/***the \vartheta-lattices with respect to \Q(\sqrt{-7})***/

S<w>:=QuadraticField(-7);

/***rank 4***/

GramRank4:=1/7*Matrix(S,[
[  14,    0,  6*w,  4*w],
[   0,   14,  4*w, -6*w],
[-6*w, -4*w,   28,    0],
[-4*w,  6*w,    0,   28]]);


/***rank 8***/

Gram1:=1/7*Matrix(S,[
[ 14 , 0 , 6*w , 4*w , 0 , 0 , 0 , 0 ],
[ 0 , 14 , 4*w , -6*w , 0 , 0 , 0 , 0 ],
[ -6*w , -4*w , 28 , 0 , 0 , 0 , 0 , 0 ],
[ -4*w , 6*w , 0 , 28 , 0 , 0 , 0 , 0 ],
[ 0 , 0 , 0 , 0 , 14 , 0 , 6*w , 4*w ],
[ 0 , 0 , 0 , 0 , 0 , 14 , 4*w , -6*w ],
[ 0 , 0 , 0 , 0 , -6*w , -4*w , 28 , 0 ],
[ 0 , 0 , 0 , 0 , -4*w , 6*w , 0 , 28 ]
]);

Gram2:=1/7*Matrix(S,[
[ 14 , 0 , 6*w , w - 7 , 0 , 0 , 0 , 0 ],
[ 0 , 28 , 4*w , -3*w + 21 , 0 , 7*w + 7 , 4*w , -6*w ],
[ -6*w , -4*w , 28 , 0 , 0 , 0 , 0 , 0 ],
[ -w - 7 , 3*w + 21 , 0 , 28 , -w - 7 , 6*w , 0 , -7*w + 7 ],
[ 0 , 0 , 0 , w - 7 , 14 , 0 , 6*w , 4*w ],
[ 0 , -7*w + 7 , 0 , -6*w , 0 , 28 , 2*w + 14 , -3*w - 21 ],
[ 0 , -4*w , 0 , 0 , -6*w , -2*w + 14 , 28 , 0 ],
[ 0 , 6*w , 0 , 7*w + 7 , -4*w , 3*w - 21 , 0 , 28 ]
]);

Gram3:=1/7*Matrix(S,[
[ 28 , 0 , 3*w - 21 , 2*w - 14 , 7*w + 7 , 0 , 6*w , 4*w ],
[ 0 , 28 , 2*w - 14 , -3*w + 21 , 0 , 7*w + 7 , 4*w , -6*w ],
[ -3*w - 21 , -2*w - 14 , 28 , 0 , -6*w , -4*w , -7*w + 7 , 0 ],
[ -2*w - 14 , 3*w + 21 , 0 , 28 , -4*w , 6*w , 0 , -7*w + 7 ],
[ -7*w + 7 , 0 , 6*w , 4*w , 28 , 0 , 3*w + 21 , 2*w + 14 ],
[ 0 , -7*w + 7 , 4*w , -6*w , 0 , 28 , 2*w + 14 , -3*w - 21 ],
[ -6*w , -4*w , 7*w + 7 , 0 , -3*w + 21 , -2*w + 14 , 28 , 0 ],
[ -4*w , 6*w , 0 , 7*w + 7 , -2*w + 14 , 3*w - 21 , 0 , 28 ]
]);