/* 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![2, -1, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [2,a], [2,a-1], [7,a+3], [3,3], [11,a+4], [11,a-5], [23,a+9], [23,a-10], [5,5], [29,a+7], [29,a-8], [37,a+8], [37,a-9], [43,a+18], [43,a-19], [53,a+14], [53,a-15], [67,a+11], [67,a-12], [71,a+31], [71,a-32], [79,a+12], [79,a-13], [107,a+48], [107,a-49], [109,a+29], [109,a-30], [113,a+42], [113,a-43], [127,a+22], [127,a-23], [137,a+16], [137,a-17], [149,a+34], [149,a-35], [151,a+69], [151,a-70], [163,a+25], [163,a-26], [13,13], [179,a+53], [179,a-54], [191,a+19], [191,a-20], [193,a+73], [193,a-74], [197,a+52], [197,a-53], [211,a+20], [211,a-21], [233,a+30], [233,a-31], [239,a+72], [239,a-73], [263,a+123], [263,a-124], [277,a+23], [277,a-24], [281,a+33], [281,a-34], [17,17], [317,a+83], [317,a-84], [331,a+156], [331,a-157], [337,a+124], [337,a-125], [347,a+74], [347,a-75], [359,a+128], [359,a-129], [19,19], [373,a+154], [373,a-155], [379,a+27], [379,a-28], [389,a+92], [389,a-93], [401,a+152], [401,a-153], [421,a+176], [421,a-177], [431,a+41], [431,a-42], [443,a+157], [443,a-158], [449,a+196], [449,a-197], [457,a+85], [457,a-86], [463,a+80], [463,a-81], [487,a+103], [487,a-104], [491,a+234], [491,a-235], [499,a+151], [499,a-152], [541,a+46], [541,a-47], [547,a+87], [547,a-88], [557,a+133], [557,a-134], [569,a+178], [569,a-179], [571,a+158], [571,a-159], [599,a+129], [599,a-130], [613,a+49], [613,a-50], [617,a+116], [617,a-117], [631,a+35], [631,a-36], [641,a+237], [641,a-238], [653,a+169], [653,a-170], [659,a+195], [659,a-196], [673,a+293], [673,a-294], [683,a+328], [683,a-329], [701,a+315], [701,a-316], [709,a+106], [709,a-107], [739,a+127], [739,a-128], [743,a+54], [743,a-55], [751,a+77], [751,a-78], [757,a+182], [757,a-183], [809,a+150], [809,a-151], [821,a+40], [821,a-41], [823,a+229], [823,a-230], [827,a+57], [827,a-58], [863,a+117], [863,a-118], [877,a+367], [877,a-368], [883,a+361], [883,a-362], [907,a+438], [907,a-439], [911,a+289], [911,a-290], [919,a+326], [919,a-327], [947,a+43], [947,a-44], [953,a+115], [953,a-116], [31,31], [967,a+267], [967,a-268], [977,a+62], [977,a-63], [991,a+44], [991,a-45], [1009,a+462], [1009,a-463], [1019,a+216], [1019,a-217], [1031,a+499], [1031,a-500], [1033,a+301], [1033,a-302], [1051,a+407], [1051,a-408], [1061,a+476], [1061,a-477], [1087,a+186], [1087,a-187], [1093,a+93], [1093,a-94], [1103,a+450], [1103,a-451], [1117,a+287], [1117,a-288], [1129,a+47], [1129,a-48], [1163,a+564], [1163,a-565], [1171,a+160], [1171,a-161], [1187,a+319], [1187,a-320], [1201,a+454], [1201,a-455], [1213,a+98], [1213,a-99], [1229,a+185], [1229,a-186], [1283,a+444], [1283,a-445], [1289,a+243], [1289,a-244], [1297,a+269], [1297