{"label":"28.4.a","level":28,"weight":4,"dims":{"new":2,"cusp":9,"eisenstein":6,"modsym":24},"old":[[7,1,3],[14,2,2]],"T":[[3,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 7, 14, 28]: [1, 2, 3, 3, 8, 15] (certified at ell = 2147483647)","T = [(3, 1), (5, 1)]; h of degree 2 = 1 x 2 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"28.4.a.a","letter":"a","dim":1,"charpoly":["18","1"],"traces":["1","0","-10","0","-8","0","-7","0","73","0","-40","0","-12","0","80","0","-58","0","26","0","70","0","-64","0","-61","0","-460","0","-62","0","252","0","400","0","56","0","26","0","120","0","6","0","416","0","-584","0","-396","0","49","0","580","0","-450","0","320","0","-260","0","274","0","-576","0","-511","0","96","0","-476","0","640","0","-448","0","-158","0","610","0","280","0","-936","0","2629","0","530","0","464","0","620","0","-390","0","84","0","-2520","0","-208","0","214","0","-2920","0","1432","0","764","0","-560","0","324","0","-1334","0","-260","0","1798","0","512","0","-876","0","406","0","269","0","-60","0","1488","0","-384","0","-4160","0","-1814","0","-182","0","3680","0","1666","0","1126","0","3960","0","480","0","496","0","-490","0","2694","0","-2648","0","-4234","0","-2016","0","-556","0","4500","0","448","0","-328","0","-3200","0","-4268","0","-2053","0","1898","0","-3476","0","427","0","-2740","0","2268","0","-276","0","5760","0","-208","0","2320","0","3220","0","-3000","0","3278","0","-960","0","-2362","0","-1036","0","4760","0","434","0","-48","0","-4672","0","-1040","0","3524","0","4480","0","-3328","0","-1764","0","1580","0","696","0","-1336","0","-4453","0","1290","0","5524","0","-2800","0","6314","0","3168","0","9360","0","-3960","0","-7018","0","-13870","0","-392","0","-312","0","-5300","0","-2394","0","2560","0","-4640","0","-2766","0","-182","0","-4526","0","7968","0","3600","0","3900","0","-2900","0","2640","0","-840","0","2440","0","-1522","0","18396","0","-4534","0","4834","0","2080","0","-42","0","-1549","0","-2140","0","-4656","0","-2192","0","18400","0","768","0","-2912","0","-14320","0","4608","0","-7238","0","-7640","0","1096","0","-3818","0","4088","0","1998","0","2480","0","-3240","0","-1508","0","732","0","13340","0","2772","0","-7936","0","1898","0","3808","0","2766","0","-17980","0","-10080","0","-343","0","-5120","0","8352","0","-5924","0","5520","0","2226","0","3584","0","-4060","0","3880","0","-6183","0","-2690","0","1264","0","-2584","0","438","0","3150","0","10534","0","-14880","0","744","0","-4472","0","3840","0","2468","0","-2240","0","30368","0","-1046","0","3712","0","18140","0","7488","0","2124","0","1820","0","11598","0","-3024","0","-21032","0","-1040","0","-2770","0","-16660","0","-1918","0","-4240","0","-11260","0","9438","0","5550","0","-28908","0","3538","0","4032","0","-4800","0","-3000","0","12926","0","-4960","0","-1664","0","-408","0","3577","0","-14452","0","3120","0","-26940","0","10258","0","-240","0","26480","0","-672","0","-5498","0","26680","0","-16316","0","8944","0","20160","0","-9422","0","3332","0","5560","0","-16640","0","-1586","0","-32850","0","13820","0","-312","0","-4480","0","-1712","0","-13264","0","3280","0","-5940","0","3596","0","23360","0","3136","0","-8252","0","42680","0","4704","0","-11456","0","20530","0","-10788","0","1106","0","-11960","0","-6112","0","15840","0","34760","0","-14586","0","26","0","-4270","0","-14616","0","-8071","0","20002","0","-72","0","-2592","0","-22680","0","-1960","0","11214","0","2760","0","10672","0","-5424","0","-42048","0","-1612","0","6552","0","2080","0","-17618","0","-4992","0","-23200","0","-3562","0","-14384","0","-18403","0","2838","0","-360","0","30000","0","3904","0","22018","0","-32780","0","-3710","0","18000","0","7008","0","1454","0","6552","0","23620","0","13818","0","-3248","0","10360","0","6696","0","10010","0","-34748","0","-2152","0","2880","0","-4340","0","4752","0","6522","0","480","0","6614","0","5266","0","29440","0","2730","0","-4279","0","10400","0","-1508","0","3344","0","-35240","0","3072","0","-588","0","-32704","0","-4882","0","-15898","0