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### Modular forms on the theta group

The theta group $\Gamma$ is the subgroup of $SL(2;\mathbb{Z})$ generated by $T=\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$ and $S=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}.$ It ...
I need examples of Jacobi forms for full congruence subgroups $\Gamma(N)$ of $SL(2,Z)$. As a particular case, take the theta function $\theta_{1,1}(t,z) := \sum_{n\in\mathbb{Z}} exp(\pi it(n + ... 1answer 134 views ### Monstrous Moonshine for$M_{24}$? This is connected to my MO post "Monstrous Moonshine for$M_{24}$and K3?". In page 44 of this paper, eqn(7.16) and (7.19) yield, ... 1answer 90 views ### Coefficients of powers of the theta function Let$q=\exp(2 \pi i z)$and $$\theta(z)=\sum_{n=-\infty}^\infty q^{n^2}.$$ Now, I shall show that the powers of$\theta$are given by $$\theta(z)^r = \sum_{n=0}^\infty S_r(n) q^n$$ where$S_r(n)$... 0answers 144 views ### A Dedekind eta function sum of form$y_0^k+y_1^k+y_2^k+y_3^k+… = 0$Given the Dedekind eta function$\eta(\tau)$. Define,$y_p = e^{\pi i p/6}\,\eta(\tfrac{\tau+2p}{5})$Prove the multi-grade identity [1],$y_0^k + y_1^k + y_2^k + y_3^k + y_4^k + ...
In A Course in Arithmetic, Serre works out some of the theory of theta functions for even, self-dual lattices, e.g. such theta functions are modular forms of weight $n/2$, where $n$ is the dimension ...