acb_theta_g2_covariants

The order and normalisation are: C_{1,6}=f, C_{2,0}= 60(f,f)_6, C_{2,4}= 75(f,f)_4, C_{2,8}= 90(f,f)_2, C_{3,2}= 30(f,C_{2,4})_4, C_{3,6}= 30(f,C_{2,4})_2, C_{3,8}= 6(f,C_{2,4})_1, C_{3,12}= 6 (f,C_{2,8})_1, C_{4,0}= 2 (C_{2,4},C_{2,4})_4, C_{4,4}= 30 (f,C_{3,2})_2, C_{4,6}= 6(f,C_{3,2})_1, C_{4,10}= 2(C_{2,8},C_{2,4})_1, C_{5,2}=(C_{2,4},C_{3,2})_2, C_{5,4}=\frac 25 (C_{2,4},C_{3,2})_1, C_{5,8}= 2(C_{2,8},C_{3,2})_1, C_{6,0}= 2(C_{3,2},C_{3,2})_2, C_{6,6}^{(1)}= \frac 25(C_{3,6},C_{3,2})_1, C_{6,6}^{(2)}= \frac 83(C_{3,8},C_{3,2})_2, C_{7,2}= 30(f,C_{3,2}^2)_4, C_{7,4}= 12(f,C_{3,2}^2)_3, C_{8,2}= \frac 25(C_{2,4},C_{3,2}^2)_3, C_{9,4}= 4(C_{3,8},C_{3,2}^2)_4, C_{10,0}= 20(f,C_{3,2}^3)_6, C_{10,2}= \frac 65(f,C_{3,2}^3)_5, C_{12,2}= \frac 85(C_{3,8},C_{3,2}^3)_6, C_{15,0}= \frac{1}{30000} (C_{3,8},C_{3,2}^4)_8. The factors make the covariants of the generic sextic f = \sum a_i x_1^{6-i}x_2^i integral and primitive as polynomials in a_0,\ldots,a_6,x_1,x_2.