207860182033739174784, 1097347246163688264680095168, 792205818047813274741123840, 681836145350188755253006400, 445192313164987369139226176, 249602130262017443726290368, 124028706819309948682593152, 106164293186891028450709760, 28634429052442651820382336, -6367077047763640442262176, 72441826731714839880358144, 38770285286183192033638944, -31019410423401664002572960, -28531119589204776811679392, -1114960534083362733345888, 15672033569001681215764420, -3642999563861270247410560, 2358851338165592961270272, 876819149769774169253856, -1484824841798908037293248, -1224506409101530847675840, 705102964901057599457824, 663833700831936282199680, 61447936388364515433344, -106599784061556324399616, -20865669778226578866784, 15613046229634953586784, -2803095189743783583144, -4018764134013563270752, -2466331338098931315360, -47690708359387566480, 1121592788857692035776, 19839037550599485600, -4803203171019003296, -4273004831642363760, -858845127708143792, -104321348947397712, -1150897785585419024, 641481022417350832, -29302653505849976, -158599507518606832, 27965170808741712, 26188311035282624, 2825281573660128, -5462717000260032, -4233555437688368, -106636455459120, 1555625257303764, 2830970133328, -74898885248704, -15014396466704, 4656420240332, 2767895439664, -690801147232, -500141381240, -13591000960, 55282720512, 14527267608, -2102794296, -1687387452, -399878048, 2269552, -45895176, 133526009, -5823256, -149576, -1376472, -95056, 94232, -11240, 224, -768, 184, 216, -96, 0, 8, 0, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4507585390576296, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 85, 15, 1, 16, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "680.2.cg.b", "level": 680, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 5, 17], "level_radical": 170, "minimal_twist": "680.2.cg.b", "prim_orbit_index": 15, "related_objects": [], "relative_dim": 14, "rm_discs": [], "sato_tate_group": "1.2.3.c16", "self_twist_discs": [], "self_twist_type": 0, "space_label": "680.2.cg", "trace_display": [0, 0, 0, 0], "traces": [112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -8, 0, 16, 0, -48, 0, -32, 0, -16, 0, 0, 0, -16, 0, 48, 0, -24, 0, -16, 0, -80, 0, 32, 0, -8, 0, 24, 0, 0, 0, -80, 0, -24, 0, -72, 0, 16, 0, -48, 0, 0, 0, -40, 0, -16, 0, 16, 0, 24, 0, 40, 0, 0, 0, -24, 0, 16, 0, 16, 0, -16, 0, 0, 0, 16, 0, -8, 0, 64, 0, 48, 0, 0, 0, -32, 0, 280, 0, 24, 0, 32, 0, -24, 0, 88, 0, 16, 0, 16, 0, 16, 0, 64, 0, 0, 0, -48, 0, 32, 0, 112, 0, -32, 0, 32, 0, 120, 0, -48, 0, -48, 0, 112, 0, 32, 0, -80, 0, 56, 0, 128, 0, 8, 0, -232, 0, 24, 0, 0, 0, 200, 0, -144, 0, 0, 0, -88, 0, -144, 0, -160, 0, 256, 0, -32, 0, -296, 0, -48, 0, 64, 0, -152, 0, 0, 0, 88, 0, -120, 0, -240, 0, -112, 0, 32, 0, -56, 0, -120, 0, -32, 0, -64, 0, -80, 0, -56, 0, 0, 0, 80, 0, -288, 0, 160, 0, 40, 0, -192, 0, -160, 0, 96, 0, -128, 0, -56, 0, -32, 0, -8, 0, -136, 0, -8, 0, -16, 0, 128, 0, 0, 0, -144, 0, 192, 0, 32, 0, -144, 0, -16, 0, 80, 0, 32, 0, 0, 0, 32, 0, -96, 0, -64, 0, 320, 0, 32, 0, 160, 