Gallery of Maass Waveforms

This area is intended to display some of the Maas Waveforms that I have computed for Hecke Congruence subgroups of the modular group of prime index P. (I hope I will get time later to make a short layman explanation for what these are.)

Since it is quite messy to make all these pictures simultaneously there will probably be some errors that I have missed around here.

So far I have looked mostly at modest Ps and small eigenvalues. This gallery will continue to be extended when I have time.

I show the sine and cosine forms for the different P values on different pages, and all pages include both color pictures and b/w pictures. The pictures are mostly (so far) of the region -0.5<x<0.5, 0.05<y<1.05 and show a set of filled level curves. I have tried to automate as much as possible using perl and matlab, hence some pictures look better than others with the parameters I have been using.

Note also that the sample of Fourier coefficients given are only computed to the accuracy and in such numbers that I am able to make the pictures.

Another thing: If you look at the filename of the picture you can see whether the form is even or odd under the involution z->-1/(Pz). Note that for oldforms I just choose one of the symmetries usually even.

Amongst all these pictures there is one picture that is not of a true Maass waveform. Which one?

Answer: (mark the next paragraph with your mouse)

P=3, 13.5079 is not a cosine form, only a sine form. I simply took the same eigenvalue and solved for a cosine function instead, and out came this picture with some features resembling a Maass waveform (well, of course I accidentally fed the wrong paramters into the program, I didn't do it deliberately, it took some time to figure out what was wrong with this picture).