# On Hecke’s decomposition of the regular differentials on the modular curve of prime level

On Hecke’s decomposition of the regular differentials on the modular curve of prime level In this paper, we review Hecke’s decomposition of the regular differentials on the modular curve of prime level p under the action of the group $${{\mathrm{SL}}}_2(p)/\langle {\pm 1}\rangle$$ SL 2 ( p ) / ⟨ ± 1 ⟩ . We show that his distinguished subspace corresponds to a factor of the Jacobian which decomposes as a product of conjugate, isogenous elliptic curves with complex multiplication. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

# On Hecke’s decomposition of the regular differentials on the modular curve of prime level

, Volume 5 (1) – Jan 22, 2018
19 pages

/lp/springer_journal/on-hecke-s-decomposition-of-the-regular-differentials-on-the-modular-mGu5AOkx8S
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
D.O.I.
10.1007/s40687-018-0121-9
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we review Hecke’s decomposition of the regular differentials on the modular curve of prime level p under the action of the group $${{\mathrm{SL}}}_2(p)/\langle {\pm 1}\rangle$$ SL 2 ( p ) / ⟨ ± 1 ⟩ . We show that his distinguished subspace corresponds to a factor of the Jacobian which decomposes as a product of conjugate, isogenous elliptic curves with complex multiplication.

### Journal

Research in the Mathematical SciencesSpringer Journals

Published: Jan 22, 2018

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