Geodesic
An explicit trace formula for Brandt matrices
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part II, Tome 63 (1976), pp. 67-94

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An. explicit formula is found for the traces of Hecke-Brandt operators which correspond to finite-dimensional representations of the groups of units of various orders in quaternion algebras over $\mathbf Q$, which are ramified over $\mathbf R$; it is not assumed that the divisors of the level which are relatively prime to the discriminant of the algebra are square-free. 
@article{ZNSL_1976_63_a2,
     author = {V. L. Kalinin},
     title = {An explicit trace formula for {Brandt} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--94},
     publisher = {mathdoc},
     volume = {63},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_63_a2/}
}
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V. L. Kalinin. An explicit trace formula for Brandt matrices. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part II, Tome 63 (1976), pp. 67-94. http://geodesic.mathdoc.fr/item/ZNSL_1976_63_a2/