[was@form fearnley]$ [was@form fearnley]$ Magma V2.7-1      Thu Nov 16 2000 21:07:37 on form     [Seed = 3454253939]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/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
> M:=ModularSymbols(11,2);
> M;
Full Modular symbols space of level 11, weight 2, and dimension 3
> Basis(M);
[
{-1/7, 0},
{-1/5, 0},
{oo, 0}
]
> D:=Decomposition(M,7);
> D;
[
Modular symbols space of level 11, weight 2, and dimension 1,
Modular symbols space of level 11, weight 2, and dimension 2
]
> qEigenform(D[2],17);
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + q^11 - 2*q^12 + 4*q^13 + 4*q^14 - q^15 - 4*q^16 + O(q^17)
> E:=D[2];
> qEigenform(E,200);
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + q^11 - 2*q^12 + 4*q^13 + 4*q^14 - q^15 - 4*q^16 - 2*q^17 + 4*q^18 + 2*q^20 + 2*q^21 - 2*q^22 - q^23 - 4*q^25 - 8*q^26 + 5*q^27 - 4*q^28 + 2*q^30 + 7*q^31 + 8*q^32 - q^33 + 4*q^34 - 2*q^35 - 4*q^36 + 3*q^37 - 4*q^39 - 8*q^41 - 4*q^42 - 6*q^43 + 2*q^44 - 2*q^45 + 2*q^46 + 8*q^47 + 4*q^48 - 3*q^49 + 8*q^50 + 2*q^51 + 8*q^52 - 6*q^53 - 10*q^54 + q^55 + 5*q^59 - 2*q^60 + 12*q^61 - 14*q^62 + 4*q^63 - 8*q^64 + 4*q^65 + 2*q^66 - 7*q^67 - 4*q^68 + q^69 + 4*q^70 - 3*q^71 + 4*q^73 - 6*q^74 + 4*q^75 - 2*q^77 + 8*q^78 - 10*q^79 - 4*q^80 + q^81 + 16*q^82 - 6*q^83 + 4*q^84 - 2*q^85 + 12*q^86 + 15*q^89 + 4*q^90 - 8*q^91 - 2*q^92 - 7*q^93 - 16*q^94 - 8*q^96 - 7*q^97 + 6*q^98 - 2*q^99 - 8*q^100 + 2*q^101 - 4*q^102 - 16*q^103 + 2*q^105 + 12*q^106 + 18*q^107 + 10*q^108 + 10*q^109 - 2*q^110 - 3*q^111 + 8*q^112 + 9*q^113 - q^115 - 8*q^117 - 10*q^118 + 4*q^119 + q^121 - 24*q^122 + 8*q^123 + 14*q^124 - 9*q^125 - 8*q^126 + 8*q^127 + 6*q^129 - 8*q^130 - 18*q^131 - 2*q^132 + 14*q^134 + 5*q^135 - 7*q^137 - 2*q^138 + 10*q^139 - 4*q^140 - 8*q^141 + 6*q^142 + 4*q^143 + 8*q^144 - 8*q^146 + 3*q^147 + 6*q^148 - 10*q^149 - 8*q^150 + 2*q^151 + 4*q^153 + 4*q^154 + 7*q^155 - 8*q^156 - 7*q^157 + 20*q^158 + 6*q^159 + 8*q^160 + 2*q^161 - 2*q^162 + 4*q^163 - 16*q^164 - q^165 + 12*q^166 - 12*q^167 + 3*q^169 + 4*q^170 - 12*q^172 - 6*q^173 + 8*q^175 - 4*q^176 - 5*q^177 - 30*q^178 - 15*q^179 - 4*q^180 + 7*q^181 + 16*q^182 - 12*q^183 + 3*q^185 + 14*q^186 - 2*q^187 + 16*q^188 - 10*q^189 + 17*q^191 + 8*q^192 + 4*q^193 + 14*q^194 - 4*q^195 - 6*q^196 - 2*q^197 + 4*q^198 + O(q^200)
> phi:=PeriodMapping(E,200);
> phi;
Mapping from: ModSym: M to Full Vector space of degree 1 over Complex Field given by a rule [no inverse]
> M;
Full Modular symbols space of level 11, weight 2, and dimension 3
> Basis(M);
[
{-1/7, 0},
{-1/5, 0},
{oo, 0}
]
> M.1;
{-1/7, 0}
> M.2;
{-1/5, 0}
> M.3;
{oo, 0}
> phi(M.1);
(-0.6346046521397767108443973084 - 1.458816616938495229330889613*i)
> phi(M!<1,[17/3,5/19]>);
( 0.E-28 + 2.917633233876990458661779226*i)
> M:=ModularSymbols(40);
> D:=Decomposition(M,7);
> D;
[
Modular symbols space of level 40, weight 2, and dimension 7,
Modular symbols space of level 40, weight 2, and dimension 2,
Modular symbols space of level 40, weight 2, and dimension 4
]
> C:=CuspidalSubspace(M);
> C;
Modular symbols space of level 40, weight 2, and dimension 6
> D:=Decomposition(C,7);
> D;
[
Modular symbols space of level 40, weight 2, and dimension 2,
Modular symbols space of level 40, weight 2, and dimension 4
]
> E:=EllipticCurve(D[1]);
> E;
Elliptic Curve defined by y^2 = x^3 - 7*x - 6 over Rational Field
> phi:=PeriodMapping(D[1],200);
> phi(M!<1,[17/3,5/19]>);
(1.484412473422423143066783777 +  0.E-38*i)
> Periods(D[1],200);
[
(1.484412473422423143066783777),
(-1.484412473422423143066783777 + 2.018905819978457432553363756*i)
]
> Periods(E);
[ 1.48441247342238645290734388792589795816719556345366739111,  0.E-57 + 2.01890581997842321558401443999893246506804199670414762466*i ]
> quit;

Total time: 8.210 seconds
[was@form fearnley]$ exit
exit

Process magma finished