/***the \vartheta-lattices with respect to \Q(\sqrt{-11})***/

S<w>:=QuadraticField(-11);

/***rank 4***/

GramRank4:=1/11*Matrix(S,[
[  22,    0,  6*w,  2*w],
[   0,   22,  2*w, -6*w],
[-6*w, -2*w,   22,    0],
[-2*w,  6*w,    0,   22]]);


/***rank 8***/

Gram1:=1/11*Matrix(S,[
[        44,          0,        6*w,        4*w,  -2*w + 22,   6*w + 22,        -22,  11*w + 11],
[         0,         22,        2*w,    -w + 11,          0,          0,          0,          0],
[      -6*w,       -2*w,         22,          0,          0,          0,          0,          0],
[      -4*w,     w + 11,          0,         22,  -5*w - 11,  -3*w + 11,          0,         22],
[  2*w + 22,          0,          0,   5*w - 11,         44,   8*w + 22,   4*w - 22,       12*w],
[ -6*w + 22,          0,          0,   3*w + 11,  -8*w + 22,         44,   8*w - 22,   8*w + 44],
[       -22,          0,          0,          0,  -4*w - 22,  -8*w - 22,         44, -11*w - 11],
[-11*w + 11,          0,          0,         22,      -12*w,  -8*w + 44,  11*w - 11,         66]]);

Gram2:=1/11*Matrix(S,[
[       132,         66, -10*w - 22,        4*w,   2*w + 44,  14*w - 22, -33*w - 33,  22*w + 22],
[        66,         66,  -7*w - 11,    -w + 11,   4*w + 22,   8*w - 22, -22*w - 22,  11*w + 11],
[ 10*w - 22,   7*w - 11,         22,          0,   3*w - 11,  -5*w - 11,         44,        -22],
[      -4*w,     w + 11,          0,         22,  -5*w - 11,  -3*w + 11,          0,         22],
[ -2*w + 44,  -4*w + 22,  -3*w - 11,   5*w - 11,         44,       12*w,  -9*w - 33,       12*w],
[-14*w - 22,  -8*w - 22,   5*w - 11,   3*w + 11,      -12*w,         44,  15*w - 33,  -3*w + 33],
[ 33*w - 33,  22*w - 22,         44,          0,   9*w - 33, -15*w - 33,        132,        -66],
[-22*w + 22, -11*w + 11,        -22,         22,      -12*w,   3*w + 33,        -66,         66]]);

Gram3:=1/11*Matrix(S,[
[       132,        -66, -21*w - 33,        4*w,   2*w + 44,  14*w - 22, -33*w - 33,  22*w + 22],
[       -66,         66,  15*w + 11,    -w + 11,  -4*w - 22,  -8*w + 22,  22*w + 22, -11*w - 11],
[ 21*w - 33, -15*w + 11,         66,          0,   6*w - 22, -10*w - 22,         88,        -44],
[      -4*w,     w + 11,          0,         22,  -5*w - 11,  -3*w + 11,          0,         22],
[ -2*w + 44,   4*w - 22,  -6*w - 22,   5*w - 11,         44,       12*w,  -9*w - 33,       12*w],
[-14*w - 22,   8*w + 22,  10*w - 22,   3*w + 11,      -12*w,         44,  15*w - 33,  -3*w + 33],
[ 33*w - 33, -22*w + 22,         88,          0,   9*w - 33, -15*w - 33,        132,        -66],
[-22*w + 22,  11*w - 11,        -44,         22,      -12*w,   3*w + 33,        -66,         66]]);

Gram4:=1/11*Matrix(S,[
[        44,         22,   2*w - 22,   4*w + 22,  -2*w + 22,   6*w + 22, -11*w - 11,  11*w + 11],
[        22,         66,  -2*w - 22,    -w + 55,   4*w + 22,   8*w + 22, -22*w - 22,  11*w + 11],
[ -2*w - 22,   2*w - 22,         22,     w - 11,  -2*w - 22,  -5*w - 11,   8*w + 22,       -6*w],
[ -4*w + 22,     w + 55,    -w - 11,         66,    -w + 11,   5*w + 33, -22*w - 22,  11*w + 33],
[  2*w + 22,  -4*w + 22,   2*w - 22,     w + 11,         44,   8*w + 22,  -9*w - 33,       12*w],
[ -6*w + 22,  -8*w + 22,   5*w - 11,  -5*w + 33,  -8*w + 22,         44,  -7*w - 55,   8*w + 44],
[ 11*w - 11,  22*w - 22,  -8*w + 22,  22*w - 22,   9*w - 33,   7*w - 55,        132,        -66],
[-11*w + 11, -11*w + 11,        6*w, -11*w + 33,      -12*w,  -8*w + 44,        -66,         66]]);

Gram5:=1/11*Matrix(S,[
[       132, -11*w - 77,        6*w,  19*w - 11, -14*w + 22,  -2*w + 66,  22*w + 44,  44*w - 22],
[ 11*w - 77,         88,        2*w, -13*w - 11,       12*w,   8*w - 44, -11*w - 55, -33*w - 33],
[      -6*w,       -2*w,         22,          0,          0,          0,          0,          0],
[-19*w - 11,  13*w - 11,          0,         44,    -w - 33, -11*w - 11, -11*w + 33,         88],
[ 14*w + 22,      -12*w,          0,     w - 33,         44,   8*w + 22,  16*w - 22,   6*w - 66],
[  2*w + 66,  -8*w - 44,          0,  11*w - 11,  -8*w + 22,         44,  16*w + 22,  26*w - 22],
[-22*w + 44,  11*w - 55,          0,  11*w + 33, -16*w - 22, -16*w + 22,         88,  22*w + 88],
[-44*w - 22,  33*w - 33,          0,         88,  -6*w - 66, -26*w - 22, -22*w + 88,        198]]);

Gram6:=1/11*Matrix(S,[
[        44,        8*w,   6*w - 22,   4*w + 22,       -6*w,       -2*w,  11*w + 11,          0],
[      -8*w,        176,    -w - 55, -13*w + 77,  -3*w - 77, -20*w - 44,  30*w + 44,      -28*w],
[ -6*w - 22,     w - 55,         66,        -44,   4*w + 22,   8*w + 22, -22*w - 22,  11*w + 11],
[ -4*w + 22,  13*w + 77,        -44,         66,  -9*w - 33, -11*w - 11,  22*w + 22, -11*w + 11],
[       6*w,   3*w - 77,  -4*w + 22,   9*w - 33,         44,   8*w + 22,  -9*w - 33,       12*w],
[       2*w,  20*w - 44,  -8*w + 22,  11*w - 11,  -8*w + 22,         44,  -7*w - 55,   8*w + 44],
[-11*w + 11, -30*w + 44,  22*w - 22, -22*w + 22,   9*w - 33,   7*w - 55,        132,        -66],
[         0,       28*w, -11*w + 11,  11*w + 11,      -12*w,  -8*w + 44,        -66,         66]]);