[was@modular 11-06-01]$ [was@modular 11-06-01]$ Magma V2.8-2      Tue Nov  6 2001 15:26:27 on modular  [Seed = 2809453452]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> Attach("11-06-01.m");
> JE(13,7);
0
false
> JE(13,7);
Creating space of modular symbols of level 338 mod 7.
Time: 0.240
0
false
> JE(13,7);
Creating space of modular symbols of level 338 mod 7.
Time: 0.240
Computing Wp
Time: 0.220
Computing W2
Time: 0.130
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
0
false
> JE(11,7);
Creating space of modular symbols of level 242 mod 7.
Time: 0.160
Computing Wp
Time: 0.180
Computing W2
Time: 0.090
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
0
false
> JE(19,7);
Creating space of modular symbols of level 722 mod 7.
Time: 0.500
Computing Wp
Time: 0.520
Computing W2
Time: 0.280
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
0
false
> JE(19,7);
Creating space of modular symbols of level 722 mod 7.
Time: 0.510
Computing Wp
Time: 0.530
Computing W2
Time: 0.290
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
0
0
0
false
> x := JE(13,7);
Creating space of modular symbols of level 338 mod 7.
Time: 0.170
Computing Wp
Time: 0.470
Computing W2
Time: 0.270
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
{-1/224, 0} + 6*{-1/226, 0} + 6*{-1/334, 0} + {-1/336, 0}
{-1/108, 0} + 6*{-1/148, 0} + {-1/150, 0} + 6*{-1/166, 0} + {-1/176, 0} + 6*{-1/184, 0} + {-1/190, 0} + 6*{-1/196, 0} + {-1/204, 0} + 6*{-1/210, 0} + {-1/214, 0} + 6*{-1/222, 0} + 2*{-1/224, 0} + 6*{-1/226, 0} + 6*{-1/244, 0} + {-1/248, 0} + 6*{-1/252, 0} + 6*{-1/264, 0} + {-1/266, 0} + 6*{-1/290, 0} + {-1/294, 0} + 6*{-1/300, 0} + {-1/302, 0} + 6*{-1/318, 0} + {-1/320, 0} + 6*{-1/322, 0} + {-1/326, 0} + 6*{-1/332, 0} + {-1/336, 0}
2*{-1/108, 0} + 5*{-1/148, 0} + 2*{-1/150, 0} + 5*{-1/166, 0} + 2*{-1/176, 0} + 5*{-1/184, 0} + 2*{-1/190, 0} + 5*{-1/196, 0} + 2*{-1/204, 0} + 5*{-1/210, 0} + 2*{-1/214, 0} + 5*{-1/222, 0} + 4*{-1/224, 0} + 5*{-1/226, 0} + 5*{-1/244, 0} + 2*{-1/248, 0} + 5*{-1/252, 0} + 5*{-1/264, 0} + 2*{-1/266, 0} + 5*{-1/290, 0} + 2*{-1/294, 0} + 5*{-1/300, 0} + 2*{-1/302, 0} + 5*{-1/318, 0} + 2*{-1/320, 0} + 5*{-1/322, 0} + 2*{-1/326, 0} + 5*{-1/332, 0} + 2*{-1/336, 0}
false
> JE(13,7);
Creating space of modular symbols of level 338 mod 7.
Time: 0.230
Computing Wp
Time: 0.240
Computing W2
Time: 0.140
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/112, 0} + 5*{-1/114, 0}
2*{-1/88, 0} + 5*{-1/100, 0} + 2*{-1/108, 0} + 2*{-1/112, 0} + 5*{-1/114, 0} + 5*{-1/138, 0} + 2*{-1/144, 0} + 5*{-1/162, 0} + 2*{-1/164, 0} + 5*{-1/166, 0}
4*{-1/88, 0} + 3*{-1/100, 0} + 4*{-1/108, 0} + 4*{-1/112, 0} + 3*{-1/114, 0} + 3*{-1/138, 0} + 4*{-1/144, 0} + 3*{-1/162, 0} + 4*{-1/164, 0} + 3*{-1/166, 0}
false
> M := ModularSymbols(22);
> OldSubspace(M);

