{"label":"107.4.a","level":107,"weight":4,"dims":{"new":26,"cusp":26,"eisenstein":2,"modsym":54},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 107]: [1, 28] (certified at ell = 2147482621)","T = [(2, 1), (3, 1)]; h of degree 26 = 1 x 26 (phi(ord eps) x dim S_k^new); 4 primes, 0 rejected"],"newforms":[{"label":"107.4.a.a","letter":"a","dim":10,"charpoly":["44752","5184","-90676","-22536","40797","13327","-2819","-1030","21","19","1"],"traces":["10","-2","-17","20","-31","-39","-44","-21","27","-138","-59","-228","-259","-125","-46","-44","-162","30","-79","-323","-172","-363","-236","-373","-105","36","-437","-233","192","1120","-248","650","157","148","434","1741","-1043","1366","843","-44","-20","1631","-867","1007","-649","1004","503","487","-386","2319","1072","-738","-1075","77","28","894","-1253","783","901","2955","-1247","-417","-540","-1129","332","2091","-451","-343","-1397","241","-14","2568","-2450","265","-833","-106","-1724","2674","-1132","-1016","-446","-2115","34","1388","-3004","-352","-2390","-4304","-790","-4387","-2240","1066","-1072","737","-628","-1370","-1442","-741","146","-1226","-3723","-783","-4408","-1442","-1958","-1281","1070","-7709","-3612","2879","5869","-3203","2362","-3878","-2071","2325","-3568","-2820","5382","8021","-1627","1807","5845","-403","981","-2395","2336","-486","7746","3992","5493","4646","-4484","5609","10800","-277","1061","-1439","3470","7002","-580","-545","7039","5884","-2822","-5583","7271","-9938","2811","-9038","2522","7084","-2088","6133","9186","6250","-10426","-3474","9443","-909","3434","12601","-3209","-1885","-2902","1243","3388","1071","3313","-27","9208","-11345","-3475","857","542","-3847","-2088","-2434","11474","-15130","-6743","2478","6811","5301","4250","2497","-5590","-619","6924","-11684","4354","-545","-7180","6689","2286","-11369","105","-23805","5046","3687","-378","-6659","-518","11771","-4119","2564","13687","-11106","-4585","-10510","3997","-9585","-13546","-214","5955","-12644","-5616","-5459","16946","3836","-4166","7794","-3153","245","792","-20975","-549","-23856","-9247","-5220","3254","-2664","-10952","-17976","-1353","-5275","-8949","-2870","2601","5854","-13557","-6569","-3746","10112","-2679","-182","-3805","-8004","8314","2560","1900","-9146","-14535","-6197","-2296","-7012","-8478","9600","8242","22610","5788","1264","-6877","19771","4636","-16404","8151","3577","7778","23231","-135","-7286","884","30842","-4411","-37588","-13123","2738","11336","11317","13034","-16698","-2686","19972","20938","20954","5022","11075","9124","-17181","-11806","1537","523","13006","19533","-14247","1793","20183","5791","-13387","-5160","5423","8501","24304","-2048","2633","5338","-7061","9028","24779","-4694","44614","-8771","19501","16584","25979","-2775","6549","21144","8276","-1819","5775","-4186","19715","-23951","-22513","17928","1723","10470","-16190","-4532","-11442","-35568","21063","-813","7207","9522","14774","-3084","26407","-7896","39696","15458","-15134","26382","-11333","7165","-31470","-20172","-7251","19281","6787","-19960","13128","-5216","18158","-23284","8231","3560","-53850","-10479","-26094","-15110","27882","3772","-59766","-12402","13638","-20071","38678","-20422","12738","-35208","28382","26530","16179","-16078","-12283","11433","-38740","-49212","42338","-35819","16883","4250","13483","-54987","19201","-2625","-57456","-6438","9225","-8662","4693","-7787","-15644","-34544","-46152","4024","38501","-8974","-47850","-1308","-17573","-27103","1845","-4677","-31602","12466","12779","-16664","-2793","-24976","37060","-19186","-38076","-6054","6692","16075","-29973","-16627","13025","-4809","16732","-4458","13576","-27226","2140","-50045","34743","-3815","-48479","-21064","12409","14268","-7995","-8857","-491","-1841","27211","-7171","46328","-10545","66779","-6347","-34864","-23227","41362","15034","58290","-6955","28040","-5623","63536","18224","-48820","-15800","-40575","14394","14059","17447","-23347","10978","25809","-17742","22471","-35235","-90738","-14378","-16381","-8996","21262","31098","46652","48733","-21267","-18514","-57626","11174","-21431","51963","42360","44878","35509","-32380","-66813","22854","-3465","54387","10375","2093","56968","-56924","-47908","50612","10125","29074","-35962","26144","-