# Stored data for newform 80.11.p.b, downloaded from the LMFDB on 21 July 2026.
{"Nk2": 9680, "analytic_conductor": 50.82858021389793, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 16, "char_orbit_label": "p", "char_order": 4, "char_parity": -1, "char_values": [80, 4, [31, 21, 17], [4, 4, 1]], "cm_discs": [], "conrey_index": 17, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [66978, -366, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504630604070992, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 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": false, "label": "80.11.p.b", "level": 80, "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], "level_radical": 10, "minimal_twist": "10.11.c.a", "nf_label": "2.0.4.1", "prim_orbit_index": 3, "qexp_display": "q+(-183 i+183)q^{3}+(-2500 i-1875)q^{5}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "10.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "80.11.p", "trace_display": [0, 366, -3750, 16814], "trace_hash": 1818098693758906612, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.270", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "107.433", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.247", "prec": 17}, "traces": [0, 2, 0, 366, 0, -3750, 0, 16814, 0, 0, 0, 346796, 0, -465246, 0, -1601250, 0, 3760066, 0, 0, 0, 6153924, 0, 10456526, 0, -5468750, 0, 18709920, 0, 0, 0, 20131996, 0, 63463668, 0, 10508750, 0, 112775826, 0, 0, 0, -306007196, 0, -118744914, 0, -39645000, 0, -344678706, 0, 0, 0, 1376184156, 0, 392771234, 0, -650242500, 0, 403170960, 0, 0, 0, 1812371604, 0, 133318206, 0, 2035451250, 0, 1924147934, 0, 0, 0, 6241755196, 0, -1272678526, 0, 2430468750, 0, 2915513972, 0, 0, 0, 7784229762, 0, 10367644206, 0, 2350041250, 0, -9073447440, 0, 0, 0, -7822646244, 0, 3684155268, 0, 5507800000, 0, -1280722494, 0, 0, 0, 4048687604, 0, 3005049166, 0, -11538607500, 0, -2836232386, 0, 0, 0, 41275952316, 0, -35902179646, 0, -45747301250, 0, 3688935534, 0, 0, 0, 8258883606, 0, -55999316868, 0, 57128906250, 0, -26124212146, 0, 0, 0, 104044381196, 0, -18521629840, 0, 11693700000, 0, -32762905374, 0, 0, 0, -126152406396, 0, -80672725908, 0, -123954200000, 0, -51649902066, 0, 0, 0, -227736812804, 0, 29813563314, 0, -37747492500, 0, 20885561586, 0, 0, 0, 175816028164, 0, -95661099154, 0, -277653547500, 0, 23656260334, 0, 0, 0, 17468538480, 0, -232754732126, 0, -203607031250, 0, -254029224720, 0, 0, 0, 266000650804, 0, 331664003532, 0, 70484891250, 0, 651987924268, 0, 0, 0, -262087612004, 0, 425584976514, 0, 425700090000, 0, 158049242706, 0, 0, 0, 704238143844, 0, 416833183760, 0, 573763492500, 0, -82909794654, 0, 0, 0, -275989278004, 0, 1142241200868, 0, 519508998750, 0, 169249690372, 0, 0, 0, -1749355666236, 0, 252107384526, 0, 148668750000, 0, -230536414946, 0, 0, 0, 1067078113752, 0, -199589619006, 0, -215424191250, 0, 720286770240, 0, 0, 0, -1628541219196, 0, 319711980366, 0, -705599755000, 0, -512496383760, 0, 0, 0, -906342026004, 0, 1813140695348, 0, -2580345292500, 0, 2671577745986, 0, 0, 0, -393133140720, 0, 1824130351246, 0, -1718374148750, 0, 2844326280480, 0, 0, 0, -1438889914404, 0, -1431544262652, 0, -948270312500, 0, -1725152979054, 0, 0, 0, -1578599999196, 0, 1320490269806, 0, 251981850000, 0, -2572602496772, 0, 0, 0, -468744432804, 0, 358472794914, 0, -3470344600000, 0, 3244262708160, 0, 0, 0, -1996576983996, 0, 740909831532, 0, -3398196757500, 0, 2203106746014, 0, 0, 0, -10622769817604, 0, -1680156760446, 0, -583267151250, 0, -2332695565134, 0, 0, 0, -1038061053276, 0, -4141938302960, 0, -3089524218750, 0, -2273943169680, 0, 0, 0, 