>> OldSubspace(M);
              ^
Runtime error in 'OldSubspace': Argument 1 must be cuspidal.
> x := JE(13,7);
Creating space of modular symbols of level 338 mod 7.
Time: 0.230
Computing Wp
Time: 0.220
Computing W2
Time: 0.130
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/112, 0} + 5*{-1/114, 0}
2*{-1/88, 0} + 5*{-1/100, 0} + 2*{-1/108, 0} + 2*{-1/112, 0} + 5*{-1/114, 0} + 5*{-1/138, 0} + 2*{-1/144, 0} + 5*{-1/162, 0} + 2*{-1/164, 0} + 5*{-1/166, 0}
> x;
4*{-1/88, 0} + 3*{-1/100, 0} + 4*{-1/108, 0} + 4*{-1/112, 0} + 3*{-1/114, 0} + 3*{-1/138, 0} + 4*{-1/144, 0} + 3*{-1/162, 0} + 4*{-1/164, 0} + 3*{-1/166, 0}
> x;
4*{-1/88, 0} + 3*{-1/100, 0} + 4*{-1/108, 0} + 4*{-1/112, 0} + 3*{-1/114, 0} + 3*{-1/138, 0} + 4*{-1/144, 0} + 3*{-1/162, 0} + 4*{-1/164, 0} + 3*{-1/166, 0}
> IsCuspidal(x);