9262","29408","-7284","40367","-32083","73050","-71807","-22320","3731","26748","-10211","9166","-509","-15863","-614","8418","94383","-19356","48031","-1520","34860","14662","-3393","12191","32888","65148","77761","-2466","10757","35872","34019","29551","30238","13223","-76697","-3317","-16597","15132","14345","-30829","58336","16251","-47307","51136","-18433","64788","-90794","21286","3347","6858","9933","20222","2435","-8682","-20948","-34588","-7135","46648","-27397","79524","-24427","65466","-6633","-8879","-25910","-2040","-10350","-4442","24557","24126","83478","27835","5288","-15064","2206","-17893","-79752","-43842","-84559","-40737","-42424","53408","24117","-10823","-94694","77150","-8722","-16449","23546","10804","8405","-4343","-22097","12522","122909","22382","-53790","-72623","-123312","17730","-71229","7246","36457","-37913","9148","-7345","30123","-48468","-20052","93948","35708","-75294","-87893","-39349","-44096","-29414","22238","46504","-75089","-12016","-5512","-66433","11264","7336","31032","-3988","-81841","27247","-83858","-5558","45112","1666","-48628","31948","7756","38062","11976","337","-44487","-1886","-3008","51470","-4173","-22411","-7533","-43344","-59034","-61254","75423","-21384","-88950","-51020","-20137","14264","-98379","5629","-42003","-16414","25922","49507","-137113","-19420","61299","-36106","83495","45708","-55866","-22766","-121151","39237","-14745","16865","-4372","-5710","-59440","-22409","-18062","-14264","77900","-65274","79274","23709","-74519","-65212","100492","-108499","18435","-47072","-34642","136167","41652","-105525","-59588","46320","-61891","-35630","-14009","101270","21143","-29673","-41334","38521","125362","-93237","-73762","16168","48137","-8222","-42291","-48921","-66938","67887","52325","72062","55293","-55526","68726","96617","-49216","-25220","-112727","53918","35958","85272","-84552","122172","65754","-56470","-180","50208","144071","-64826","93471","-115739","90099","-53406","7040","51634","-14577","2921","140145","129931","34981","-43107","51675","120","41449","37792","-31639","-4708","-61173","1228","76935","53960","-90382","52523","89791","-42131","-111515","-22891","-124954","118122","195207","4446","63981","83110","-616","-52102","69176","61292","13653","83824","33603","47633","-91621","-83398","71718","59060","167256","-46369","-200586","39434","101748","-72412","29871","137964","-153103","-34869","39323","-60861","3705","72180","-114357","-6899","-75394","5030","127772","-49759","25046","-106032","2996","-17033","118809","100982","142586","-67220","26670","-119610","-45268","79520","-152169","-112715","-70263","105928","56023","-64212","82927","-57176","66916","66928","74385","-21121","-37712","-57380","185169","55031","-38773","-92093","144995","-111322","-32284","45374","89604","152530","40617","-5618","-133060","85576","-58192","-5172","-96657","-6066","58312","-96994","81097","-11459","139319","28466","-7705","-12724","-73447","125061","-11193","-15079","84103","-155482","-2247","-130925","-22646","-128745","101456","-119204","50067","-15512","-73977","-6737","30099","-105129","85757","139739","81484","-50112","72334","196498","-40822","-124196","220196","-59487","14490","-42741","125147","59519","-17005","12577","-36706","-52600","-70474","-68692","205265","72452","6224","-7073","10065","-18798","60620","-130630","-112489","21149","-52359","-159150","132571","-79542","119004","50994","-78525","14369","-109161","-61090","-105015","-129276","63314","-31320","-93824","-204558","-21375","64396","-25945","-95090","-77818","-106088","-138046","23390","-21340","126042","-121246","-42985","-97799","-10230","67127","-124846","-54024","91289","-15764","40624","-133805","-21686","-207404","-14173","-37718","-14012","-101639","-35788","20698","-100260","95370","-39322","176031","-95251","-97951","-95708","31226","6696","57449","91580","16511","-142888","-48148","-110472","-4224","-15340","20763","26578","-28198","2889","-239635","-66681","-75337","-80433","-7999","13362","-146649","-67706","-36789","-44070","-142472","73329","80081","141727","127075","-9623","122623","-87658","-44344","102914","-29668","62938","121808","166744","-80066","-100999","196582","53536","17383","90182","-153457","60773","-52855","-183020","267551","109813","-105