/***the six rank 4 \vartheta-lattices with respect to \Q(\sqrt{-67})***/

S<w>:=QuadraticField(-67);

Gram1:=1/67*Matrix(S,[
[ 134 , 0 , 20*w , 20*w ],
[ 0 , 134 , 20*w , -20*w ],
[ -20*w , -20*w , 402 , 0 ],
[ -20*w , 20*w , 0 , 402 ]
]);

Gram2:=1/67*Matrix(S,[
[ 19832 , 260*w + 16884 , 334*w + 134 , 1417*w + 737 ],
[ -260*w + 16884 , 14606 , 282*w + 402 , 1196*w + 1876 ],
[ -334*w + 134 , -282*w + 402 , 402 , 1608 ],
[ -1417*w + 737 , -1196*w + 1876 , 1608 , 6834 ]
]);

Gram3:=1/67*Matrix(S,[
[ 19832 , 506*w - 134 , 100*w + 11256 , 1417*w + 737 ],
[ -506*w - 134 , 1072 , -321*w + 201 , -20*w + 2412 ],
[ -100*w + 11256 , 321*w + 201 , 6834 , 804*w + 804 ],
[ -1417*w + 737 , 20*w + 2412 , -804*w + 804 , 6834 ]
]);

Gram4:=1/67*Matrix(S,[
[ 10184 , -645*w - 1005 , -100*w + 12060 , -995*w - 1675 ],
[ 645*w - 1005 , 3082 , 749*w - 469 , -20*w + 4422 ],
[ 100*w + 12060 , -749*w - 469 , 14874 , -1206*w - 1206 ],
[ 995*w - 1675 , 20*w + 4422 , 1206*w - 1206 , 6834 ]
]);

Gram5:=1/67*Matrix(S,[
[ 134 , -27*w + 67 , 13*w + 67 , 804 ],
[ 27*w + 67 , 536 , 40*w - 402 , 191*w + 871 ],
[ -13*w + 67 , -40*w - 402 , 804 , -201*w - 201 ],
[ 804 , -191*w + 871 , 201*w - 201 , 6834 ]
]);

Gram6:=1/67*Matrix(S,[
[ 2010 , -95*w - 603 , -196*w - 536 , 258*w + 670 ],
[ 95*w - 603 , 3484 , 308*w - 1206 , 102*w + 268 ],
[ 196*w - 536 , -308*w - 1206 , 4422 , -219*w - 1809 ],
[ -258*w + 670 , -102*w + 268 , 219*w - 1809 , 3484 ]
]);