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I tried to run this through the key written by Papp L. P. coarctata should typically have a small side branch to r2 and r3 which should be visible in the second picture (see also later). However, I do not see it. P. quadripunctata can also be ruled out for the same reason. P. nubecula should have a more dusted frons, and it is rare in Hungary, so this can be ruled out. P. aquila does not have a patterned wing, which this fly clearly has. The wing veins are not wavy, which rules out undulata, which is yet to be recorder in Hungary. Then, if I see correctly this fly has 3 dc, which rules out cognata. So we are left with coarctata (it seems after all that the side branch to r2 and 3 is not always there, especially in females). The fly was largish (for an Ephydrid), and the r2and3 is quite lomng in relation to r4and5. So coarctata is likels.