Maass forms on GL(3) and GL(4)
  We describe a practical method for finding an L-function without first finding the associated underlying object. The procedure involves using the Euler product and the approximate functional equation in a new way. No use is made of the functional equation of twists of the L-function. The method is used to find a large number of Maass forms on SL(3,Z) and to give the first examples of Maass forms of higher level on GL(3), and on GL(4) and Sp(4). 
David W. Farmer, Sally Koutsoliotas, and Stefan Lemurell
math.NT