Hello everyone:
I wanted to search for weight 1 forms with a list of properties related to its level and conductor of its nebentypus. I have a question I'd like some help on. Thank you in advance for your help.
Let's set
mfall = mfinit([N, 1, 0], 0);
Occasionally, the mfgaloistype(mfall[jj]) returns a list of length more than 1. I understood this to mean that forms with the given nebentypus have projective images as indicated by this list... but that seems not to match with other databases containing similar data (most notably, lmfdb).
Let me illustrate all this in a particular example I am looking at.
? default(parisize, 100000000);
*** Warning: new stack size = 100000000 (95.367 Mbytes).
? mfall = mfinit([756, 1, 0], 0);
? mfgaloistype(mfall[1])
% [6, 12]
One can match the output of `mfall` above with the LMFDB data as follows:
mfall[1] <---> 756.1.d
mfall[2] <---> 756.1.h
mfall[3] <---> 756.1.z
mfall[4] <---> 756.1.bk (up to taking inverse of the nebentypus character)
From the LMFDB data it seems that the projective Galois image of both forms in mfall[1] should be the dihedral group of cardinality 12. But the output of mfgaloistype seems different?
I'd be grateful for any pointers you may have regarding this matter. Thank you!
Best,
Kannappan
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Kannappan Sampath
Graduate Student
Department of Mathematics | University of Michigan