Magma V2.24-6 Sun Jan 12 2020 21:03:52 on stan [Seed = 2480289706]
Type ? for help. Type -D to quit.
Computing space of Newforms.. 0.000
..done 0.281
Starting elimination.. 0.282
++++++++++++++++++++++ 0.282
working with form number => 12
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 13
trying auxiliary prime q = 17
{ 3, 5, 7 }
trying auxiliary prime q = 29
{ 7 }
{ 7 }
++++++++++++++++++++++ 0.325
working with form number => 16
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 11
trying auxiliary prime q = 13
{ 2, 13 }
trying auxiliary prime q = 17
{ 2, 13 }
trying auxiliary prime q = 29
{ 2, 13 }
{ 2, 13 }
**** not eliminated
++++++++++++++++++++++ 0.343
working with form number => 17
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5 }
trying auxiliary prime q = 13
{ 3 }
{ 3 }
++++++++++++++++++++++ 0.344
working with form number => 18
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5, 7 }
trying auxiliary prime q = 13
{ 2, 3, 7 }
{ 2, 3, 7 }
++++++++++++++++++++++ 0.344
working with form number => 19
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5, 7 }
trying auxiliary prime q = 13
{ 2, 3, 7 }
{ 2, 3, 7 }
++++++++++++++++++++++ 0.345
working with form number => 20
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 11
trying auxiliary prime q = 13
{ 3, 7, 13, 41, 71 }
trying auxiliary prime q = 17
{ 3, 7 }
{ 3, 7 }
++++++++++++++++++++++ 0.349
working with form number => 21
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 11
trying auxiliary prime q = 13
{ 3, 7, 13, 41, 71 }
trying auxiliary prime q = 17
{ 3, 7 }
{ 3, 7 }
++++++++++++++++++++++ 0.352
working with form number => 22
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 11
trying auxiliary prime q = 13
{ 3, 7, 13, 29 }
trying auxiliary prime q = 17
{ 3, 7, 13 }
trying auxiliary prime q = 29
{ 3, 7, 13 }
{ 3, 7, 13 }
**** not eliminated
++++++++++++++++++++++ 0.388
working with form number => 23
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 11
trying auxiliary prime q = 13
{ 3, 7, 13, 29 }
trying auxiliary prime q = 17
{ 3, 7, 13 }
trying auxiliary prime q = 29
{ 3, 7, 13 }
{ 3, 7, 13 }
**** not eliminated
++++++++++++++++++++++ 0.438
working with form number => 24
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5 }
trying auxiliary prime q = 13
{ 3 }
{ 3 }
++++++++++++++++++++++ 0.440
working with form number => 26
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5 }
trying auxiliary prime q = 13
{ 2 }
{ 2 }
++++++++++++++++++++++ 0.442
working with form number => 28
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 13
trying auxiliary prime q = 17
{ 3, 5, 7 }
trying auxiliary prime q = 29
{ 7 }
{ 7 }
++++++++++++++++++++++ 0.505
working with form number => 33
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5, 31 }
trying auxiliary prime q = 13
{ 2, 3 }
{ 2, 3 }
++++++++++++++++++++++ 0.507
working with form number => 38
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 7, 11, 17 }
trying auxiliary prime q = 13
{ 2, 7 }
{ 2, 7 }
++++++++++++++++++++++ 0.510
working with form number => 41
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5, 7, 17 }
trying auxiliary prime q = 13
{ 2, 3, 7 }
{ 2, 3, 7 }
++++++++++++++++++++++ 0.512
working with form number => 42
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 7, 11 }
trying auxiliary prime q = 13
{ 2, 3, 7 }
{ 2, 3, 7 }
++++++++++++++++++++++ 0.515
working with form number => 45
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 7, 11, 17, 137 }
trying auxiliary prime q = 13
{ 2, 3, 7 }
{ 2, 3, 7 }
++++++++++++++++++++++ 0.519
working with form number => 46
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 7, 19, 31 }
trying auxiliary prime q = 13
{ 3, 7 }
{ 3, 7 }
++++++++++++++++++++++ 0.522
working with form number => 47
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 7, 19, 31 }
trying auxiliary prime q = 13
{ 3, 7 }
{ 3, 7 }
++++++++++++++++++++++ 0.526
working with form number => 48
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 7 }
{ 2, 7 }
++++++++++++++++++++++ 0.529
working with form number => 51
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 7 }
{ 2, 7 }
++++++++++++++++++++++ 0.531
working with form number => 57
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5, 7, 11, 17 }
trying auxiliary prime q = 13
{ 3, 5, 7 }
trying auxiliary prime q = 17
{ 5, 7 }
trying auxiliary prime q = 29
{ 7 }
{ 7 }
++++++++++++++++++++++ 0.711
working with form number => 58
The coefficient field Kf contains K so the compositum is Kf
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 3, 5, 7, 11, 17 }
trying auxiliary prime q = 13
{ 3, 5, 7 }
trying auxiliary prime q = 17
{ 5, 7 }
trying auxiliary prime q = 29
{ 7 }
{ 7 }
Up to this point we have eliminated all but the forms indexed by i=60,61 and
those indexed by i=16,22,23 for exponent p=13
++++++++++++++++++++++ 0.906
We now apply refined elimination for the latter three forms using auxiliary
prime q=29
Applying refined elimination with form i=16 and exponent p=13 using auxiliary
prime q=29
Degree of coefficient field is 3
Degree of compositum of K and coefficient field is 3
Eliminated form i=16 completely.
++++++++++++++++++++++ 1.000
Applying refined elimination with form i=22 and exponent p=13 using auxiliary
prime q=29
Degree of coefficient field is 3
Degree of compositum of K and coefficient field is 3
Eliminated form i=22 completely.
++++++++++++++++++++++ 1.105
Applying refined elimination with form i=23 and exponent p=13 using auxiliary
prime q=29
Degree of coefficient field is 3
Degree of compositum of K and coefficient field is 3
Eliminated form i=23 completely.
++++++++++++++++++++++ 1.221
Up to this point we have eliminated all but forms i=60,61. These have field of
coefficients of degree 54 which causes the computations to take much longer for
each of them, but the elimination procedure is exactly the same.
Starting elimination of forms i=60,61
++++++++++++++++++++++ 1.221
working with form number => 60
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 5, 7, 11, 23, 47 }
trying auxiliary prime q = 13
{ 2, 7 }
{ 2, 7 }
++++++++++++++++++++++ 3.503
working with form number => 61
first bound obtained with auxiliary prime q= 5
trying auxiliary prime q = 11
{ 2, 5, 7, 11, 23, 47 }
trying auxiliary prime q = 13
{ 2, 7 }
{ 2, 7 }
We have eliminated all the forms, hence completing the proof of Theorem 6.25
++++++++++++++++++++++ 5.795
Total time: 20862.120 seconds, Total memory usage: 1954.75MB