/* This code can be loaded, or copied and pasted, into Magma. It will load the data associated to the BMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. At the *bottom* of the file, there is code to recreate the Bianchi modular form in Magma, by creating the BMF space and cutting out the corresponding Hecke irreducible subspace. From there, you can ask for more eigenvalues or modify as desired. It is commented out, as this computation may be lengthy. */ P := PolynomialRing(Rationals()); g := P![1, -1, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [3,a+1], [2,2], [7,a+2], [7,a-3], [13,a+3], [13,a-4], [19,a+7], [19,a-8], [5,5], [31,a+5], [31,a-6], [37,a+10], [37,a-11], [43,a+6], [43,a-7], [61,a+13], [61,a-14], [67,a+29], [67,a-30], [73,a+8], [73,a-9], [79,a+23], [79,a-24], [97,a+35], [97,a-36], [103,a+46], [103,a-47], [109,a+45], [109,a-46], [11,11], [127,a+19], [127,a-20], [139,a+42], [139,a-43], [151,a+32], [151,a-33], [157,a+12], [157,a-13], [163,a+58], [163,a-59], [181,a+48], [181,a-49], [193,a+84], [193,a-85], [199,a+92], [199,a-93], [211,a+14], [211,a-15], [223,a+39], [223,a-40], [229,a+94], [229,a-95], [241,a+15], [241,a-16], [271,a+28], [271,a-29], [277,a+116], [277,a-117], [283,a+44], [283,a-45], [17,17], [307,a+17], [307,a-18], [313,a+98], [313,a-99], [331,a+31], [331,a-32], [337,a+128], [337,a-129], [349,a+122], [349,a-123], [367,a+83], [367,a-84], [373,a+88], [373,a-89], [379,a+51], [379,a-52], [397,a+34], [397,a-35], [409,a+53], [409,a-54], [421,a+20], [421,a-21], [433,a+198], [433,a-199], [439,a+171], [439,a-172], [457,a+133], [457,a-134], [463,a+21], [463,a-22], [487,a+232], [487,a-233], [499,a+139], [499,a-140], [523,a+60], [523,a-61], [23,23], [541,a+129], [541,a-130], [547,a+40], [547,a-41], [571,a+109], [571,a-110], [577,a+213], [577,a-214], [601,a+24], [601,a-25], [607,a+210], [607,a-211], [613,a+65], [613,a-66], [619,a+252], [619,a-253], [631,a+43], [631,a-44], [643,a+177], [643,a-178], [661,a+296], [661,a-297], [673,a+255], [673,a-256], [691,a+253], [691,a-254], [709,a+227], [709,a-228], [727,a+281], [727,a-282], [733,a+307], [733,a-308], [739,a+320], [739,a-321], [751,a+72], [751,a-73], [757,a+27], [757,a-28], [769,a+360], [769,a-361], [787,a+379], [787,a-380], [811,a+130], [811,a-131], [823,a+174], [823,a-175], [829,a+125], [829,a-126], [29,29], [853,a+220], [853,a-221], [859,a+260], [859,a-261], [877,a+282], [877,a-283], [883,a+337], [883,a-338], [907,a+384], [907,a-385], [919,a+52], [919,a-53], [937,a+322], [937,a-323], [967,a+142], [967,a-143], [991,a+113], [991,a-114], [997,a+304], [997,a-305], [1009,a+374], [1009,a-375], [1021,a+368], [1021,a-369], [1033,a+195], [1033,a-196], [1039,a+140], [1039,a-141], [1051,a+180], [1051,a-181], [1063,a+343], [1063,a-344], [1069,a+86], [1069,a-87], [1087,a+257], [1087,a-258], [1093,a+151], [1093,a-152], [1117,a+120], [1117,a-121], [1123,a+33], [1123,a-34], [1129,a+387], [1129,a-388], [1153,a+502], [1153,a-503], [1171,a+420], [1171,a-421], [1201,a+570], [1201,a-571], [1213,a+217], [1213,a-218], [1231,a+126], [1231,a-127], [1237,a+300], [1237,a-301], [1249,a+93], [1249,a-94], [1279,a+504], [1279,a-505], [1291,a+346], [1291,a-347], [1297,a+365], [1297,a-366], [1303,a+95], [1303,a-96], [1321,a+297], [1321,a-298], [1327,a+347], [1327,a-348], [1381,a+354], [1381,a-355], [1399,a+390], [1399,a-391], [1423,a+643], [1423,a-644], [1429,a+664], [1429,a-665], [1447,a+704], [1447,a-705], [1453,a+693], [1453,a-694], [1459,a+339], [1459,a-340], [1471,a+251], [1471,a-252], [1483,a+38], [1483,a-39], [1489,a+483], [1489,a-484], [1531,a+646], [1531,a-647], [1543,a+681], [1543,a-682], [1549,a+275], [1549,a-276], [1567,a+535], [1567,a-536], [1579,a+639], [1579,a-640], [1597,a+222], [1597,a-223], [1609,a+250], [1609,a-251], [1621,a+184], [1621,a-185], [1627,a+264], [1627,a-265], [1657,a+70], [1657,a-71], [1663,a+318], [1663,a-319], [1669,a+248], [1669,a-249], [41,41], [1693,a+433], [1693,a-434], [1699,a+397], [1699,a-398], [1723,a+41], [1723,a-42], [1741,a+356], [1741,a-357], [1747,a+371], [1747,a-372], [1753,a+182], [1753,a-183], [1759,a+508], [1759,a-509], [1777,a+629], [1777,a-630], [1783,a+193], [1783,a-194], [1789,a+152], [1789,a-153], [1801,a+73], [1801,a-74], [1831,a+672], [1831,a-673], [1861,a+454], [1861,a-455], [1867,a+834], [1867,a-835], [1873,a+114], [1873,a-115], [1879,a+488], [1879,a-489], [1933,a+591], [1933,a-592], [1951,a+76], [1951,a-77], [1987,a+647], [1987,a-648], [1993,a+312], [1993,a-313], [1999,a+808], [1999,a-809], [2011,a+205], [2011,a-206], [2017,a+294], [2017,a-295], [2029,a+975], [2029,a-976], [2053,a+197], [2053,a-198], [2083,a+449], [2083,a-450], [2089,a+826], [2089,a-827], [2113,a+438], [2113,a-439], [2131,a+468], [2131,a-469], [2137,a+201], [2137,a-202], [2143,a+349], [2143,a-350], [2161,a+593], [2161,a-594], [2179,a+123], [2179,a-124], [2203,a+285], [2203,a-286], [47,47], [2221,a+543], [2221,a-544], [2239,a+295], [2239,a-296], [2251,a+708], [2251,a-709], [2269,a+82], [2269,a-83], [2281,a+663], [2281,a-664], [2287,a+804], [2287,a-805], [2293,a+989], [2293,a-990], [2311,a+882], [2311,a-883], [2341,a+1106], [2341,a-1107], [2347,a+1062], [2347,a-1063], [2371,a+464], [2371,a-465], [2377,a+721], [2377,a-722], [2383,a+1103], [2383,a-1104], [2389,a+689], [2389,a-690], [2437,a+85], [2437,a-86], [2467,a+216], [2467,a-217], [2473,a+1015], [2473,a-1016], [2503,a+1226], [2503,a-1227], [2521,a+675], [2521,a-676], [2539,a+306], [2539,a-307], [2551,a+50], [2551,a-51], [2557,a+835], [2557,a-836], [2593,a+1137], [2593,a-1138], [2617,a+1064], [2617,a-1065], [2647,a+185], [2647,a-186], [2659,a+903], [2659,a-904], [2671,a+544], [2671,a-545], [2677,a+1033], [2677,a-1034], [2683,a+636], [2683,a-637], [2689,a+391], [2689,a-392], [2707,a+1327], [2707,a-1328], [2713,a+1211], [2713,a-1212], [2719,a+1265], [2719,a-1266], [2731,a+446], [2731,a-447], [2749,a+595], [2749,a-596], [2767,a+328], [2767,a-329], [2791,a+91], [2791,a-92], [2797,a+1100], [2797,a-1101], [2803,a+413], [2803,a-414], [53,53], [2833,