305"]},{"label":"107.4.a.b","letter":"b","dim":16,"charpoly":["9713514088","472313926916","283431673162","-255574842790","-24358448723","29979347727","332845590","-1577181469","31646572","44012893","-1560379","-673834","30324","5330","-279","-17","1"],"traces":["16","4","13","80","39","9","68","51","189","42","7","132","313","-13","74","484","178","300","187","237","248","253","178","203","945","400","403","5","70","-1788","-140","-178","-341","-292","-298","-1467","913","-2552","-369","-832","-420","-2057","-173","-1729","-103","-1888","105","-637","1564","-1263","-688","1198","-39","-1269","1524","-4494","-1079","-433","1003","-3313","2713","-1425","1076","1739","-208","-4115","1455","-375","985","-733","-318","558","2730","-1043","1765","358","2124","2778","26","-640","2680","3573","1012","1390","2752","-2000","478","1226","914","-2111","1092","4534","5044","3307","1172","1652","7342","609","2660","8714","741","2457","3324","2578","2866","1801","-1712","1631","852","651","183","873","2486","-9116","1435","-2899","1250","4296","-9346","-10879","2343","4375","-7849","-889","3255","269","-6888","-1728","-2650","3488","-3253","-6958","10368","-12639","-9928","4459","-341","-4663","2022","210","-5472","5755","-10871","-11084","-5606","-479","-10227","5658","-9897","-4578","48","-16652","3320","2745","-21002","2786","13574","1662","-26045","3723","-3318","4457","-751","1459","-9114","8173","-540","-6525","-665","-1715","-11908","3531","5891","3145","-7358","-13087","-1708","18300","-2686","-13928","14919","1958","1987","-4855","2346","19453","-10414","-2155","-11220","1136","562","10743","2636","3133","-17818","20331","-4627","7895","1168","7791","2922","11647","-9918","329","11823","17980","-6893","18522","-467","4608","2559","10175","18650","-428","-28789","20778","6992","16437","-16346","38682","4138","12374","10973","-19539","6366","1909","-3111","8640","11619","9252","590","13458","-1560","15030","9977","31325","15097","35520","-16145","8968","10117","10031","-3776","14852","17091","9036","1787","14656","-5574","-10004","-19084","-5716","-2125","-18345","-23576","-16020","-6714","30212","-16374","-2438","22982","-6780","-5095","-37101","2144","-8796","-17265","6119","15174","-11717","-7177","-34156","7100","-58610","-19509","-84","21339","25166","-18472","-63491","16194","-22360","5260","-30374","22990","-16840","-29530","-8349","19062","2423","-8894","5591","9843","-41372","525","3033","843","-32399","-23189","2629","18964","-23515","8595","-25344","-21452","25297","-13674","30073","8576","-61527","13538","8462","29355","-10399","-836","-35621","15379","9885","-38276","9614","-1391","-68961","-11646","-5277","19105","41543","8312","2961","2090","-14582","-11654","6042","41138","-38725","-8965","15209","18858","23142","-13520","-93393","10260","-18530","33694","-33790","44654","36131","7475","20078","-24808","-26219","5597","-19631","14656","-20656","-7104","51338","2012","-33357","-3632","-29446","6147","-27546","5338","-106266","28824","42414","31770","72026","-14589","-104394","3858","43920","6206","14406","15662","2433","17146","16441","-17457","86412","49560","-35582","-12461","-49847","8178","5143","-28553","53479","14717","9652","-8178","5375","27866","-48001","17283","8228","39870","9592","8124","3413","16794","51966","16156","-33281","38303","-1635","24675","112598","10406","46747","38928","-82701","39412","-44658","9350","108268","16554","24642","21621","70031","14517","34965","54957","-65942","56186","25460","-14286","-8560","-22553","2275","-4943","29173","27196","56825","-3476","33415","12435","-6827","-6055","-15997","-26137","-50088","33693","76003","-1473","23286","-7631","-10284","-12126","59698","-11059","2742","11377","-62792","-42936","-27604","-10816","42853","-47190","9275","-14093","-7911","24900","-11479","-64406","-46677","-22929","-22054","-11870","1195","-17648","-5582","-93510","10166","1011","-10131","-55298","-44392","39602","-83507","-13491","33040","23770","-35575","-8712","1525","31470","72263","-90875","-100721","-59861","-8436","58636","-118910","74700","-83151","-22110","-4026","29988","6418","-49700","-8526","-34591","-50575","-80582","35979","43348","-52003","-36652","-62249","6470","13627","-74077","-78826","-18642","54659","91804","-4993","-29152","-5356","-44130