\(L\)-series of \(\Delta\)#
Thanks to wrapping work of Jennifer Balakrishnan of M.I.T., we can compute explicitly with the \(L\)-series of the modular form \(\Delta\). Like for elliptic curves, behind these scenes this uses Dokchitsers \(L\)-functions calculation Pari program.
sage: L = delta_lseries(); L L-series of conductor 1 and weight 12 sage: L(1) 0.0374412812685155
\(L\)-series of a Cusp Form#
In some cases we can also compute with \(L\)-series attached to a cusp form.
sage: f = CuspForms(2,8).newforms() sage: L = f.lseries() sage: L(1) 0.0884317737041015 sage: L(0.5) 0.0296568512531983
\(L\)-series of a General Newform is Not Implemented#
Unfortunately, computing with the \(L\)-series of a general newform is not yet implemented.
sage: S = CuspForms(23,2); S Cuspidal subspace of dimension 2 of Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(23) of weight 2 over Rational Field sage: f = S.newforms('a'); f q + a0*q^2 + (-2*a0 - 1)*q^3 + (-a0 - 1)*q^4 + 2*a0*q^5 + O(q^6)
Computing with \(L(f,s)\) totally not implemented yet, though should be easy via Dokchitser.