,a-270], [1303,a+633], [1303,a-634], [1327,a+51], [1327,a-52], [1367,a+490], [1367,a-491], [1373,a+637], [1373,a-638], [1381,a+246], [1381,a-247], [1409,a+614], [1409,a-615], [1423,a+324], [1423,a-325], [1429,a+501], [1429,a-502], [1439,a+497], [1439,a-498], [1451,a+706], [1451,a-707], [1453,a+570], [1453,a-571], [1471,a+143], [1471,a-144], [1481,a+180], [1481,a-181], [1493,a+479], [1493,a-480], [1499,a+109], [1499,a-110], [1523,a+206], [1523,a-207], [1549,a+377], [1549,a-378], [1579,a+368], [1579,a-369], [1583,a+670], [1583,a-671], [1597,a+56], [1597,a-57], [1607,a+783], [1607,a-784], [1619,a+489], [1619,a-490], [1621,a+678], [1621,a-679], [1663,a+270], [1663,a-271], [1667,a+191], [1667,a-192], [41,41], [1709,a+437], [1709,a-438], [1723,a+480], [1723,a-481], [1733,a+681], [1733,a-682], [1747,a+554], [1747,a-555], [1759,a+474], [1759,a-475], [1787,a+635], [1787,a-636], [1789,a+624], [1789,a-625], [1801,a+281], [1801,a-282], [1831,a+60], [1831,a-61], [1871,a+86], [1871,a-87], [1873,a+526], [1873,a-527], [1877,a+458], [1877,a-459], [1901,a+204], [1901,a-205], [1913,a+777], [1913,a-778], [1933,a+164], [1933,a-165], [1997,a+357], [1997,a-358], [1999,a+340], [1999,a-341], [2003,a+89], [2003,a-90], [2011,a+556], [2011,a-557], [2017,a+63], [2017,a-64], [2027,a+536], [2027,a-537], [2039,a+779], [2039,a-780], [2053,a+524], [2053,a-525], [2069,a+308], [2069,a-309], [2081,a+64], [2081,a-65], [2083,a+241], [2083,a-242], [2087,a+920], [2087,a-921], [2111,a+215], [2111,a-216], [2129,a+130], [2129,a-131], [2137,a+261], [2137,a-262], [2143,a+683], [2143,a-684], [2153,a+739], [2153,a-740], [2179,a+355], [2179,a-356], [2207,a+932], [2207,a-933], [47,47], [2213,a+1028], [2213,a-1029], [2221,a+997], [2221,a-998], [2237,a+547], [2237,a-548], [2251,a+824], [2251,a-825], [2269,a+1071], [2269,a-1072], [2293,a+700], [2293,a-701], [2297,a+720], [2297,a-721], [2311,a+1131], [2311,a-1132], [2333,a+415], [2333,a-416], [2339,a+448], [2339,a-449], [2347,a+68], [2347,a-69], [2377,a+97], [2377,a-98], [2381,a+1073], [2381,a-1074], [2389,a+331], [2389,a-332], [2417,a+529], [2417,a-530], [2423,a+784], [2423,a-785], [2437,a+473], [2437,a-474], [2447,a+335], [2447,a-336], [2459,a+881], [2459,a-882], [2473,a+466], [2473,a-467], [2503,a+141], [2503,a-142], [2521,a+235], [2521,a-236], [2531,a+599], [2531,a-600], [2543,a+334], [2543,a-335], [2549,a+384], [2549,a-385], [2557,a+71], [2557,a-72], [2591,a+477], [2591,a-478], [2633,a+410], [2633,a-411], [2647,a+192], [2647,a-193], [2657,a+1159], [2657,a-1160], [2671,a+773], [2671,a-774], [2683,a+146], [2683,a-147], [2689,a+558], [2689,a-559], [2699,a+1191], [2699,a-1192], [2711,a+1329], [2711,a-1330], [2713,a+345], [2713,a-346], [2731,a+1002], [2731