## Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms

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- by Lassina Dembélé;
- Math. Comp.
**76**(2007), 1039-1057 - DOI: https://doi.org/10.1090/S0025-5718-06-01914-4
- Published electronically: December 4, 2006
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## Abstract:

In this paper, we propose a generalization of the algorithm we developed previously. Along the way, we also develop a theory of quaternionic $M$-symbols whose definition bears some resemblance to the classical $M$-symbols, except for their combinatorial nature. The theory gives a more efficient way to compute Hilbert modular forms over totally real number fields, especially quadratic fields, and we have illustrated it with several examples. Namely, we have computed all the newforms of prime levels of norm less than 100 over the quadratic fields $\mathbb {Q}(\sqrt {29})$ and $\mathbb {Q}(\sqrt {37})$, and whose Fourier coefficients are rational or are defined over a quadratic field.## References

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## Bibliographic Information

**Lassina Dembélé**- Affiliation: Department of mathematics and statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB, Canada T2N 1N4
- Email: dembele@math.ucalgary.ca
- Received by editor(s): April 8, 2004
- Received by editor(s) in revised form: January 18, 2006
- Published electronically: December 4, 2006
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**76**(2007), 1039-1057 - MSC (2000): Primary 11-xx; Secondary 11Gxx
- DOI: https://doi.org/10.1090/S0025-5718-06-01914-4
- MathSciNet review: 2291849