MTG Conspiracy cards allowed in modern
Cards from Conspiracy are not legal in Modern unless they were already printed in a Modern legal set. There were 65 new cards in that set, 52 are legal in Legacy and Vintage the remaining 13 are not legal in any Constructed format. The 13 that aren't legal are the ones with the Conspiracy type.

The only things that add new cards to the Modern card pool are sets that are Standard legal. Supplementary sets like Conspiracy, Commander, or Planechase do not, new cards from those sets are only legal in Legacy and Vintage.