a+1300], [2833,a-1301], [2851,a+1014], [2851,a-1015], [2857,a+350], [2857,a-351], [2887,a+698], [2887,a-699], [2917,a+247], [2917,a-248], [2953,a+800], [2953,a-801], [2971,a+54], [2971,a-55], [3001,a+934], [3001,a-935], [3019,a+239], [3019,a-240], [3037,a+745], [3037,a-746], [3049,a+532], [3049,a-533], [3061,a+561], [3061,a-562], [3067,a+973], [3067,a-974], [3079,a+546], [3079,a-547], [3109,a+1085], [3109,a-1086], [3121,a+1121], [3121,a-1122], [3163,a+536], [3163,a-537], [3169,a+97], [3169,a-98], [3181,a+440], [3181,a-441], [3187,a+1315], [3187,a-1316], [3217,a+204], [3217,a-205], [3229,a+914], [3229,a-915], [3253,a+1439], [3253,a-1440], [3259,a+852], [3259,a-853], [3271,a+842], [3271,a-843], [3301,a+1574], [3301,a-1575], [3307,a+57], [3307,a-58], [3313,a+1123], [3313,a-1124], [3319,a+1527], [3319,a-1528], [3331,a+1463], [3331,a-1464], [3343,a+1424], [3343,a-1425], [3361,a+892], [3361,a-893], [3373,a+654], [3373,a-655], [3391,a+555], [3391,a-556], [3433,a+268], [3433,a-269], [3457,a+722], [3457,a-723], [3463,a+367], [3463,a-368], [3469,a+1683], [3469,a-1684], [59,59], [3499,a+156], [3499,a-157], [3511,a+756], [3511,a-757], [3517,a+258], [3517,a-259], [3529,a+448], [3529,a-449], [3541,a+59], [3541,a-60], [3547,a+1162], [3547,a-1163], [3559,a+1435], [3559,a-1436], [3571,a+103], [3571,a-104], [3583,a+1038], [3583,a-1039], [3607,a+1399], [3607,a-1400], [3613,a+1675], [3613,a-1676], [3631,a+335], [3631,a-336], [3637,a+695], [3637,a-696], [3643,a+422], [3643,a-423], [3673,a+1151], [3673,a-1152], [3691,a+474], [3691,a-475], [3697,a+519], [3697,a-520], [3709,a+498], [3709,a-499], [3727,a+1188], [3727,a-1189], [3733,a+948], [3733,a-949], [3739,a+694], [3739,a-695], [3769,a+463], [3769,a-464], [3793,a+1068], [3793,a-1069], [3823,a+1184], [3823,a-1185], [3847,a+1892], [3847,a-1893], [3853,a+1139], [3853,a-1140], [3877,a+224], [3877,a-225], [3889,a+1890], [3889,a-1891], [3907,a+62], [3907,a-63], [3919,a+1169], [3919,a-1170], [3931,a+617], [3931,a-618], [3943,a+1135], [3943,a-1136], [3967,a+888], [3967,a-889], [4003,a+822], [4003,a-823], [4021,a+1812], [4021,a-1813], [4027,a+1820], [4027,a-1821], [4051,a+797], [4051,a-798], [4057,a+1408], [4057,a-1409], [4093,a+902], [4093,a-903], [4099,a+2017], [4099,a-2018], [4111,a+1055], [4111,a-1056], [4129,a+1979], [4129,a-1980], [4153,a+170], [4153,a-171], [4159,a+1604], [4159,a-1605], [4177,a+1102], [4177,a-1103], [4201,a+1124], [4201,a-1125], [4219,a+112], [4219,a-113], [4231,a+620], [4231,a-621], [4243,a+298], [4243,a-299], [4261,a+1647], [4261,a-1648], [4273,a+1610], [4273,a-1611], [4297,a+1410], [4297,a-1411], [4327,a+627], [4327,a-628], [4339,a+237], [4339,a-238], [4357,a+1318], [4357,a-1319], [4363,a+412], [4363,a-413], [4423,a+66], [4423,a-67], [4441,a+901], [4441,a-902], [4447,a+115], [4447,a-116], [4483,a+505], [4483,a-506], [4507,a+791], [4507,a-792], [4513,a+814], [4513,a-815], [4519,a+1056], [4519,a-1057], [4549,a+1744], [4549,a-1745], [4561,a+243], [4561,a-244], [4567,a+1112], [4567,a-1113], [4591,a+310], [4591,a-311], [4597,a+377], [4597,a-378], [4603,a+179], [4603,a-180], [4621,a+1763], [4621,a-1764], [4639,a+1360], [4639,a-1361], [4651,a+786], [4651,a-787], [4657,a+967], [4657,a-968], [4663,a+2092], [4663,a-2093], [4723,a+717], [4723,a-718], [4729,a+2036], [4729,a-2037], [4759,a+1525], [4759,a-1526], [4783,a+1745], [4783,a-1746], [4789,a+1679], [4789,a-1680], [4801,a+2340], [4801,a-2341], [4813,a+1888], [4813,a-1889], [4831,a+69], [4831,a-70], [4861,a+319], [4861,a-320], [4903,a+2416], [4903,a-2417], [4909,a+573], [4909,a-574], [4933,a+2131], [4933,a-2132], [4951,a+2261], [4951,a-2262], [4957,a+2282], [4957,a-2283], [4969,a+186], [4969,a-187], [4987,a+1136], [4987,a-1137], [4993,a+2342], [4993,a-2343], [4999,a+2337], [4999,a-2338], [5011,a+2103], [5011,a-2104], [5023,a+953], [5023,a-954], [71,71], [5059,a+1912], [5059,a-1913], [5077,a+1629], [5077,a-1630], [5101,a+1614], [5101,a-1615], [5107,a+311], [5107,a-312], [5113,a+71], [5113,a-72], [5119,a+1682], [5119,a-1683], [5167,a+124], [5167,a-125], [5179,a+1497], [5179,a-1498], [5197,a+1878], [5197,a-1879], [5209,a+1192], [5209,a-1193], [5227,a+451], [5227,a-452], [5233,a+331], [5233,a-332], [5281,a+1403], [5281,a-1404], [5323,a+1282], [5323,a-1283], [5347,a+479], [5347,a-480], [5407,a+1042], [5407,a-1043], [5413,a+1224], [5413,a-1225], [5419,a+127], [5419,a-128], [5431,a+1533], [5431,a-1534], [5437,a+2271], [5437,a-2272], [5443,a+2588], [5443,a-2589], [5449,a+1474], [5449,a-1475], [5479,a+2702], [5479,a-2703], [5503,a+929], [5503,a-930], [5521,a+340], [5521,a-341], [5527,a+876], [5527,a-877], [5557,a+1827], [5557,a-1828], [5563,a+711], [5563,a-712], [5569,a+2242], [5569,a-2243], [5581,a+2458], [5581,a-2459], [5623,a+2013], [5623,a-2014], [5641,a+2044], [5641,a-2045], [5647,a+853], [5647,a-854], [5653,a+740], [5653,a-741], [5659,a+1464], [5659,a-1465], [5683,a+1110], [5683,a-1111], [5689,a+2419], [5689,a-2420], [5701,a+75], [5701,a-76], [5737,a+2469], [5737,a-2470], [5743,a+200], [5743,a-201], [5749,a+330], [5749,a-331], [5779,a+2851], [5779,a-2852], [5791,a+1572], [5791,a-1573], [5821,a+2148], [5821,a-2149], [5827,a+1350], [5827,a-1351], [5839,a+1854], [5839,a-1855], [5851,a+577], [5851,a-578], [5857,a+1264], [5857,a-1265], [5869,a+777], [5869,a-778], [5881,a+276], [5881,a-277], [5923,a+428], [5923,a-429], [5953,a+869], [5953,a-870], [6007,a+77], [6007,a-78], [6037,a+509], [6037,a-510], [6043,a+1715], [6043,a-1716], [6067,a+665], [6067,a-666], [6073,a+1842], [6073,a-1843], [6079,a+1553], [6079,a-1554], [6091,a+744], [6091,a-745], [6121,a+1152], [6121,a-1153], [6133,a+949], [6133,a-950], [6151,a+207], [6151,a-208], [6163,a+78], [6163,a-79], [6199,a+2645], [6199,a-2646], [6211,a+136], [6211,a-137], [6217,a+2459], [6217,a-2460], [6229,a+930], [6229,a-931], [6247,a+2316], [6247,a-2317], [6271,a+2020], [6271,a-2021], [6277,a+2308], [6277,a-2309], [6301,a+2977], [6301,a-2978], [6337,a+1512], [6337,a-1513], [6343,a+557], [6343,a-558], [6361,a+1858], [6361,a-1859], [6367,a