Geodesic
On Vector-Valued Siegel Modular Forms of Degree 2 and Weight $(j,2)$
Documenta mathematica, Tome 23 (2018), pp. 1129-1156.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We formulate a conjecture that describes the vector-valued Siegel modular forms of degree 2 and level 2 of weight $\mathrm{Sym}^j\otimes\mathrm{det}^2$ and provide some evidence for it. We construct such modular forms of weight $(j,2)$ via covariants of binary sextics and calculate their Fourier expansions illustrating the effectivity of the approach via covariants. Two appendices contain related results of Chenevier; in particular a proof of the fact that every modular form of degree 2 and level 2 and weight $(j,1)$ vanishes.
Classification : 11F46, 11F70, 14J15
Keywords: Siegel modular forms, small weight 
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     author = {Cl\'ery, Fabien and van der Geer, Gerard},
     title = {On {Vector-Valued} {Siegel} {Modular} {Forms} of {Degree} 2 and {Weight} $(j,2)$},
     journal = {Documenta mathematica},
     pages = {1129--1156},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a29/}
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Cléry, Fabien; van der Geer, Gerard. On Vector-Valued Siegel Modular Forms of Degree 2 and Weight $(j,2)$. Documenta mathematica, Tome 23 (2018), pp. 1129-1156. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a29/