,a-1003], [2741,a+1075], [2741,a-1076], [2753,a+1289], [2753,a-1290], [2767,a+452], [2767,a-453], [2797,a+544], [2797,a-545], [2801,a+1330], [2801,a-1331], [2837,a+722], [2837,a-723], [2843,a+199], [2843,a-200], [2851,a+75], [2851,a-76], [2857,a+831], [2857,a-832], [2879,a+858], [2879,a-859], [2909,a+1020], [2909,a-1021], [2927,a+76], [2927,a-77], [2963,a+675], [2963,a-676], [2969,a+1261], [2969,a-1262], [3011,a+1029], [3011,a-1030], [3019,a+1309], [3019,a-1310], [3049,a+568], [3049,a-569], [3061,a+259], [3061,a-260], [3067,a+1195], [3067,a-1196], [3089,a+1003], [3089,a-1004], [3109,a+1123], [3109,a-1124], [3119,a+601], [3119,a-602], [3137,a+1169], [3137,a-1170], [3187,a+1441], [3187,a-1442], [3203,a+926], [3203,a-927], [3217,a+1472], [3217,a-1473], [3221,a+113], [3221,a-114], [3229,a+987], [3229,a-988], [3257,a+1014], [3257,a-1015], [3259,a+694], [3259,a-695], [3271,a+911], [3271,a-912], [3299,a+1397], [3299,a-1398], [3301,a+162], [3301,a-163], [3313,a+723], [3313,a-724], [3319,a+877], [3319,a-878], [3329,a+1082], [3329,a-1083], [3343,a+1353], [3343,a-1354], [3347,a+1371], [3347,a-1372], [3361,a+1267], [3361,a-1268], [3371,a+1656], [3371,a-1657], [3389,a+1617], [3389,a-1618], [3413,a+1008], [3413,a-1009], [3467,a+1324], [3467,a-1325], [3469,a+1340], [3469,a-1341], [59,59], [3511,a+118], [3511,a-119], [3529,a+1500], [3529,a-1501], [3539,a+1067], [3539,a-1068], [3557,a+404], [3557,a-405], [3571,a+84], [3571,a-85], [3581,a+1408], [3581,a-1409], [3593,a+456], [3593,a-457], [3607,a+1773], [3607,a-1774], [3613,a+1560], [3613,a-1561], [3623,a+318], [3623,a-319], [3637,a+1718], [3637,a-1719], [3677,a+752], [3677,a-753], [3691,a+121], [3691,a-122], [3697,a+227], [3697,a-228], [3719,a+1374], [3719,a-1375], [61,61], [3733,a+1550], [3733,a-1551], [3739,a+1544], [3739,a-1545], [3761,a+1033], [3761,a-1034], [3767,a+245], [3767,a-246], [3803,a+578], [3803,a-579], [3823,a+904], [3823,a-905], [3833,a+471], [3833,a-472], [3847,a+1756], [3847,a-1757], [3851,a+1894], [3851,a-1895], [3889,a+292], [3889,a-293], [3907,a+661], [3907,a-662], [3917,a+88], [3917,a-89], [3929,a+1231], [3929,a-1232], [3931,a+1525], [3931,a-1526], [3943,a+1412], [3943,a-1413], [4001,a+126], [4001,a-127], [4013,a+1367], [4013,a-1368], [4019,a+1199], [4019,a-1200], [4027,a+787], [4027,a-788], [4057,a+422], [4057,a-423], [4099,a+1101], [4099,a-1102], [4111,a+1860], [4111,a-1861], [4127,a+978], [4127,a-979], [4139,a+853], [4139,a-854], [4153,a+951], [4153,a-952], [4159,a+682], [4159,a-683], [4201,a+1137], [4201,a-1138], [4211,a+1342], [4211,a-1343], [4229,a+1825], [4229,a-1826], [4243,a+1312], [4243,a-1313], [4253,a+1079], [4253,a-1080], [4271,a+433], [4271,a-434], [4327,a+1398], [4327,a-1399], [4337,a+1