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