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Questions about modular forms and related areas

4 votes
Accepted

Is the weight in Serre's conjecture "minimal"?

I believe a modular form as you describe indeed cannot exist. I think it's easier to think about these issues if they're translated into the representation-theoretic language of Serre weights. Associa …
D. Savitt's user avatar
  • 2,713
21 votes
Accepted

A sentence in Shimura's "On The Periods of Modular Forms"

Suppose that a co-finite subset of the $a_p$'s generate a field $L$. Applying any element $\sigma$ of the absolute Galois group of $L$ to $f$ yields another form $g$ whose Fourier coefficients $b_p$ a …
D. Savitt's user avatar
  • 2,713