634], [4337,a-1635], [4349,a+493], [4349,a-494], [4363,a+2148], [4363,a-2149], [4391,a+1668], [4391,a-1669], [4397,a+2039], [4397,a-2040], [4421,a+1992], [4421,a-1993], [4447,a+1816], [4447,a-1817], [4463,a+353], [4463,a-354], [4481,a+2129], [4481,a-2130], [4517,a+1112], [4517,a-1113], [4519,a+2078], [4519,a-2079], [4523,a+134], [4523,a-135], [4547,a+1921], [4547,a-1922], [4561,a+95], [4561,a-96], [4603,a+1301], [4603,a-1302], [4621,a+2147], [4621,a-2148], [4643,a+856], [4643,a-857], [4649,a+812], [4649,a-813], [4657,a+96], [4657,a-97], [4663,a+255], [4663,a-256], [4673,a+2048], [4673,a-2049], [4691,a+642], [4691,a-643], [4729,a+194], [4729,a-195], [4733,a+2275], [4733,a-2276], [4783,a+917], [4783,a-918], [4789,a+1214], [4789,a-1215], [4799,a+1446], [4799,a-1447], [4813,a+277], [4813,a-278], [4817,a+1356], [4817,a-1357], [4831,a+2162], [4831,a-2163], [4909,a+1449], [4909,a-1450], [4937,a+921], [4937,a-922], [4943,a+1120], [4943,a-1121], [4951,a+99], [4951,a-100], [4957,a+1811], [4957,a-1812], [4967,a+1059], [4967,a-1060], [4993,a+727], [4993,a-728], [4999,a+761], [4999,a-762], [5009,a+374], [5009,a-375], [5021,a+2220], [5021,a-2221], [5023,a+1314], [5023,a-1315], [5051,a+100], [5051,a-101], [5077,a+142], [5077,a-143], [5107,a+1229], [5107,a-1230], [5119,a+663], [5119,a-664], [5147,a+336], [5147,a-337], [5153,a+1923], [5153,a-1924], [5167,a+1626], [5167,a-1627], [5189,a+1819], [5189,a-1820], [5209,a+1623], [5209,a-1624], [5231,a+2063], [5231,a-2064], [5233,a+1087], [5233,a-1088], [5237,a+2498], [5237,a-2499], [5261,a+1719], [5261,a-1720], [5273,a+492], [5273,a-493], [5279,a+205], [5279,a-206], [5303,a+2189], [5303,a-2190], [73,73], [5387,a+790], [5387,a-791], [5399,a+756], [5399,a-757], [5413,a+2584], [5413,a-2585], [5419,a+1266], [5419,a-1267], [5441,a+2049], [5441,a-2050], [5443,a+1863], [5443,a-1864], [5471,a+1246], [5471,a-1247], [5483,a+2704], [5483,a-2705], [5503,a+2343], [5503,a-2344], [5527,a+1189], [5527,a-1190], [5531,a+1217], [5531,a-1218], [5569,a+298], [5569,a-299], [5573,a+1822], [5573,a-1823], [5581,a+2331], [5581,a-2332], [5623,a+2482], [5623,a-2483], [5639,a+1347], [5639,a-1348], [5651,a+572], [5651,a-573], [5653,a+1394], [5653,a-1395], [5657,a+1515], [5657,a-1516], [5693,a+2298], [5693,a-2299], [5737,a+726], [5737,a-727], [5741,a+283], [5741,a-284], [5749,a+1119], [5749,a-1120], [5779,a+107], [5779,a-108], [5783,a+2853], [5783,a-2854], [5791,a+2618], [5791,a-2619], [5807,a+2007], [5807,a-2008], [5821,a+1678], [5821,a-1679], [5839,a+960], [5839,a-961], [5849,a+2611], [5849,a-2612], [5861,a+1881], [5861,a-1882], [5867,a+519], [5867,a-520], [5881,a+613], [5881,a-614], [5903,a+712], [5903,a-713], [5923,a+510], [5923,a-511], [5987,a+309], [5987