+769], [6367,a-770], [6373,a+623], [6373,a-624], [6379,a+3006], [6379,a-3007], [6397,a+2294], [6397,a-2295], [6421,a+3104], [6421,a-3105], [6427,a+1084], [6427,a-1085], [6451,a+212], [6451,a-213], [6469,a+1476], [6469,a-1477], [6481,a+80], [6481,a-81], [6529,a+491], [6529,a-492], [6547,a+2332], [6547,a-2333], [6553,a+1944], [6553,a-1945], [6571,a+2979], [6571,a-2980], [6577,a+353], [6577,a-354], [6607,a+1518], [6607,a-1519], [6619,a+569], [6619,a-570], [6637,a+1370], [6637,a-1371], [6661,a+1348], [6661,a-1349], [6673,a+1393], [6673,a-1394], [6679,a+942], [6679,a-943], [6691,a+2918], [6691,a-2919], [6703,a+1480], [6703,a-1481], [6709,a+1239], [6709,a-1240], [6733,a+619], [6733,a-620], [6763,a+2155], [6763,a-2156], [6781,a+2926], [6781,a-2927], [6793,a+1168], [6793,a-1169], [6823,a+2685], [6823,a-2686], [6829,a+734], [6829,a-735], [6841,a+2808], [6841,a-2809], [6871,a+1466], [6871,a-1467], [6883,a+219], [6883,a-220], [83,83], [6907,a+1856], [6907,a-1857], [6949,a+1942], [6949,a-1943], [6961,a+507], [6961,a-508], [6967,a+382], [6967,a-383], [6991,a+1381], [6991,a-1382], [6997,a+2908], [6997,a-2909], [7027,a+523], [7027,a-524], [7039,a+302], [7039,a-303], [7057,a+145], [7057,a-146], [7069,a+2040], [7069,a-2041], [7129,a+1249], [7129,a-1250], [7159,a+2880], [7159,a-2881], [7177,a+2038], [7177,a-2039], [7207,a+1838], [7207,a-1839], [7213,a+2602], [7213,a-2603], [7219,a+2725], [7219,a-2726], [7237,a+1830], [7237,a-1831], [7243,a+3426], [7243,a-3427], [7297,a+3535], [7297,a-3536], [7309,a+3416], [7309,a-3417], [7321,a+308], [7321,a-309], [7333,a+3062], [7333,a-3063], [7351,a+148], [7351,a-149], [7369,a+2559], [7369,a-2560], [7393,a+1717], [7393,a-1718], [7411,a+394], [7411,a-395], [7417,a+2312], [7417,a-2313], [7459,a+228], [7459,a-229], [7477,a+3468], [7477,a-3469], [7489,a+2467], [7489,a-2468], [7507,a+606], [7507,a-607], [7537,a+1962], [7537,a-1963], [7549,a+528], [7549,a-529], [7561,a+1298], [7561,a-1299], [7573,a+2057], [7573,a-2058], [7591,a+2453], [7591,a-2454], [7603,a+2094], [7603,a-2095], [7621,a+3124], [7621,a-3125], [7639,a+2975], [7639,a-2976], [7669,a+2070], [7669,a-2071], [7681,a+684], [7681,a-685], [7687,a+2274], [7687,a-2275], [7699,a+2269], [7699,a-2270], [7717,a+3439], [7717,a-3440], [7723,a+917], [7723,a-918], [7741,a+2452], [7741,a-2453], [7753,a+403], [7753,a-404], [7759,a+1759], [7759,a-1760], [7789,a+233], [7789,a-234], [7867,a+1465], [7867,a-1466], [7873,a+1394], [7873,a-1395], [7879,a+1366], [7879,a-1367], [89,89], [7927,a+3759], [7927,a-3760], [7933,a+2005], [7933,a-2006], [7951,a+321], [7951,a-322]]; primes := [ideal : I in primesArray]; heckePol := x; K := Rationals(); e := 1; heckeEigenvaluesList := [* 1, -3, -1, -1, -2, -2, 4, 4, -6, 0, 0, 6, 6, -4, -4, -2, -2, 4, 4, -6, -6, -16, -16, 18, 18, 8, 8, -18, -18, -6, 0, 0, 12, 12, 8, 8, -2, -2, 4, 4, -26, -26, 2, 2, 24, 24, 4, 4, 16, 16, -10, -10, 2, 2, 16, 16, 22, 22, -20, -20, 2, 4, 4, 26, 26, -4, -4, -14, -14, -2, -2, 0, 0, -10, -10, 12, 12, -18, -18, -22, -22, 