Journal of the Ramanujan Mathematical Society
Volume 41, Issue 3, September 2026 pp. 287–291.
The index of a certain quotient of the Hecke algebra in its normalization
Authors:
Amod Agashe
Author institution:Department of Mathematics, Florida State University, 208 Love Building, 1017 Academic Way Tallahassee, FL 32306, U.S.A.
Summary:
Let Γ be a congruence subgroup of SL{2}(ℤ), and let f be a
normalized eigenform of weight k on Γ. Let K denote the number
field generated over Q by the Fourier coefficients of f. Let R
denote the the order in K generated by the Fourier coefficients of f,
which is contained in the ring of integers 𝒪 of K. We relate the
primes that divide the index of R in 𝒪 to primes p such that f is
congruent to a conjugate of f modulo a prime ideal of residue
characteristic p. The index mentioned above is the same as the index of
the quotient of the Hecke algebra by the annihilator ideal of f in its
normalization.
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