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AndrewVSutherland
GitHub Repository: AndrewVSutherland/lmfdb
 Path: blob/main/scripts/siegel_modular_forms/Yoshida_Lift.py
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# This script was created using the 2012 paper of Johnson-Leung and Roberts.

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# INPUTS:

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# F is a real quadratic number field

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# hhecke_evals is a dictionary of eigenvalues of a hilbert modular form over F. It should contain primes up to norm of primeprec**2

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# hweight is the pair even integers that gives the weight of the hilbert modular form, no reason to default to [2,2]

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# primeprec is the uper bound on the size of the rational primes which will have eigenvalues calculated

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# OUTPUTS:

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# Paramodular Level: An int

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# Paramodular Weight: an Int

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# T(1,1,p,p): a dictionary which has keys all the primes up to primeprec, and has values which are hecke eigenvalues

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# T(1,p,p,p^2): See above

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from sage.all import prime_range

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def Yoshida_Lift(F, hhecke_evals, hlevel, hweight=[2, 2], primeprec=100):

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    weight = (hweight[1] + 2)//2

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    level = F.disc()**2*hlevel.norm()

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    lam = {}

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    mu = {}

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    for p in prime_range(primeprec):

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        v = level.valuation(p)

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        if v == 0:

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            if len(F.primes_above(p)) == 1:

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                lam[p] = 0

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                mu[p] = p**(2*(weight -3))*(-p**2 - p*hhecke_evals[F.prime_above(p)] - 1)

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            else:

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                lam[p] = p**(weight  - 3)*p*(hhecke_evals[F.primes_above(p)[0]] + hhecke_evals[F.primes_above(p)[1]])

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                mu[p] = p**(2*(weight - 3))*(p**2 + p*hhecke_evals[F.primes_above(p)[0]]*hhecke_evals[F.primes_above(p)[1]] - 1)

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        if v == 1:

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            if hlevel.valuation(F.primes_above(p)[0]) == 1:

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                po = F.primes_above(p)[0]

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                pt = F.primes_above(p)[1]

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            else:

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                pt = F.primes_above(p)[0]

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                po = F.primes_above(p)[1]

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            lam[p] =  p**(weight  - 3)*(p*hhecke_evals[po] + (p + 1)*hhecke_evals[pt])

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            mu[p] = p**(2*(weight  - 3))*(p*hhecke_evals[F.primes_above(p)[0]]*hhecke_evals[F.primes_above(p)[1]])

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        else:

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            if len(F.primes_above(p)) == 2:

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                lam[p] = p**(weight  - 3)*p*(hhecke_evals[F.primes_above(p)[0]] + hhecke_evals[F.primes_above(p)[1]])

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                if hlevel.valuation(F.primes_above(p)[0])*hlevel.valuation(F.primes_above(p)[1]) == 0:

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                    mu[p] = 0

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                else:

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                    mu[p] = p**(2*(weight  - 3))*(-p**2)

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            else:

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                if F.ideal(p).valuation(F.prime_above(p)) == 2:

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                    lam[p] = p*hhecke_evals[F.prime_above(p)]

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                    if hlevel.valuation(F.prime_above(p)) == 0:

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                        mu[p] = 0

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                    else:

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                        mu[p] = p**(2*(weight  - 3))*(-p**2)

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                else:

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                    lam[p] = 0

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                    mu[p] = p**(2*(weight  - 3))*(-p**2-p*hhecke_evals[F.prime_above(p)])

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    return {'paramodular_level':level, 'weight':weight, 'T(1,1,p,p)':lam, 'T(1,p,p,p^2)':mu}

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    #return lam,mu,level,weight

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