Magma V2.7-1 Wed Feb 7 2001 11:16:40 on modular [Seed = 230037943] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Victor Miller with field: Finite field of size 123456791 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456803 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456811 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456821 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456841 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456871 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456887 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0.01 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456919 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456937 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456967 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123456979 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457067 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457099 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457121 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457127 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0.01 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457129 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0.01 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457157 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457163 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457189 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457199 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Victor Miller with field: Finite field of size 123457211 Computing basis. Compute the primitive Eisenstein series. Find all pairs of integers a, b such that 4*a + 6*b = k. Making power list. made pow lists: 0 Compute generators. There are 9 generators. Coerce into vectors. Compute corresponding vector space. The space has dimension 9 Computing Hecke operator. Breaking out after 20 iterations. 1 p= 17 1 p= 19 1 p= 23 1 p= 29 2 p= 31 2 p= 37 3 p= 41 3 p= 43 4 p= 47 Doing a CRT: time = 0 5 p= 53 6 p= 59 7 p= 61 8 p= 67 8 p= 71 9 p= 73 Doing a CRT: time = 0 10 p= 79 11 p= 83 12 p= 89 12 p= 97 12 p= 101 13 p= 103 14 p= 107 Doing a CRT: time = 0 15 p= 109 16 p= 113 17 p= 127 18 p= 131 19 p= 137 Doing a CRT: time = 0 20 p= 139 21 p= 149 22 p= 151 23 p= 157 24 p= 163 Doing a CRT: time = 0 25 p= 167 26 p= 173 27 p= 179 28 p= 181 29 p= 191 Doing a CRT: time = 0.009 30 p= 193 30 p= 197 31 p= 199 31 p= 211 32 p= 223 33 p= 227 34 p= 229 Doing a CRT: time = 0.01 35 p= 233 36 p= 239 37 p= 241 38 p= 251 39 p= 257 Doing a CRT: time = 0 40 p= 263 41 p= 269 42 p= 271 43 p= 277 44 p= 281 Doing a CRT: time = 0 45 p= 283 46 p= 293 47 p= 307 48 p= 311 49 p= 313 Doing a CRT: time = 0 50 p= 317 51 p= 331 52 p= 337 53 p= 347 54 p= 349 Doing a CRT: time = 0 55 p= 353 56 p= 359 57 p= 367 58 p= 373 59 p= 379 Doing a CRT: time = 0 60 p= 383 61 p= 389 62 p= 397 63 p= 401 64 p= 409 Doing a CRT: time = 0 65 p= 419 66 p= 421 67 p= 431 68 p= 433 69 p= 439 Doing a CRT: time = 0.009 70 p= 443 71 p= 449 72 p= 457 73 p= 461 74 p= 463 Doing a CRT: time = 0 75 p= 467 76 p= 479 77 p= 487 78 p= 491 79 p= 499 Doing a CRT: time = 0 80 p= 503 81 p= 509 82 p= 521 83 p= 523 84 p= 541 Doing a CRT: time = 0 85 p= 547 86 p= 557 87 p= 563 88 p= 569 89 p= 571 Doing a CRT: time = 0 Total time = 0.37 Time: 0.729 f := x^8 + 282956306495420632223520*x^7 - 654930413212732504946037995131166975954933115456*x^6 - 165084966533836923243242194489634139612218430138052186401310505844195840*x^5 + 128010129805587224356741983272929408572588510991554487029097551300827491744958425758052558603776*x^4 + 27828062861342031000873723366489473709613551545625213947045384494597043043323942316541045445147159734981550998263029760*x^3 - 7405672740767834783569517900919951149976885933538812161802297775958129508065708267325587520657920704715370150302089518665227636512179481624576*x^2 - 906509290182180272584987516355636913194979730795718259864303969373341758643306084838039507296439446869091964642899632253565890263434825597403607792348839745082490880*x + 136742805179979708140223733532725681956637673190338132609727104888361887293463930399407517597419013706280943396451013911232196374125336766062775904004423451101820001374465617876193409826816 Saving Magma state to "100a.session" slopes := [* 4, 4, 9, 14, 14, 18, 22, 22 *] Saving Magma state to "100b.session" Total time: 2.270 seconds