9640844145196, 0, 894199524354, 0, 1202592458750, 0, -7370995549374, 0, 0, 0, 3490847842408, 0, 7122329692800, 0, -9567721290000, 0, 10768996895294, 0, 0, 0, -8704715440320, 0, 10985474770434, 0, -11703290992500, 0, 11569580199492, 0, 0, 0, 9835263648402, 0, 1511375699898, 0, 5567968551250, 0, -3507197681266, 0, 0, 0, 6604055528476, 0, 8514344779874, 0, 6522949218750, 0, 11533839146640, 0, 0, 0, -9561461645436, 0, 13876636653006, 0, 1822196232500, 0, 941528423106, 0, 0, 0, 39317227890716, 0, 19040121758868, 0, 9839983200000, 0, -15892552748494, 0, 0, 0, 17621445713604, 0, -4683165305508, 0, -14595430803750, 0, 19555102676748, 0, 0, 0, -11991223366884, 0, 11670074820880, 0, -45358443401250, 0, 9570518671920, 0, 0, 0, -9370006856396, 0, -2732957459874, 0, -45532049218750, 0, 15236608074828, 0, 0, 0, -47825288484004, 0, -1483645350206, 0, -5670904650000, 0, 11518490780560, 0, 0, 0, -2237880182958, 0, 47781852837486, 0, 38856916400000, 0, 1578787189200, 0, 0, 0, -53061035772008, 0, -41675836743132, 0, 14667461707500, 0, 13770413245986, 0, 0, 0, -34407700181996, 0, 934383695246, 0, -16118179297500, 0, -32553610472866, 0, 0, 0, 7644115540476, 0, -20590130597772, 0, -20654250000000, 0, -3114283114386, 0, 0, 0, -52468501943196, 0, 32174333154012, 0, -800451558750, 0, -7832332905426, 0, 0, 0, 3338909524396, 0, 93215194595440, 0, -6874363710000, 0, 52474435932772, 0, 0, 0, 8658191282244, 0, -47100244298034, 0, -7591289257500, 0, 10845155202306, 0, 0, 0, -21398816736164, 0, -20610099475200, 0, -13147090101250, 0, -59766598262988, 0, 0, 0, -125465257890396, 0, -2979024166674, 0, -16827135937500, 0, 37848816835868, 0, 0, 0, -11006544933360, 0, 71184311955108, 0, -1772645241250, 0, 66249999809040, 0, 0, 0, -179423024404396, 0, 48678119097132, 0, -31064797400000, 0, -67990957863906, 0, 0, 0, 54617195420800, 0, -33089895504960, 0, -77392410592500, 0, 19038290057586, 0, 0, 0, 238627580282088, 0, -72730295262354, 0, 157072035951250, 0, 65442019609134, 0, 0, 0, -4384018842004, 0, -47962032996732, 0, 69437867968750, 0, -59515718696254, 0, 0, 0, 174321569679684, 0, 68105746433132, 0, 2305584708750, 0, -92066508634626, 0, 0, 0, 57846022830396, 0, -12354274645886, 0, 158054374310000, 0, -165672568432800, 0, 0, 0, 249500714829604, 0, 15256568968686, 0, -15485406761250, 0, 186836756588814, 0, 0, 0, 160360389251676, 0, 28560346310754, 0, 244997011297500, 0, -8354806533534, 0, 0, 0, 195640764937920, 0, -130668038469920, 0, -160827636718750, 0, 69909038122080, 0, 0, 0, -160711144441604, 0, -50506037874732, 0, -16327632591250, 0, 65655492722946, 0, 0, 0, 188695424209604, 0, -39784923765714, 0, 108651596310000, 0, -119457742618706, 0, 0, 0, 61945386676152, 0, -197414496423966, 0, -195083214742500, 0, 10091068032654, 0, 0, 0, -306274927184396, 0, -320132086921188, 0, 81032130550000, 0, -259226063021840, 0, 0, 0, 314261611390392, 0, -175071942222526, 0, -226565437500000, 0, 3189048622546, 0, 0, 0, -84376327870236, 0, 113159149055406, 0, -20476815858750, 0, -120459397483440, 0, 0, 0, -9971153735604, 0, 23117110283988, 0, 130744790600000, 0, -575303626717468, 0, 0, 0, -360606515257196, 0, -124229338888560, 0, 236535761992500, 0, 34037316686828, 0, 0, 0, 31208490717120, 0, 105255369802948, 0, 352943175847500, 0, 14479779078720, 0, 0, 0, 50526896677124, 0, -298023043112868, 0, 464828250000000, 0, -430627933878546, 0, 0, 0, -446488713804324, 0, -557573233965406, 0, -32281188791250, 0, 333643403459732, 0, 0, 0, -187573676456160, 0, -318094419353714, 0, 21568131000000, 0, -82205050909374, 0, 0, 0, 280015739163996, 0, -165860590758732, 0, 427006524007500, 0, 141576179991186, 