38, 38, -14, -14, -24, -24, 10, 10, 16, 16, -8, -8, 4, 4, -20, -20, -46, -34, -34, 4, 4, -4, -4, 34, 34, -6, -6, -16, -16, -26, -26, -20, -20, -40, -40, 20, 20, 22, 22, 34, 34, 20, 20, 6, 6, -40, -40, -18, -18, 36, 36, -32, -32, -10, -10, 2, 2, -44, -44, 44, 44, 24, 24, 14, 14, -54, -10, -10, 44, 44, 46, 46, -28, -28, -4, -4, 8, 8, 42, 42, 40, 40, -16, -16, -26, -26, -14, -14, 30, 30, -22, -22, 32, 32, 28, 28, -24, -24, 46, 46, 32, 32, 38, 38, -2, -2, 4, 4, 10, 10, -14, -14, -28, -28, 50, 50, 30, 30, 32, 32, 6, 6, -14, -14, -48, -48, 28, 28, 18, 18, -56, -56, 10, 10, -64, -64, 38, 38, -8, -8, 32, 32, -10, -10, 8, 8, 46, 46, 4, 4, -16, -16, -36, -36, -62, -62, -36, -36, -72, -72, 46, 46, -32, -32, -20, -20, -34, -34, 58, 58, -10, -10, 12, 12, 26, 26, 32, 32, -10, -10, -78, -34, -34, -28, -28, 28, 28, -50, -50, 68, 68, 10, 10, -16, -16, -62, -62, 56, 56, 30, 30, 10, 10, -24, -24, 70, 70, 44, 44, 82, 82, 56, 56, -50, -50, -80, -80, 68, 68, -54, -54, -80, -80, 60, 60, 66, 66, 30, 30, -26, -26, -12, -12, 26, 26, -14, -14, -28, -28, -38, -38, -16, -16, 34, 34, 4, 4, 44, 44, -94, -50, -50, 32, 32, -20, -20, -34, -34, -70, -70, 16, 16, -74, -74, -8, -8, -74, -74, 28, 28, 52, 52, -54, -54, 96, 96, 22, 22, 6, 6, -28, -28, -86, -86, 40, 40, 90, 90, -36, -36, 56, 56, -2, -2, 2, 2, -54, -54, 40, 40, -60, -60, 32, 32, 70, 70, -4, -4, 34, 34, -28, -28, 58, 58, 16, 16, 12, 12, -34, -34, -80, -80, -8, -8, -18, -18, -76, -76, -70, 50, 50, 52, 52, -54, -54, -88, -88, 70, 70, 74, 74, -36, -36, 42, 42, 12, 12, -34, -34, 10, 10, -10, -10, -36, -36, -40, -40, -90, -90, -30, -30, 92, 92, -62, -62, 94, 94, -108, -108, 18, 18, -2, -2, -26, -26, 76, 76, 40, 40, -58, -58, 108, 108, 18, 18, -24, -24, 100, 100, -16, -16, -30, -30, -98, -98, 32, 32, 26, 26, 18, 18, -56, -56, 14, 14, 26, -100, -100, 56, 56, -2, -2, -54, -54, 86, 86, -52, -52, 72, 72, -12, -12, 32, 32, -88, -88, 62, 62, 80, 80, 22, 22, 44, 44, -70, -70, -20, -20, 50, 50, 62, 62, 0, 0, 54, 54, 44, 44, -70, -70, 34, 34, -64, -64, -40, -40, 62, 62, -58, -58, -14, -14, 36, 36, -32, -32, -4, -4, 120, 120, -64, -64, -76, -76, -26, -26, -52, -52, -28, -28, -38, -38, -50, -50, -12, -12, -48, -48, 34, 34, -6, -6, 96, 96, 98, 98, 10, 10, 28, 28, -40, -40, -76, -76, -58, -58, 34, 34, -22, -22, -8, -8, 100, 100, 38, 38, 92, 92, 56, 56, 90, 90, 112, 112, 84, 84, -116, -116, -62, -62, -40, -40, -90, -90, 82, 82, 8, 8, -16, -16, 54, 54, 12, 12, 46, 46, 32, 32, -100, -100, 114, 114, 88, 88, 100, 100, -38, -38, 56, 56, -96, -96, 22, 22, -30, -30, 46, 46, 112, 112, 78, 78, 88, 88, -50, -50, 54, 54, -88, -88, -66, -66, -54, -54, -36, -36, 2, 2, 120, 120, 20, 20, -64, -64, -142, -60, -60, 22, 22, 62, 62, -76, -76, -102, -102, -32, -32, 112, 112, 76, 76, -82, -82, 90, 90, -132, -132, 114, 114, -62, -62, -84, -84, -44, -44, 0, 0, -122, -122, 76, 76, 72, 72, 14, 14, -44, -44, 10, 10, -120, -120, 0, 0, 114, 114, -56, -56, -58, -58, 28, 28, -62, -62, -50, -50, -88, -88, 58, 58, -128, -128, -10, -10, 28, 28, -76, -76, 74, 