Conjectures about Discriminants of Hecke Algebras of Prime Level
- Cite this paper as:
- Calegari F., Stein W.A. (2004) Conjectures about Discriminants of Hecke Algebras of Prime Level. In: Buell D. (eds) Algorithmic Number Theory. ANTS 2004. Lecture Notes in Computer Science, vol 3076. Springer, Berlin, Heidelberg
In this paper, we study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. By considering cusp forms of weight bigger than 2, we are are led to make a precise conjecture about indexes of Hecke algebras in their normalisation which implies (if true) the surprising conjecture that there are no mod p congruences between non-conjugate newforms in S2(Γ0(p)), but there are almost always many such congruences when the weight is bigger than 2.
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