>> IsCuspidal(x);
             ^
Runtime error in 'IsCuspidal': Bad argument types
Argument types given: ModSymElt
> C := CS(Parent(x));
> x in C;
true
> x := JE(13,7);
Creating space of modular symbols of level 338 mod 7.
Time: 0.240
Time: 0.080
Computing Wp
Time: 0.230
Computing W2
Time: 0.130
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/112, 0} + 5*{-1/114, 0}
2*{-1/88, 0} + 5*{-1/100, 0} + 2*{-1/108, 0} + 2*{-1/112, 0} + 5*{-1/114, 0} + 5*{-1/138, 0} + 2*{-1/144, 0} + 5*{-1/162, 0} + 2*{-1/164, 0} + 5*{-1/166, 0}
> x := JE(19,7);
Creating space of modular symbols of level 722 mod 7.
Time: 0.500
Time: 0.170
Computing Wp
Time: 0.520
Computing W2
Time: 0.280
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/240, 0} + 5*{-1/248, 0} + 2*{-1/308, 0} + 5*{-1/310, 0} + 2*{-1/332, 0} + 5*{-1/334, 0}
2*{-1/186, 0} + 5*{-1/216, 0} + 2*{-1/218, 0} + 2*{-1/240, 0} + 5*{-1/248, 0} + 5*{-1/280, 0} + 2*{-1/282, 0} + 2*{-1/308, 0} + 5*{-1/310, 0} + 2*{-1/332, 0} + 5*{-1/334, 0} + 5*{-1/358, 0}
> x := JE(5,7);
Creating space of modular symbols of level 50 mod 7.
Time: 0.040
Time: 0.010
Computing Wp
Time: 0.030
Computing W2
Time: 0.020
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/16, 0} + 5*{-1/22, 0}
4*{-1/16, 0} + 3*{-1/22, 0}
> OldSubspace(C);
Modular symbols space of level 338, weight 2, and dimension 19
> t, x := JE(5,7);t;
Creating space of modular symbols of level 50 mod 7.
Time: 0.040
Time: 0.010
Computing Wp
Time: 0.030
Computing W2
Time: 0.020
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/16, 0} + 5*{-1/22, 0}
4*{-1/16, 0} + 3*{-1/22, 0}
Dimension of old subspace =  0
false
> t, x := JE(5,7);t;
Creating space of modular symbols of level 50 mod 7.
Time: 0.040
Time: 0.010
Computing Wp
Time: 0.020
Computing W2
Time: 0.020
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/16, 0} + 5*{-1/22, 0}
4*{-1/16, 0} + 3*{-1/22, 0}
Dimension of old subspace =  0
false
> t, x := JE(5,389);t;
Creating space of modular symbols of level 50 mod 389.
Time: 0.040
Time: 0.010
Computing Wp
Time: 0.030
Computing W2
Time: 0.020
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/16, 0} + 387*{-1/22, 0}
4*{-1/16, 0} + 385*{-1/22, 0}
Dimension of old subspace =  0
false
> t, x := JE(17,389);t;
Creating space of modular symbols of level 578 mod 389.
Time: 0.410
Time: 0.130
Computing Wp
Time: 0.410
Computing W2
Time: 0.230
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/192, 0} + 387*{-1/194, 0}
2*{-1/150, 0} + 387*{-1/172, 0} + 2*{-1/174, 0} + 2*{-1/192, 0} + 387*{-1/194, 0} + 387*{-1/224, 0} + 2*{-1/228, 0} + 387*{-1/274, 0} + 2*{-1/276, 0} + 387*{-1/286, 0}
Dimension of old subspace =  36
false
> t, x := JE(17,389);t;
Creating space of modular symbols of level 578 mod 389.
Time: 0.420
Time: 0.130
Computing Wp
Time: 0.410
Computing W2
Time: 0.250
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/192, 0} + 387*{-1/194, 0}
2*{-1/150, 0} + 387*{-1/172, 0} + 2*{-1/174, 0} + 2*{-1/192, 0} + 387*{-1/194, 0} + 387*{-1/224, 0} + 2*{-1/228, 0} + 387*{-1/274, 0} + 2*{-1/276, 0} + 387*{-1/286, 0}
Computing old subspace
Time: 1.320
Dimension of old subspace =  36
false
> t, x := JE(17,389);t;
Creating space of modular symbols of level 578 mod 389.
Time: 0.420
Time: 0.130
Computing Wp
Time: 0.410
Computing W2
Time: 0.230
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/192, 0} + 387*{-1/194, 0}
2*{-1/150, 0} + 387*{-1/172, 0} + 2*{-1/174, 0} + 2*{-1/192, 0} + 387*{-1/194, 0} + 387*{-1/224, 0} + 2*{-1/228, 0} + 387*{-1/274, 0} + 2*{-1/276, 0} + 387*{-1/286, 0}
Computing old subspace
Time: 1.400
Dimension of old subspace =  36
Dimension of new subspace =  23
false
> t, x := JE(19,389);t;
Creating space of modular symbols of level 722 mod 389.
Time: 0.530
Time: 0.170
Computing Wp
Time: 0.530
Computing W2
Time: 0.310
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/240, 0} + 387*{-1/248, 0} + 2*{-1/308, 0} + 387*{-1/310, 0} + 2*{-1/332, 0} + 387*{-1/334, 0}
2*{-1/186, 0} + 387*{-1/216, 0} + 2*{-1/218, 0} + 2*{-1/240, 0} + 387*{-1/248, 0} + 387*{-1/280, 0} + 2*{-1/282, 0} + 2*{-1/308, 0} + 387*{-1/310, 0} + 2*{-1/332, 0} + 387*{-1/334, 0} + 387*{-1/358, 0}
Computing old subspace
Time: 2.010
Dimension of old subspace =  48
Dimension of new subspace =  28
false
> t, x := JE(23,389);t;
Creating space of modular symbols of level 1058 mod 389.
Time: 0.800
Time: 0.260
Computing Wp
Time: 0.850
Computing W2
Time: 0.460
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/352, 0} + 387*{-1/356, 0} + 2*{-1/452, 0} + 387*{-1/454, 0}
2*{-1/268, 0} + 387*{-1/316, 0} + 2*{-1/318, 0} + 2*{-1/352, 0} + 387*{-1/356, 0} + 2*{-1/452, 0} + 387*{-1/454, 0} + 387*{-1/526, 0}
Computing old subspace
Time: 3.710
Dimension of old subspace =  72
Dimension of new subspace =  43
false
> t, x := JE(23,5);t;
Creating space of modular symbols of level 1058 mod 5.
Time: 0.760
Time: 0.240
Computing Wp
Time: 0.820
Computing W2
Time: 0.430
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0}
2*{-1/268, 0} + 3*{-1/316, 0} + 2*{-1/318, 0} + 2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0} + 3*{-1/526, 0}
Computing old subspace
Time: 2.840
Dimension of old subspace =  72
Dimension of new subspace =  43
false
> t, x := JE(23,2);t;
Creating space of modular symbols of level 1058 mod 2.
Time: 0.760
Time: 0.270
WARNING: Dimensions are off because of spurious torsion -- trust nothing!
Computing Wp
Time: 0.810
Computing W2
Time: 0.420
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
0
0
Computing old subspace


[Interrupted]
false
> > > 
> 
> 
> 
> ;
> t, x := JE(23,2);t;
Creating space of modular symbols of level 1058 mod 2.
Time: 0.740
Time: 0.280
Computing Wp
Time: 0.830
Computing W2
Time: 0.450
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
0
0
Computing old subspace

[Interrupted]
false
> t, x := JE(23,2);t;

In file "/home/was/people/ellenberg/11-06-01/11-06-01.m", line 12, column 4:
>>    /* I'm just computing in the -1 quotient by complex conjugation, since
      ^
User error: Unterminated /* comment