","-31517","57189","-22812","-25244","68055","1710","78169","-62686","67531","-41023","75266","56049","10705","-4173","-127177","27392","-45391","-17195","-88626","37241","72403","-29152","-73133","-159372","-15834","-10116","44435","27846","-55841","27642","16023","-73306","-41360","18996","35793","31868","58811","44612","16613","-178906","4439","30179","-37662","45376","40060","234","42345","-49282","177294","13173","-87884","32704","-93418","-11995","8932","14086","18329","14491","-153910","-20144","55741","6061","-35254","-199902","36862","-16787","101414","71716","153877","-16977","6299","-67462","37141","20802","-62754","-52599","23598","24884","90581","-86942","82667","-23483","-67672","21493","89911","47036","-70288","-113408","29476","-33714","157913","-18007","106704","-60358","38690","-26676","109735","56084","-113920","20293","-43640","82840","-41848","-16950","-101105","20443","105840","-20554","157994","32802","197818","60428","-51844","-15306","-356","90277","34325","102990","172980","-145890","-963","49239","47121","-30596","-3326","27882","37465","19244","132478","-28532","52023","-57216","169029","50589","119837","-74930","128394","41469","83007","30030","102547","64586","58775","-43548","197588","57446","154047","11279","-28143","-96571","9968","-41322","91430","45575","-42070","107094","-48524","-73466","-62068","-128297","-84407","28492","-62852","6307","3019","-78192","87314","23497","-68504","1545","-51574","61472","-136755","48242","291679","-27678","-153049","-21705","-90008","5203","33590","-14689","-72542","-174152","41037","-49226","-233815","67557","10688","-54011","70073","-102182","-55879","-42422","80612","126421","-111216","55544","-196675","19350","-52196","95000","-20368","-49122","104106","-9688","-142116","-89052","99929","61858","72343","35287","-137337","54614","-142240","-46182","39089","28763","108197","-113815","108025","-79777","120051","24372","-27887","18694","-112803","-7276","-160529","44400","-182977","-225640","-71630","105073","-187175","94315","-5187","96657","-129854","-146902","-29425","-18538","-45327","151074","92516","-40902","-187036","28140","-137321","30136","8843","149023","-88137","-15534","177010","-150352","-32896","-35917","-252862","66830","-45752","19762","243595","-16804","21913","90729","-213641","-48425","-38235","-19868","-311493","34475","6800","-67054","74884","-39711","-197310","-26164","8738","-136403","-25343","101790","4938","6688","-194450","-13446","229626","-14616","-15369","-47237","-287833","940","-76863","-47992","59239","48208","35600","211852","131075","54381","-121232","78120","42537","-326559","18653","-43567","-103945","62666","73440","143894","59436","-207946","-55383","96162","159876","143236","-174144","88366","-127059","-34154","-250432","-100422","34247","154163","85047","131798","-26741","52308","141613","-47155","68347","130943","-42065","-97266","-5457","-118981","-147228","100029","-378376","-67408","7529","36908","178657","-67249","127675","-37959","-24575","8839","75844","38036","156982","-2898","13942","141856","53902","72535","-36328","-48421","217593","-73729","-195581","106567","143002","198244","73846","-117400","88555","88220","-134756","235243","164549","-20990","83122","54834","-251633","-162321","148349","18454","130331","48418","23812","179898","19095","-147999","-200671","92958","-201507","-21802","196366","126684","-156028","34114","-86691","180688","124225","-67046","-387122","34628","301402","-226586","-121454","7174","30244","237719","241863","269898","21277","17582","176522","202075","-394712","81600","-87523","148026","-74004","150403","72250","202148","314571","-454","-194558","72168","345546","-299730","79899","105047","-144775","115056","-341176","75768","331523","6932","338111","136728","110756","-21954","103308","211416","160249","83624","49518","-20223","-71375","-82267","-12021","-105113","-358593","111306","12713","61546","-387017","169906","-193476","36749","365833","-135105","-86435","52115","531325","-69202","91576","88918","-37356","111102","-190240","214256","-283998","28475","431938","-4816","94499","-101538","-287255","41971","160225","117038","132167","135723","-193617"]}],"seconds":0.104,"computed":"atlas","estimate":{"seconds":0.28,"low":0.171,"high":0.485,"bytes":2008584}}