1Function: mffrometaquo 2Section: modular_forms 3C-Name: mffrometaquo 4Prototype: GD0,L, 5Help: mffrometaquo(eta,{flag=0}): modular form corresponding to the eta 6 quotient matrix eta. If the valuation v at infinity is fractional, return 0. 7 If the eta quotient is not holomorphic but simply meromorphic, return 0 if 8 flag=0; return the eta quotient (divided by q to the power -v if v < 0, i.e., 9 with valuation 0) if flag is set. 10Doc: modular form corresponding to the eta quotient matrix \kbd{eta}. 11 If the valuation $v$ at infinity is fractional, return $0$. If the eta 12 quotient is not holomorphic but simply meromorphic, return $0$ if 13 \kbd{flag=0}; return the eta quotient (divided by $q$ to the power $-v$ if 14 $v < 0$, i.e., with valuation $0$) if flag is set. 15 \bprog 16 ? mffrometaquo(Mat([1,1]),1) 17 %1 = 0 18 ? mfcoefs(mffrometaquo(Mat([1,24])),6) 19 %2 = [0, 1, -24, 252, -1472, 4830, -6048] 20 ? mfcoefs(mffrometaquo([1,1;23,1]),10) 21 %3 = [0, 1, -1, -1, 0, 0, 1, 0, 1, 0, 0] 22 ? F = mffrometaquo([1,2;2,-1]); mfparams(F) 23 %4 = [16, 1/2, 1, y, t - 1] 24 ? mfcoefs(F,10) 25 %5 = [1, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0] 26 ? mffrometaquo(Mat([1,-24])) 27 %6 = 0 28 ? f = mffrometaquo(Mat([1,-24]),1); mfcoefs(f,6) 29 %7 = [1, 24, 324, 3200, 25650, 176256, 1073720] 30 @eprog\noindent For convenience, a \typ{VEC} is also accepted instead of 31 a factorization matrix with a single row: 32 \bprog 33 ? f = mffrometaquo([1,24]); \\ also valid 34 @eprog 35