","33280","0","6132","0","-10960","0","17640","0","-24198","0","14512","0","-11534","0","17456","0","-656","0","-6960","0","1456","0","3968","0","13360","0","23040","0","-18214","0","28060","0","30252","0","-1498","0","-12900","0","-10836","0","-13328","0","-55240","0","5400","0","9578","0","20440","0","-9008","0","-348","0","-63140","0","12442","0","676","0","-31680","0","-10024","0","-25174","0","-68328","0","-16128","0","-3840","0","39600","0","34188","0","-5348","0","70180","0","3782","0","-5204","0","67717","0","-24128","0","-32880","0","3920","0","19040","0","-3912","0","3120","0","-16008","0","-21552","0","38690","0","-2268","0","9960","0","23940","0","21184","0","12378","0","-25600","0","34670","0","9338","0","33872","0","-3288","0","-10898","0","27660","0","-25808","0","-15372","0","1820","0","156","0","17920","0","28520","0","4448","0","-21054","0","-79680","0","-12586","0","6912","0","-36000","0","-24276","0","22968","0","-28470","0","6320","0","-3584","0","29000","0","21526","0","-12806","0","-26400","0","2624","0","10816","0","6132","0","13214","0","32248","0","-24400","0","-14316","0","25168","0","15220","0","-2842","0","34144","0","-115920","0","9356","0","-20545","0","45340","0","16424","0","-1883","0","-48340","0","-1664","0","2372","0","-15184","0","11694","0","-20506","0","420","0","-28136","0","27808","0","15490","0","37440","0","5712","0","15622","0","-10416","0","-37070","0","46560","0","-6198","0","-31876","0","21920","0","-132","0","2688","0","-105160","0","-10296","0","-18144","0","-7680","0","-15624","0","26100","0","29120","0","2208","0","38244","0","104536","0","-7008","0","-21200","0","-46080","0","12698","0","36664","0","72380","0","5376","0","-1586","0","55772","0","45510","0","1274","0","-10960","0","-18560","0","-3838","0","38180","0","-16832","0","-384","0","-25760","0","-40928","0","1896","0","-19980","0","-24070","0","24000","0","-24800","0","-11662","0","33713","0","23652","0","-26224","0","-17152","0","15080","0","-32910","0","-7882","0","-7320","0","-6822","0","15600","0","-97382","0","-48420","0","18896","0","-27720","0","-26624","0","-49216","0","79360","0","8288","0","35264","0","-11960","0"]},{"label":"28.4.a.b","letter":"b","dim":1,"charpoly":["-10","1"],"traces":["1","0","4","0","6","0","7","0","-11","0","-12","0","-82","0","24","0","-30","0","68","0","28","0","216","0","-89","0","-152","0","246","0","-112","0","-48","0","42","0","110","0","-328","0","-246","0","-172","0","-66","0","192","0","49","0","-120","0","558","0","-72","0","272","0","540","0","110","0","-77","0","-492","0","140","0","864","0","-840","0","-550","0","-356","0","-84","0","-208","0","-311","0","516","0","-180","0","984","0","-1398","0","-574","0","-448","0","408","0","1586","0","132","0","-1242","0","680","0","168","0","996","0","1382","0","440","0","-750","0","1296","0","902","0","-210","0","-1187","0","-984","0","-1284","0","176","0","-688","0","-1548","0","476","0","-912","0","378","0","-2500","0","768","0","984","0","1476","0","196","0","846","0","-2536","0","330","0","-672","0","-1186","0","2232","0","1512","0","2108","0","-288","0","-1944","0","4527","0","-748","0","-1362","0","-623","0","2160","0","1596","0","-1690","0","440","0","660","0","360","0","-1064","0","3552","0","-2686","0","-1968","0","-1410","0","-2968","0","560","0","1722","0","-1476","0","-2376","0","-816","0","-1348","0","-3360","0","-1032","0","-784","0","-2200","0","2460","0","3872","0","979","0","5364","0","-874","0","-336","0","378","0","1152","0","-832","0","1920","0","4322","0","2860","0","294","0","-5576","0","2064","0","5292","0","-2592","0","-720","0","-5118","0","770","0","-2706","0","3768","0","3348","0","-5592","0","3918","0","4880","0","-2296","0","1068","0","-3538","0","1232","0","-5430","0","-6436","0","1632","0","-1722","0","-4013","0","6344","0","1350","0","3240","0","1824","0","-17712","0","-1204","0","-4968","0","660","0","3332","0","2720","0","-4728","0","5114","0","-462","0","7206","0","-2952","0","3984","0","-2040","0","7298","0","5528","0","1344","0","6260","0","-1210","