>> t, x := JE(23,2);t;
           ^
User error: Identifier 'JE' has not been declared or assigned
false
> t, x := JE(23,5);t;
Creating space of modular symbols of level 1058 mod 5.
Time: 0.760
Time: 0.240
Computing Wp
Time: 0.810
Computing W2
Time: 0.430
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0}
2*{-1/268, 0} + 3*{-1/316, 0} + 2*{-1/318, 0} + 2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0} + 3*{-1/526, 0}
Computing old subspace
Time: 3.020
Dimension of old subspace =  72
Dimension of new subspace =  43
false
> t, x := JE(23,5);t;
Creating space of modular symbols of level 1058 mod 5.
Time: 0.810
Time: 0.240
Computing Wp
Time: 0.820
Computing W2
Time: 0.450
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0}
2*{-1/268, 0} + 3*{-1/316, 0} + 2*{-1/318, 0} + 2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0} + 3*{-1/526, 0}
Computing old subspace
Time: 3.080
Dimension of old subspace =  72
Dimension of new subspace =  43
true
> t, x := JE(23,5);t;
Creating space of modular symbols of level 1058 mod 5.
Time: 0.760
Time: 0.240
Computing Wp
Time: 0.810
Computing W2
Time: 0.450
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0}
2*{-1/268, 0} + 3*{-1/316, 0} + 2*{-1/318, 0} + 2*{-1/352, 0} + 3*{-1/356, 0} + 2*{-1/452, 0} + 3*{-1/454, 0} + 3*{-1/526, 0}
Computing old subspace
Time: 2.910
Dimension of old subspace =  72
Dimension of new subspace =  43
Total time =  5.21  seconds
true
> t, x := JE(29,5);t;
Creating space of modular symbols of level 1682 mod 5.
Time: 1.250
Time: 0.320
Computing Wp
Time: 1.350
Computing W2
Time: 0.710
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
2*{-1/560, 0} + 3*{-1/562, 0}
2*{-1/432, 0} + 3*{-1/452, 0} + 2*{-1/454, 0} + 3*{-1/466, 0} + 2*{-1/470, 0} + 3*{-1/504, 0} + 2*{-1/506, 0} + 2*{-1/560, 0} + 3*{-1/562, 0} + 3*{-1/642, 0} + 2*{-1/644, 0} + 3*{-1/760, 0} + 2*{-1/762, 0} + 3*{-1/788, 0} + 2*{-1/790, 0} + 3*{-1/838, 0}
Computing old subspace
Time: 6.940
Dimension of old subspace =  121
Dimension of new subspace =  67
Total time =  10.599  seconds
true
> t, x := JE(29,5);t;

In file "/home/was/people/ellenberg/11-06-01/11-06-01.m", line 9, column 26:
>> (1+w_p)(1-w_2){-1/4,1/4} in S_2(Gamma_0(2*p^2);GF(ell)) 
                            ^
User error: bad syntax

>> t, x := JE(29,5);t;
           ^
User error: Identifier 'JE' has not been declared or assigned
true
> > t, x := JE(29,5);t;
Creating space of modular symbols of level 1682 mod 5.
Time: 1.290
Time: 0.320
Computing Wp
Time: 1.350
Computing W2
Time: 0.710
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/432, 0} + {-1/452, 0} + 4*{-1/454, 0} + {-1/466, 0} + 4*{-1/470, 0} + {-1/504, 0} + 4*{-1/506, 0} + 4*{-1/560, 0} + {-1/562, 0} + {-1/642, 0} + 4*{-1/644, 0} + {-1/760, 0} + 4*{-1/762, 0} + {-1/788, 0} + 4*{-1/790, 0} + {-1/838, 0}
Computing old subspace
Time: 6.960
Dimension of old subspace =  121
Dimension of new subspace =  67
Total time =  10.65  seconds
true
> t, x := JE(31,5);t;
Creating space of modular symbols of level 1922 mod 5.
Time: 1.460
Time: 0.470
Computing Wp
Time: 1.490
Computing W2
Time: 0.780
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/484, 0} + {-1/576, 0} + 4*{-1/578, 0} + 4*{-1/640, 0} + {-1/642, 0} + {-1/958, 0}
Computing old subspace (this takes the most time, by far)