74, 118, 118, -86, -86, -80, -80, -42, -42, -44, -44, 32, 32, 94, 94, 20, 20, -80, -80, -4, -4, -46, -46, 62, 62, -38, -38, 20, 20, -110, -110, 72, 72, -74, -74, 28, 28, 52, 52, -70, -70, -80, -80, -68, -68, -6, -6, -106, -106, 24, 24, 116, 116, -8, -8, 20, 20, -54, -54, 54, 54, -88, -88, 96, 96, 38, 38, 62, 62, 130, 130, -24, -24, -86, -86, 112, 112, -58, -58, -100, -100, -130, -130, 86, 86, -52, -52, -12, -12, 6, 6, -158, -158, -62, -62, -12, -12, -38, -38, 12, 12, 82, 82, -112, -112, 76, 76, -50, -50, -154, -154, 146, 146, -56, -56, -76, -76, 80, 80, -74, -74, 94, 94, 124, 124, -50, -50, 74, 74, -136, -136, -18, -18, -6, -6, -120, -120, 84, 84, -22, 60, 60, 150, 150, 2, 2, -104, -104, 96, 96, 22, 22, 36, 36, 96, 96, -110, -110, 46, 46, 10, 10, 40, 40, -118, -118, -72, -72, -82, -82, 20, 20, 54, 54, 140, 140, 82, 82, 14, 14, 26, 26, 6, 6, 56, 56, 10, 10, 98, 98, -108, -108, -134, -134, -156, -156, -42, -42, 82, 82, 4, 4, -46, -46, -98, -98, -22, -22, 38, 38, -8, -8, 84, 84, 86, 86, -136, -136, 150, 150, -62, -62, 136, 136, 68, 68, 54, 54, 76, 76, 14, 14, 42, 42, 160, 160, -18, -18, 124, 124, -46, -46, 136, 136, 18, 168, 168, -34, -34, -144, -144 *]; heckeEigenvalues := AssociativeArray(); for i in [1..#heckeEigenvaluesList] do heckeEigenvalues[primes[i]] := heckeEigenvaluesList[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := -1; ALEigenvalues[ideal] := 1; ALEigenvalues[ideal] := 1; // EXAMPLE: // pp := Factorization(2*ZF)[1][1]; // heckeEigenvalues[pp]; print "To reconstruct the Bianchi newform f, type f, iso := Explode(make_newform());"; function make_newform(); M := BianchiCuspForms(F, NN); S := NewSubspace(M); // SetVerbose("Bianchi", 1); NFD := NewformDecomposition(S); newforms := [* Eigenform(U) : U in NFD *]; if #newforms eq 0 then; print "No Bianchi newforms at this level"; return 0; end if; print "Testing ", #newforms, " possible newforms"; newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *]; print #newforms, " newforms have the correct Hecke field"; if #newforms eq 0 then; print "No Bianchi newform found with the correct Hecke field"; return 0; end if; autos := Automorphisms(K); xnewforms := [* *]; for f in newforms do; if K eq RationalField() then; Append(~xnewforms, [* f, autos[1] *]); else; flag, iso := IsIsomorphic(K,BaseField(f)); for a in autos do; Append(~xnewforms, [* f, a*iso *]); end for; end if; end for; newforms := xnewforms; for P in primes do; if Valuation(NN,P) eq 0 then; xnewforms := [* *]; for f_iso in newforms do; f, iso := Explode(f_iso); if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then; Append(~xnewforms, f_iso); end if; end for; newforms := xnewforms; if #newforms eq 0 then; print "No Bianchi newform found which matches the Hecke eigenvalues"; return 0; else if #newforms eq 1 then; print "success: unique match"; return newforms[1]; end if; end if; end if; end for; print #newforms, "Bianchi newforms found which match the Hecke eigenvalues"; return newforms[1]; end function;