0","840","0","-5326","0","-3000","0","1344","0","343","0","5184","0","36","0","3134","0","12464","0","1218","0","-5040","0","-840","0","-10008","0","-2235","0","-4748","0","-3300","0","-1072","0","2706","0","3906","0","-274","0","-5136","0","-20172","0","7652","0","704","0","2160","0","-504","0","1892","0","-1074","0","-6480","0","-6192","0","-1248","0","6926","0","1904","0","1938","0","9184","0","-1866","0","-1320","0","-9574","0","1512","0","3780","0","3096","0","-10000","0","-5052","0","3422","0","-2112","0","2670","0","770","0","3936","0","2208","0","-6814","0","5904","0","14688","0","12584","0","-539","0","6996","0","-8388","0","3384","0","9474","0","2952","0","-10144","0","-3444","0","5786","0","4560","0","3438","0","9392","0","-2688","0","-4956","0","980","0","-4744","0","2064","0","-6052","0","-6138","0","-20592","0","-9020","0","6048","0","9516","0","-13432","0","8432","0","-14172","0","-7380","0","792","0","-5880","0","-5956","0","-7776","0","16968","0","-7452","0","18108","0","5214","0","-3850","0","-10336","0","4080","0","-2304","0","-5448","0","-1398","0","-18580","0","-2492","0","3360","0","34489","0","-5940","0","20172","0","5976","0","6384","0","-588","0","-18970","0","-6760","0","8292","0","-16036","0","-1210","0","16728","0","-1456","0","2640","0","8310","0","14104","0","1440","0","7092","0","-4500","0","-2177","0","-7158","0","6500","0","14208","0","-19224","0","21794","0","-10744","0","3612","0","-6696","0","5412","0","9756","0","-7616","0","-5640","0","5586","0","-1260","0","-11872","0","-24","0","4298","0","-1540","0","-7122","0","8480","0","6888","0","-15744","0","-1906","0","-5904","0","7482","0","-7348","0","-32832","0","-9786","0","3421","0","-3264","0","-3300","0","4520","0","-5392","0","1056","0","-4018","0","9240","0","-19806","0","-5020","0","-4128","0","28392","0","-6480","0","-3136","0","-17562","0","-9288","0","6050","0","4716","0","-22762","0","9840","0","2856","0","53136","0","15488","0","-1320","0","4802","0","13528","0","21558","0","11102","0","21456","0","3780","0","2268","0","-3496","0","-45756","0","-5500","0","924","0","-15000","0","7380","0","1512","0","10230","0","7480","0","4608","0","-8694","0","10190","0","2288","0","-24192","0","5904","0","7680","0","9408","0","4760","0","17288","0","-21894","0","-33064","0","19837","0","5160","0","-6322","0","1176","0","-1680","0","-20740","0","-22304","0","32040","0","5076","0","-5676","0","6972","0","-12832","0","21168","0","-15216","0","-19906","0","-10368","0","10842","0","9674","0","1980","0","-44280","0","28274","0","-20472","0","-32346","0","9968","0","3080","0","-16728","0","10080","0","-37392","0","-7116","0","30116","0","15072","0","-5250","0","-9020","0","13392","0","-6594","0","-5760","0","15378","0","6600","0","9072","0","15672","0","-43014","0","-14164","0","19520","0","12648","0","-11696","0","6314","0","34830","0","31016","0","4272","0","9876","0","-3154","0","-14152","0","-1470","0","-11664","0","17024","0","36936","0","36127","0","-21720","0","27162","0","-8309","0","-25744","0","23760","0","9638","0","-4488","0","10266","0","-4084","0","-6888","0","-192","0","-8172","0","-16052","0","2496","0","-11480","0","-17446","0","-8988","0","19910","0","5400","0","14802","0","-32548","0","12960","0","1464","0","1232","0","3732","0","13056","0","9576","0","-70848","0","-27552","0","-16740","0","-4816","0","-10140","0","-49564","0","13662","0","8448","0","-6192","0","2640","0","-10836","0","14600","0","13328","0","68880","0","-9790","0","-7480","0","-21102","0","3332","0","-18912","0","2160","0","-20806","0","20456","0","24510","0","-53136","0","-6384","0","-44148","0","45100","0","28824","0","27114","0","21312","0","-11808","0","2646","0","-17247","0","-10956","0","-16116","0","-10264","0","-8160","0","51468","0","-17500","0","29192","0","-23790","0","16776","0","-15202","0","26424","0","-8460","0","5376","0","-37152","0","39488","0","25040","0","-17808","0","30854","0","-16720","0"]}],"seconds":0.104,"computed":"atlas","estimate":{"seconds":0.238,"low":0.145,"high":0.412,"bytes":1830340}}