,a-310], [6007,a+1437], [6007,a-1438], [6029,a+2106], [6029,a-2107], [6043,a+1674], [6043,a-1675], [6073,a+1902], [6073,a-1903], [6091,a+3006], [6091,a-3007], [6101,a+2228], [6101,a-2229], [6113,a+2074], [6113,a-2075], [6133,a+221], [6133,a-222], [6143,a+953], [6143,a-954], [6197,a+2395], [6197,a-2396], [6199,a+2688], [6199,a-2689], [6203,a+2293], [6203,a-2294], [6211,a+2248], [6211,a-2249], [6217,a+111], [6217,a-112], [6269,a+1547], [6269,a-1548], [6287,a+1409], [6287,a-1410], [6301,a+3045], [6301,a-3046], [6311,a+2651], [6311,a-2652], [6323,a+2008], [6323,a-2009], [6329,a+112], [6329,a-113], [6337,a+2907], [6337,a-2908], [6343,a+2462], [6343,a-2463], [6353,a+2372], [6353,a-2373], [6367,a+2696], [6367,a-2697], [6379,a+1690], [6379,a-1691], [6421,a+2033], [6421,a-2034], [6427,a+453], [6427,a-454], [6449,a+2187], [6449,a-2188], [6451,a+2612], [6451,a-2613], [6469,a+754], [6469,a-755], [6491,a+2467], [6491,a-2468], [6521,a+161], [6521,a-162], [6547,a+605], [6547,a-606], [6553,a+616], [6553,a-617], [6563,a+2149], [6563,a-2150], [6577,a+1292], [6577,a-1293], [6581,a+380], [6581,a-381], [6619,a+430], [6619,a-431], [6637,a+755], [6637,a-756], [6659,a+765], [6659,a-766], [6661,a+1221], [6661,a-1222], [6673,a+2512], [6673,a-2513], [6679,a+1737], [6679,a-1738], [6689,a+2921], [6689,a-2922], [6701,a+2156], [6701,a-2157], [6703,a+3102], [6703,a-3103], [6763,a+545], [6763,a-546], [6791,a+2957], [6791,a-2958], [6827,a+330], [6827,a-331], [6829,a+1934], [6829,a-1935], [6833,a+1492], [6833,a-1493], [6841,a+711], [6841,a-712], [6857,a+3060], [6857,a-3061], [6869,a+2967], [6869,a-2968], [6871,a+1440], [6871,a-1441], [6883,a+3077], [6883,a-3078], [83,83], [6899,a+2061], [6899,a-2062], [6911,a+2264], [6911,a-2265], [6917,a+1708], [6917,a-1709], [6959,a+1876], [6959,a-1877], [6967,a+391], [6967,a-392], [6983,a+3266], [6983,a-3267], [6997,a+2751], [6997,a-2752], [7001,a+885], [7001,a-886], [7039,a+2477], [7039,a-2478], [7043,a+2793], [7043,a-2794], [7057,a+2500], [7057,a-2501], [7079,a+1839], [7079,a-1840], [7109,a+1455], [7109,a-1456], [7121,a+2000], [7121,a-2001], [7127,a+1954], [7127,a-1955], [7151,a+1315], [7151,a-1316], [7177,a+1233], [7177,a-1234], [7193,a+2135], [7193,a-2136], [7207,a+2753], [7207,a-2754], [7211,a+814], [7211,a-815], [7219,a+2273], [7219,a-2274], [7247,a+2309], [7247,a-2310], [7253,a+1834], [7253,a-1835], [7309,a+3449], [7309,a-3450], [7331,a+1642], [7331,a-1643], [7333,a+3524], [7333,a-3525], [7351,a+242], [7351,a-243], [7393,a+1732], [7393,a-1733], [7417,a+3015], [7417,a-3016], [7457,a+1980], [7457,a-1981], [7459,a+1257], [7459,a-1258], [7477,a+3122], [7477,a-3123], [7487,a+2711], [7487,a-2712], [7499,a+659], [7499,a-660], [7529,a+588], [7529,a-589], [7541,a+3626], [7541,a-3627], [7547,a+2131], [7547,a-2132], [7561,a+1699], [7561,a-1700], [7583,a+2038], [7583,a-2039], [7589,a+1142], [7589,a-1143], [7603,a+986], [7603,a-987], [7639,a+2893], [7639,a-2894], [7669,a+2173], [7669,a-2174], [7673,a+2392], [7673,a-2393], [7681,a+2869], [7681,a-2870], [7687,a+3377], [7687,a-3378], [7723,a+2691], [7723,a-2692], [7753,a+2098], [7753,a-2099], [7757,a+1341], [7757,a-1342], [7793,a+1095], [7793,a-1096], [7823,a+3642], [7823,a-3643], [7841,a+2154], [7841,a-2155], [7877,a+177], [7877,a-178], [7879,a+3700], [7879,a-3701], [7883,a+2669], [7883,a-2670], [7907,a+915]]; primes := [ideal : I in primesArray]; heckePol := x; K := Rationals(); e := 1; heckeEigenvaluesList := [* 0, 0, 0, 2, -4, 4, 0, 0, 2, -2, -2, -10, -10, 4, -4, 6, 6, 12, -12, 0, 0, 8, -8, 12, -12, -2, -2, 10, 10, -8, 8, 10, 10, -10, -10, 16, -16, 20, -20, 18, -20, 20, 24, -24, 10, 10, 22, 22, 4, -4, 10, 10, -8, 8, 16, -16, -10, -10, -6, -6, 2, -18, -18, -20, 20, 10, 10, -20, 20, 0, 0, -30, -10, -10, 4, -4, 22, 22, -6, -6, 6, 6, -24, 24, 4, -4, 2, 2, 18, 18, 40, -40, 0, 0, 4, -4, -28, 28, -34, -34, -20, 20, 30, 30, -30, -30, -20, 20, -32, 32, 6, 6, -30, -30, -16, 16, 10, 10, 14, 14, -12, 12, -30, -30, -20, 20, -34, -34, 22, 22, 12, -12, -16, 16, 24, -24, -10, -10, 18, 18, 54, 54, -16, 16, -20, 20, 24, -24, -2, -2, 20, -20, 20, -20, -40, 40, 32, -32, 12, -12, -6, -6, -30, 48, -48, 18, 18, -8, 8, 58, 58, -60, 60, -16, 16, 10, 10, -44, 44, 6, 6, 40, -40, 54, 54, 40, -40, -18, -18, 42, 42, -36, 36, -4, 4, 60, -60, -54, -54, -34, -34, 30, 30, -60, 60, -30, -30, -38, -38, 16, -16, 40, -40, -32, 32, 30, 30, 70, 70, 2, 2, 56, -56, -10, -10, -72, 72, 52, -52, -50, -50, 40, -40, -54, -54, -10, -10, 12, -12, -60, 60, 30, 30, 28, -28, -24, 24, -2, -2, 48, -48, -68, 68, -10, -10, -24, 24, -60, 60, 50, -18, -18, 4, -4, 54, 54, 12, -12, -40, 40, -20, 20, -50, -50, 34, 34, -16, 16, 24, -24, -46, -46, 38, 38, -66, -66, -46, -46, 46, 46, 30, 30, -72, 72, 20, -20, -76, 76, -30, -30, 12, -12, 16, -16, 6, 6, -58, -58, -30, -30, 44, -44, 48, -48, -24, 24, 18, 18, -38, -38, 24, -24, -14, -14, 28, -28, -8, 8, -62, -26, -26, 30, 30, -2, -2, 20, -20, -18, -18, 70, 70, -62, -62, -64, 64, 30, 30, -20, 20, -20, 20, 10, 10, -66, -66, -58, -58, -78, -78, 80, -80, 70, 70, 8, -8, -12, 12, 34, 34, 16, -16, -94, -94, -36, 36, -56, 56, 22, 22, -2, -2, -56, 56, 50, 50, 48, -48, -30, -30, -24, 24, 20, -20, -38, -38, -12, 12, 64, -64, 90, 90, -36, 36, -42, -42, 66, 66, -40, 40, -50, -50, -6, -6, 22, 22, 20, -20, -100, 100, 10, 10, -8, 8, -82, -82, 8, -8, 84, -84, -70, -70, -20, 20, -60, 60, 98, 98, 86, 86, -92, 92, 42, 42, -10, -10, -88, 88, -102, -102, -20, 20, -60, 60, 42, 42, 6, 6, -2, -2, 