• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.183-200
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• 2017

Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3/2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with Bringmann-Guerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.509-514
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• 2016

By constructing a canonical basis for the space $M_k^{\sharp}({\Gamma}_0(N))$ explicitly, we find a basis of the space of cusp forms for ${\Gamma}_0(N)$ consisting of $Poincar{\acute{e}}$ series.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.375-386
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• 2007

Let p be a prime and $f(z)=\Sigma_{n}a(n)q^n$ be a weakly holomorphic modular function for ${\Gamma}^*_0(p)$ with a(0) = 0. We use Bruinier and Funke's work to find the generating series of modular traces of f(z) as Jacobi forms.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.281-285
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• 2018

Let $S_k(N)$ be the space of cusp forms of weight k for ${\Gamma}_0(N)$. We show that $S_k(N)$ is the direct sum of subspaces $S_k^+(N)$ and $S_k^-(N)$. Where $S_k^+(N)$ is the vector space of cusp forms of weight k for the group ${\Gamma}_0^+(N)$ generated by ${\Gamma}_0(N)$ and $W_N$ and $S_k^-(N)$ is the subspace consisting of elements f in $S_k(N)$ satisfying $f{\mid}_kW_N=-f$. We find generators spanning the space $S_k^-(N)$ from $Poincar{\acute{e}}$ series and give all linear relations among such generators.