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# \(L\)-series

## \(L\)-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 associated to the modular form Delta
    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()[0]
    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')[0]; 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.

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