0, -32, 0, 0, 0, -208, 0, 128, 0, -40, 0, 40, 0, -16, 0, 0, 0, -184, 0, 352, 0, 96, 0, 64, 0, 0, 0, -72, 0, 152, 0, 192, 0, -88, 0, -16, 0, 176, 0, 48, 0, -136, 0, 184, 0, 184, 0, 40, 0, 224, 0, 80, 0, 48, 0, -112, 0, 168, 0, 0, 0, 80, 0, -32, 0, 432, 0, 24, 0, 40, 0, -192, 0, 416, 0, 96, 0, -112, 0, 120, 0, 56, 0, -40, 0, 0, 0, 216, 0, 0, 0, -8, 0, 96, 0, 72, 0, 48, 0, 120, 0, 144, 0, 240, 0, -64, 0, -96, 0, 64, 0, -16, 0, -312, 0, 40, 0, -32, 0, -80, 0, -200, 0, 288, 0, -176, 0, 32, 0, -208, 0, -80, 0, 16, 0, 176, 0, -104, 0, 64, 0, 0, 0, -32, 0, -224, 0, 104, 0, 40, 0, 32, 0, 64, 0, -240, 0, 112, 0, 48, 0, 16, 0, -48, 0, -56, 0, -376, 0, 40, 0, 16, 0, 0, 0, -176, 0, 488, 0, -248, 0, -64, 0, -64, 0, 128, 0, -32, 0, -120, 0, -80, 0, 72, 0, -16, 0, -128, 0, -104, 0, 216, 0, -200, 0, -40, 0, 512, 0, -144, 0, -264, 0, 128, 0, -72, 0, -536, 0, -224, 0, 240, 0, -112, 0, -496, 0, 144, 0, 0, 0, 320, 0, -440, 0, 200, 0, 16, 0, -664, 0, -272, 0, 304, 0, -336, 0, -416, 0, 40, 0, 408, 0, -448, 0, 0, 0, 432, 0, -56, 0, -304, 0, 0, 0, 104, 0, -184, 0, -456, 0, -240, 0, 272, 0, -320, 0, -160, 0, 272, 0, 296, 0, -504, 0, 312, 0, 88, 0, -64, 0, -272, 0, 320, 0, -144, 0, 32, 0, 96, 0, 48, 0, -144, 0, 176, 0, -184, 0, 208, 0, 0, 0, -88, 0, 160, 0, 72, 0, -208, 0, 8, 0, 240, 0, -200, 0, -288, 0, 152, 0, 48, 0, -16, 0, 672, 0, -368, 0, 208, 0, -16, 0, 0, 0, -160, 0, 112, 0, -368, 0, 160, 0, -32, 0, 152, 0, -144, 0, 416, 0, 24, 0, 216, 0, -48, 0, -288, 0, 144, 0, 160, 0, -240, 0, -320, 0, 264, 0, -16, 0, -160, 0, 192, 0, 432, 0, -376, 0, 704, 0, 48, 0, 136, 0, 40, 0, 280, 0, 0, 0, -136, 0, -296, 0, 256, 0, 240, 0, 224, 0, -96, 0, 1200, 0, -16, 0, -264, 0, 304, 0, 320, 0, -368, 0, 0, 0, -80, 0, 96, 0, -80, 0, 256, 0, -96, 0, 160, 0, 176, 0, -264, 0, 560, 0, -176, 0, 96, 0, 248, 0, 272, 0, -400, 0, 224, 0, 120, 0, -272, 0, -144, 0, 608, 0, -264, 0, 440, 0, 112, 0, 304, 0, -24, 0, -152, 0, -352, 0, -32, 0, 0, 0, -96, 0, -208, 0, 200, 0, 176, 0, 40, 0, 288, 0, -312, 0, 448, 0, -176, 0, -128, 0, -112, 0, 160, 0, -296, 0, -40, 0, 224, 0, 0, 0, -448, 0, 648, 0, -32, 0, 24, 0, 40, 0, 128, 0, -360, 0, -320, 0, -320, 0, 64, 0, -208, 0, -120, 0, 208, 0, 304, 0, -512, 0, -144, 0, 464, 0, -384, 0, -736, 0, 24, 0, 192, 0, -1104, 0, 32, 0, 160, 0, -152, 0, -376, 0, 184, 0, 0, 0, 64, 0, -656, 0, 176, 0, 144, 0, -488, 0, -688, 0, 416, 0, -360, 0, -824, 0, 56, 0, 304, 0, -1080, 0, 0, 0, 424, 0, -96, 0, -296, 0, -288, 0, 528, 0, -144, 0, -432, 0, 160, 0, 224, 0, -560, 0, -312, 0, 352, 0, 528, 0, -1536, 0, 560, 0, 216, 0, -96, 0, -144, 0, 280, 0, -704, 0, -352, 0, -120, 0, 480, 0, -200, 0, 472, 0, -160, 0, 352, 0, 0, 0, -112, 0, 280, 0, -56, 0, -392, 0, -336, 0, 112, 0, -304, 0, 40, 0, 136, 0, 64, 0, -160, 0, 400, 0, -656, 0, 0, 0, 112, 0, 0, 0, -272, 0, 80, 0, -384, 0, -224, 0, -32, 0, 416, 0, -344, 0, 512, 0, -64, 0, 400, 0, 256, 0, -32, 0, 64, 0, 176, 0, -480, 0, 136, 0, 336, 0, 48, 0, -216, 0, 560, 0, 472, 0, -56, 0, 368, 0, -176, 0], "weight": 2, "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}