mfTheta

Function: mfTheta
Section: modular_forms
C-Name: mfTheta
Prototype: DG
Help: mfTheta({psi=1}): the unary theta function corresponding to the primitive
 Dirichlet character psi, hence of weight 1/2 if psi is even, of weight 3/2
 if psi is odd.
Doc: the unary theta function corresponding to the primitive Dirichlet
 character $\psi$. Its level is $4 F(\psi)^2$ and its weight is
 $1 - \psi(-1)/2$.
 \bprog
 ? Ser(mfcoefs(mfTheta(),30))
 %1 = 1 + 2*x + 2*x^4 + 2*x^9 + 2*x^16 + 2*x^25 + O(x^31)

 ? f = mfTheta(8); Ser(mfcoefs(f,30))
 %2 = 2*x - 2*x^9 - 2*x^25 + O(x^31)
 ? mfparams(f)
 %3 = [256, 1/2, 8, y, t + 1]

 ? g = mfTheta(-8); Ser(mfcoefs(g,30))
 %4 = 2*x + 6*x^9 - 10*x^25 + O(x^31)
 ? mfparams(g)
 %5 = [256, 3/2, 8, y, t + 1]

 ? h = mfTheta(Mod(2,5)); mfparams(h)
 %6 = [100, 3/2, Mod(7, 20), y, t^2 + 1]
 @eprog