Soma Purkait

Department of Mathematics
Tokyo Institute of Technology
2-12-1 Ookayama Meguro-ku
Tokyo 152-8550


  Soma Purkait

I am currently a special associate professor at Department of Mathematics, Tokyo Institute of Technology. My research interests broadly lie in number theory and specifically on modular forms of half-integral weight. Recently I am working towards characterization of the newspace through the local Hecke algebra approach and thereby extending the works of Kohnen and Ueda.
Previously I was a postdoctoral fellow at Tokyo University of Science and a JSPS Postdoctoral fellow at Kyushu University under Prof. Masanobu Kaneko. I completed my PhD at University of Warwick under the supervision of Professor Samir Siksek.  


  1. (Joint with E. M. Baruch) Hecke algebra and Whittaker functions (in preparation).
  2. (Joint with Jerome Dimabayao) A variant of the congruent number problem (in preparation).
  3. (Joint with E. M. Baruch) Newforms of half-integral weight: the minus space of S_{k+1/2}(Γ_0(8M)), Israel Journal of Mathematics, vol 232 (2019), 41-73.
  4. (Joint with E. M. Baruch) Newforms of half-integral weight: The minus space counterpart, Canadian Journal of Mathematics, vol 72 (2020), Issue 2, 326-372.
  5. (Joint with E. M. Baruch) Hecke algebras, new vectors and newforms on Γ_0(m), Mathematische Zeitschrift, Vol. 287 (2017), Issue 1-2, 705-733.
  6. (Joint with N. Kumar) A note on the Fourier coefficients of half-integral weight modular forms, Archiv der Mathematik (Basel) 102, Vol. 4 (2014), 369-378.
  7. Hecke operators in half-integral weight, Journal de Thoérie des Nombres de Bordeaux 26 (2014), no. 01, 233-251.
  8. Explicit application of Waldspurger's theorem, LMS Journal of Computation and Mathematics, Vol. 16 (2013), 216-245.
  9. On Shimura's decomposition, International Journal of Number Theory, Vol. 9, no. 06, (2013), 1431-1445.
  10. (Joint with B. Sury) Some vanishing sums involving binomial coeffcients in the denominator, Albanian Journal of Mathematics,Vol. 2 (2008), 27-32.

Some MAGMA Codes

  1. For computing Shimura's decomposition (shimuraspacewtk.m)
  2. For computing the Shimura equivalent space of an elliptic curve that comes from theta series of ternary quadratic forms; it includes implementation of Dickson's algorithm (quadratic.m)


I am currently teaching Linear Algebra I, Calculus I, Linear Algebra II, Calculus II.
Previously, I was a lecturer for MA3H1 Topics in Number Theory at University of Warwick. Here is my lecture note.  


Curriculum Vitae

Here is my CV.