0, 0, 0, -569905598186396, 0, 104464700696720, 0, -130434339498750, 0, 322912788754320, 0, 0, 0, 977797455030876, 0, 280063433234274, 0, -55048426562500, 0, 347006931120612, 0, 0, 0, 1082307867476008, 0, 463834633132800, 0, 13053475991250, 0, -599776253056226, 0, 0, 0, -603659248567844, 0, -421599319637292, 0, -359385679110000, 0, -428866012252494, 0, 0, 0, 123238596054240, 0, -220679911051348, 0, -329655052807500, 0, 381912427709040, 0, 0, 0, -851777455736404, 0, -263316854335932, 0, 418517308798750, 0, -130804647465840, 0, 0, 0, 947888173724404, 0, 786756177294926, 0, 421438420312500, 0, 465643346373054, 0, 0, 0, -631405990333764, 0, 530620329676766, 0, 14785162708750, 0, 188334017300160, 0, 0, 0, -387757029210798, 0, -288883799852868, 0, 148157857955000, 0, 69432434475642, 0, 0, 0, 1179243356740476, 0, 851835053521634, 0, -32753509650000, 0, -716993052408414, 0, 0, 0, -941572513818552, 0, -297026294131954, 0, 1018301953051250, 0, 1849417859792814, 0, 0, 0, -895202129701764, 0, -10154848654926, 0, 660901855468750, 0, -77121721963854, 0, 0, 0, -822527935459196, 0, 1268231121841006, 0, -158768265450000, 0, -1430481490545426, 0, 0, 0, 1349769872271276, 0, 379684275381360, 0, 905054642200000, 0, 890268811857468, 0, 0, 0, 1476845762741444, 0, -365373588071268, 0, -498751220257500, 0, -925485647803586, 0, 0, 0, 482623071490396, 0, 1797728770031988, 0, -1451030015452500, 0, 874701112714772, 0, 0, 0, 806337069041124, 0, -1451975818959108, 0, -1365644767968750, 0, -23827034837214, 0, 0, 0, 310904186447120, 0, -1943966876621532, 0, 407492452667500, 0, -468430113554974, 0, 0, 0, -76105136095596, 0, -1599886100580548, 0, 786471487200000, 0, -25313341175906, 0, 0, 0, -853766576839044, 0, -1547087136570366, 0, 491414272507500, 0, -1573317639201120, 0, 0, 0, -1436607942489594, 0, -22488486588594, 0, -1861934272248750, 0, 1115807155937134, 0, 0, 0, -202174826750804, 0, -439668581829680, 0, -1596375337500000, 0, -1426732612211454, 0, 0, 0, -98525111433840, 0, 1029461205771406, 0, 98780776691250, 0, -1060563280571172, 0, 0, 0, -2267125027189604, 0, 1764274478570868, 0, -2263286454000000, 0, 1311369129394706, 0, 0, 0], "weight": 11, "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, 0], [183, -183], [0, 0], [-1875, -2500], [0, 0], [8407, 8407], [0, 0], [0, -7929], [0, 0], [173398, 0], [0, 0], [-232623, 232623], [0, 0], [-800625, -114375], [0, 0], [1880033, 1880033], [0, 0], [0, 1101560], [0, 0], [3076962, 0], [0, 0], [5228263, -5228263], [0, 0], [-2734375, 9375000], [0, 0], [9354960, 9354960], [0, 0], [0, -24790840], [0, 0], [10065998, 0], [0, 0], [31731834, -31731834], [0, 0], [5254375, -36780625], [0, 0], [56387913, 56387913], [0, 0], [0, 85140018], [0, 0], [-153003598, 0], [0, 0], [-59372457, 59372457], [0, 0], [-19822500, 14866875], [0, 0], [-172339353, -172339353], [0, 0], [0, -141119951], [0, 0], [688092078, 0], [0, 0], [196385617, -196385617], [0, 0], [-325121250, -433495000], [0, 0], [201585480, 201585480], [0, 0], [0, -694068920], [0, 0], [906185802, 0], [0, 0], [66659103, -66659103], [0, 0], [1017725625, 145389375], [0, 0], [962073967, 962073967], [0, 0], [0, -1913544258], [0, 0], [3120877598, 0], [0, 0], [-636339263, 636339263], [0, 0], [1215234375, 2216015625], [0, 0], [1457756986, 1457756986], [0, 0], [0, 1967996640], [0, 0], [3892114881, 0], [0, 0], [5183822103, -5183822103], [0, 0], [1175020625, -8225144375], [0, 0], [-4536723720, -4536723720], [0, 0], [0, 7771383280], [0, 0], [-3911323122, 0], [0, 0], [1842077634, -1842077634], [0, 0], [2753900000, -2065425000], [0, 0], [-640361247, -640361247], [0, 0], [0, -1374872742], [0, 0]]}