18, 18, -52, 52, 96, -96, 12, -12, -26, -26, -14, -14, 80, -80, -54, -54, -40, 40, -20, 20, -6, -6, -84, 84, 30, 30, 86, 86, -60, 60, 30, 30, -110, -80, 80, 42, 42, 68, -68, 22, 22, 4, -4, -82, -82, 74, 74, -80, 80, -50, -50, 16, -16, 38, 38, -98, -98, 44, -44, 50, 50, 112, -112, -78, -10, -10, -12, 12, 10, 10, -48, 48, 36, -36, 40, -40, -6, -6, -80, 80, 84, -84, 58, 58, -60, 60, -50, -50, 98, 98, 44, -44, 16, -16, 66, 66, 30, 30, -60, 60, 68, -68, -78, -78, -28, 28, 24, -24, -88, 88, 12, -12, 50, 50, 120, -120, 66, 66, -4, 4, 54, 54, -20, 20, 30, 30, 40, -40, -112, 112, -102, -102, 78, 78, 76, -76, -80, 80, 30, 30, 54, 54, -40, 40, 40, -40, -6, -6, -90, -90, 128, -128, 100, -100, 60, -60, -46, -46, 100, -100, 94, 94, 100, -100, 42, 42, 82, 82, 0, 0, 130, 130, 36, -36, 58, 58, 126, 126, -40, 40, -58, -58, 8, -8, -114, -114, 50, 50, -56, 56, -2, -2, 130, 130, 120, -120, -80, 80, 110, 110, 0, 0, 34, 34, -48, 48, 122, 122, -50, -50, -56, 56, -84, 84, -90, -90, -20, 20, 88, -88, -28, 28, -54, -54, -40, 40, 102, 102, 50, 50, 120, -120, 10, 10, 70, 70, -66, -66, -30, -30, 8, -8, 0, 0, 146, 60, -60, -48, 48, -74, -74, -28, 28, 74, 74, -140, 140, -56, 56, 60, -60, -56, 56, -80, 80, 68, -68, 26, 26, 54, 54, -34, -34, 96, -96, -48, 48, 36, -36, -26, -26, 90, 90, -130, -130, -22, -22, -114, -114, -90, -90, 12, -12, 0, 0, 8, -8, 120, -120, 94, 94, 88, -88, -102, -102, 86, 86, -132, 132, 50, 50, -40, 40, 116, -116, 60, -60, 112, -112, -2, -2, 76, -76, 34, 34, -60, 60, 70, 70, -86, -86, 54, 54, 40, -40, 70, 70, -64, 64, 60, -60, -36, 36, -118, -118, 62, 62, -8, 8, -50, -50, -16, 16, 84, -84, 58, 58, 10, 10, -80, 80, -54, -54, -8, 8, 52, -52, 6, 6, -68, 68, 42, 42, -124, 124, 118, 118, -20, 20, -6, -6, -20, 20, -14, -14, -84, 84, 122, 122, 86, 86, -148, 148, -130, -130, 28, -28, -154, -154, -6, -6, 80, -80, 2, 2, -98, -98, 104, -104, 36, -36, -96, 96, -148, 148, -82, -82, 50, 50, 114, 114, -150, -150, -10, -10, -16, 16, -60, 60, 34, -100, 100, 24, -24, 118, 118, -56, 56, 32, -32, 0, 0, 22, 22, -102, -102, -40, 40, 100, -100, 82, 82, 32, -32, -122, -122, 50, 50, 0, 0, 120, -120, -78, -78, -30, -30, 80, -80, -12, 12, 52, -52, 120, -120, -10, -10, 142, 142, 36, -36, -170, -170, -64, 64, 34, 34, 2, 2, -30, -30, 20, -20, 102, 102, -40, 40, -132, 132, 2, 2, 6, 6, -52, 52, 74, 74, -104, 104, -170, -170, 60, -60, 48, -48, 102, 102, -30, -30, -86, -86, -160, 160, 20, -20, -30, -30, 30, 30, 50, 50, 120, -120, -6, -6, -10, -10, 0, 0, 84, -84, 52 *]; heckeEigenvalues := AssociativeArray(); for i in [1..#heckeEigenvaluesList] do heckeEigenvalues[primes[i]] := heckeEigenvaluesList[i]; end for; ALEigenvalues := AssociativeArray(); 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;