Sharedwww / Tables / hecke.psOpen in CoCalc
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%%Title: hecke.dvi
%%CreationDate: Tue Sep 30 19:24:14 2003
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%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips.exe -P pdf -G0 hecke
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 46 /period put
dup 66 /B put
dup 72 /H put
dup 75 /K put
dup 76 /L put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 102 /f put
dup 105 /i put
dup 107 /k put
dup 110 /n put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 74 /J put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 83 /S put
dup 84 /T put
dup 87 /W put
dup 97 /a put
dup 102 /f put
dup 105 /i put
dup 107 /k put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 115 /s put
dup 116 /t put
dup 120 /x put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 46 /period put
dup 58 /colon put
dup 67 /C put
dup 70 /F put
dup 72 /H put
dup 77 /M put
dup 81 /Q put
dup 82 /R put
dup 84 /T put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 123 /endash put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 8 /circleplus put
dup 10 /circlemultiply put
dup 15 /bullet put
dup 21 /greaterequal put
dup 24 /similar put
dup 25 /approxequal put
dup 26 /propersubset put
dup 33 /arrowright put
dup 49 /infinity put
dup 50 /element put
dup 92 /intersection put
dup 106 /bar put
dup 110 /backslash put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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0 1 255 {1 index exch /.notdef put} for
dup 101 /e put
dup 102 /f put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 116 /t put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTT10
%!PS-AdobeFont-1.1: CMTT10 1.00B
%%CreationDate: 1992 Apr 26 10:42:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 35 /numbersign put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /less put
dup 61 /equal put
dup 62 /greater put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
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dup 75 /K put
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dup 81 /Q put
dup 82 /R put
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dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 94 /asciicircum put
dup 95 /underscore put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
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dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
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dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 126 /asciitilde put
readonly def
/FontBBox{-4 -235 731 800}readonly def
/UniqueID 5000832 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTT12
%!PS-AdobeFont-1.1: CMTT12 1.0
%%CreationDate: 1991 Aug 20 16:45:46
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 69 /E put
dup 72 /H put
dup 75 /K put
readonly def
/FontBBox{-1 -234 524 695}readonly def
/UniqueID 5000833 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 14 /ffi put
dup 19 /acute put
dup 34 /quotedblright put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 58 /colon put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 75 /K put
dup 77 /M put
dup 84 /T put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 104 /h put
dup 108 /l put
dup 109 /m put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueID 5000772 def
currentdict end
currentfile eexec
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Fg(Q)p Fn(\))385 b Fh(\012)e Fg(Q)651 b Fh(\031)g Fg(Q)383
b Fh(\010)g Fg(Q)p Fn(.)1111 b(This)575 b(is)g(in)h(fact)g(the)f(case,)
627 b(though)576 b(w)-31 b(e)576 b(will)h(not)f(pro)-31
b(v)g(e)6863 37083 y(it)512 b(here.)916 b(\(I)511 b(ha)-31
b(v)g(en't)513 b(y)-31 b(et)511 b(implemen)-31 b(ted)513
b(a)e(function)h(for)f(computation)j Ff(L)40162 36681
y Fa(0)40473 37083 y Fn(\()p Ff(A;)184 b Fn(1\),)549
b(so)6863 38412 y(the)452 b(rank)f(can't)h(y)-31 b(et)452
b(b)31 b(e)451 b(b)31 b(ounded)451 b(from)h(within)h
Fk(HECKE)p Fn(.\))f(What)g(ab)31 b(out)452 b(the)f(torsion?)6863
39740 y(T)-31 b(yp)31 b(e)414 b Fk(125.torsionbound\(13\))i
Fn(to)e(get)g(an)f(upp)31 b(er)412 b(b)31 b(ound)413
b(on)h(the)f(torsion)h(subgroup)6863 41068 y(of)470 b
Ff(J)8838 41234 y Fi(0)9335 41068 y Fn(\(125\).)796 b(Then)470
b(t)-31 b(yp)31 b(e)470 b Fk(125.cusporder)h Fn(to)f(compute)h(the)f
(order)f(of)h(\(0\))315 b Fh(\000)e Fn(\()p Fh(1)p Fn(\))475
b Fh(2)6863 42397 y Ff(J)7477 42563 y Fi(0)7974 42397
y Fn(\(125\)\()p Fg(Q)p Fn(\).)8607 44610 y Fk(?)581
b(125.torsionbound\(13\))8607 45939 y(5^2)8607 47267
y(?)g(125.cusporder)8607 48596 y(5^2)6863 50809 y Fn(W)-92
b(e're)516 b(luc)-31 b(ky)518 b({)g(the)f(lo)-31 b(w)g(er)518
b(and)g(upp)31 b(er)516 b(b)31 b(ounds)516 b(matc)-31
b(h)519 b(up)d(and)i(w)-31 b(e)517 b(conclude)h(that)6863
52138 y Ff(J)106 b Fn(\()p Fg(Q)p Fn(\))310 b Fh(\031)e
Fg(Z)11656 51736 y Fi(2)12398 52138 y Fh(\010)246 b Fn(\()p
Fg(Z)p Ff(=)p Fn(25)p Fg(Z)p Fn(\).)496 b(Next)370 b(t)-31
b(yp)31 b(e)370 b Fk(125A.intersection\(B\))j Fn(to)d(obtain)h(the)f
(struc-)6863 53466 y(ture)412 b(of)h(the)g(\014nite)g(ab)31
b(elian)414 b(group)f Ff(A)23272 53064 y Fa(0)23857 53466
y Fh(\\)275 b Ff(B)25766 53064 y Fa(0)26455 53466 y Fh(\032)380
b Ff(J)106 b Fn(,)424 b(where)412 b Ff(A)33221 53064
y Fa(0)33532 53466 y Fn(,)423 b Ff(B)35158 53064 y Fa(0)35880
53466 y Fn(are)413 b(the)f(ab)31 b(elian)414 b(v)-61
b(a-)6863 54795 y(rieties)371 b(dual)h(to)f Ff(A)g Fn(and)g
Ff(B)56 b Fn(.)496 b(The)371 b(answ)-31 b(er)371 b Fk([2,2,2,2])h
Fn(indicates)g(that)g(the)e(in)-31 b(tersection)6863
56123 y(is)354 b(\()p Fg(Z)p Ff(=)p Fn(2)p Fg(Z)p Fn(\))11483
55721 y Fi(4)11982 56123 y Fn(.)487 b(This)355 b(implies)g(that)h(the)e
(corresp)31 b(onding)354 b(newforms)h(satisfy)g(a)g(congruence)6863
57451 y(in)370 b(c)-31 b(haracteristic)370 b(2.)493 b(T)-92
b(o)370 b(exit)g Fk(calc)g Fn(mo)31 b(de,)370 b(t)-31
b(yp)31 b(e)370 b Fh(n)p Fk(q)p Fn(.)8524 58780 y(This)263
b(tutorial)i(has)e(barely)g(scratc)-31 b(hed)263 b(the)g(surface)g(of)g
(what)h(is)f(p)31 b(ossible)263 b(using)g Fk(HECKE)p
Fn(.)6863 60108 y(If)369 b(y)-31 b(ou)370 b(are)f(in)-31
b(teresting)371 b(in)e(learning)i(more,)f(talk)g(to)g(me.)25681
70071 y(6)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF