Geodesic
On Vector-Valued Siegel Modular Forms of Degree 2 and Weight $(j,2)$ (with two Appendices by Gaëtan Chenevier)
Documenta mathematica, Tome 23 (2018), pp. 1129-1156
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We formulate a conjecture that describes the vector-valued Siegel modular forms of degree 2 and level 2 of weight Symj⊗det2 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.
DOI : 10.4171/dm/643
Classification : 11F46, 11F70, 14J15
Mots-clés : Siegel modular forms, small weight 
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     author = {Fabien Cl\'ery and Gerard van der Geer},
     title = {On {Vector-Valued} {Siegel} {Modular} {Forms} of {Degree} 2 and {Weight} $(j,2)$ (with two {Appendices} by {Ga\"etan} {Chenevier)}},
     journal = {Documenta mathematica},
     pages = {1129--1156},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/643},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/643/}
}
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Fabien Cléry; Gerard van der Geer. On Vector-Valued Siegel Modular Forms of Degree 2 and Weight $(j,2)$ (with two Appendices by Gaëtan Chenevier). Documenta mathematica, Tome 23 (2018), pp. 1129-1156. doi: 10.4171/dm/643

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