[Interrupted]
true
> t, x := JE(31,997);t;
Creating space of modular symbols of level 1922 mod 997.
Time: 1.580
Time: 0.440
Computing Wp
Time: 1.650
Computing W2
Time: 0.810
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/484, 0} + 993*{-1/576, 0} + 4*{-1/578, 0} + 4*{-1/640, 0} + 993*{-1/642, 0} + 993*{-1/958, 0}
Computing old subspace (this takes the most time, by far)
Time: 13.240
Dimension of old subspace =  140
Dimension of new subspace =  77
Total time =  17.74  seconds
true
> t, x := JE(11,0);t;
Creating space of modular symbols of level 242 mod 0.
Time: 0.190
Time: 0.060
Computing Wp
Time: 0.170
Computing W2
Time: 0.120
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/68, 0} + -4*{-1/72, 0} + 4*{-1/74, 0} + 4*{-1/80, 0} + -4*{-1/82, 0} + -4*{-1/118, 0}
Computing old subspace (this takes the most time, by far)
Time: 0.640
Dimension of old subspace =  12
Dimension of new subspace =  10
Total time =  1.199  seconds
true
> t, x := JE(29,0);t;
Creating space of modular symbols of level 1682 mod 0.
Time: 1.690
Time: 0.380
Computing Wp
Time: 1.430
Computing W2
Time: 0.770
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/432, 0} + -4*{-1/452, 0} + 4*{-1/454, 0} + -4*{-1/466, 0} + 4*{-1/470, 0} + -4*{-1/504, 0} + 4*{-1/506, 0} + 4*{-1/560, 0} + -4*{-1/562, 0} + -4*{-1/642, 0} + 4*{-1/644, 0} + -4*{-1/760, 0} + 4*{-1/762, 0} + -4*{-1/788, 0} + 4*{-1/790, 0} + -4*{-1/838, 0}
Computing old subspace (this takes the most time, by far)
Time: 20.050
Dimension of old subspace =  120
Dimension of new subspace =  68
Total time =  24.36  seconds
true
> x;
4*{-1/432, 0} + -4*{-1/452, 0} + 4*{-1/454, 0} + -4*{-1/466, 0} + 4*{-1/470, 0} + -4*{-1/504, 0} + 4*{-1/506, 0} + 4*{-1/560, 0} + -4*{-1/562, 0} + -4*{-1/642, 0} + 4*{-1/644, 0} + -4*{-1/760, 0} + 4*{-1/762, 0} + -4*{-1/788, 0} + 4*{-1/790, 0} + -4*{-1/838, 0}
> JE;
Intrinsic 'JE'

Signatures:

(<RngIntElt> p, <RngIntElt> ell) -> BoolElt, ModSymElt

True if and only if the modular symbol (1+w_p)(1-w_2){-1/4,1/4} in S_2(Gamma_0(2*p^2);GF(ell)) is not old. Use ell = 0 to do the computation in characteristic 0.


> SetColumns(70);
> JE;
Intrinsic 'JE'

Signatures:

    (<RngIntElt> p, <RngIntElt> ell) -> BoolElt, ModSymElt

        True if and only if the modular symbol 
        (1+w_p)(1-w_2){-1/4,1/4} in S_2(Gamma_0(2*p^2);GF(ell)) is not
        old. Use ell = 0 to do the computation in characteristic 0.


> JE(11,997);
Creating space of modular symbols of level 242 mod 997.
Time: 0.190
Time: 0.050
Computing Wp
Time: 0.170
Computing W2
Time: 0.110
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/68, 0} + 993*{-1/72, 0} + 4*{-1/74, 0} + 4*{-1/80, 0} + 
993*{-1/82, 0} + 993*{-1/118, 0}
Computing old subspace (this takes the most time, by far)
Time: 0.510
Dimension of old subspace =  12
Dimension of new subspace =  10
Total time =  1.039  seconds
true 4*{-1/68, 0} + 993*{-1/72, 0} + 4*{-1/74, 0} + 4*{-1/80, 0} + 
993*{-1/82, 0} + 993*{-1/118, 0}
> JE(31,997);
Creating space of modular symbols of level 1922 mod 997.
Time: 1.530
Time: 0.440
Computing Wp
Time: 1.580
Computing W2
Time: 0.780
Computing x = {-1/4,1/4}(1-w_2)(1+w_p).
x =  4*{-1/484, 0} + 993*{-1/576, 0} + 4*{-1/578, 0} + 4*{-1/640, 0} +
993*{-1/642, 0} + 993*{-1/958, 0}
Computing old subspace (this takes the most time, by far)
Time: 13.240
Dimension of old subspace =  140
Dimension of new subspace =  77
Total time =  17.6  seconds
true 4*{-1/484, 0} + 993*{-1/576, 0} + 4*{-1/578, 0} + 4*{-1/640, 0} +
993*{-1/642, 0} + 993*{-1/958, 0}
>