Final answer:
The least important genre during the modern era from the options given is the symphonic poem, which was more characteristic of the Romantic period.
Step-by-step explanation:
The genre that was not important during the modern era out of the options provided is symphonic poem. Operas, string quartets, symphonies, and ballet music all had significant roles in the musical landscape of the modern era. By contrast, the symphonic poem, or tone poem, was established in the Romantic period and is most closely associated with composers like Franz Liszt. While it did carry into the early modern era, it was not as defining a genre during this time compared to the others listed. This era instead saw significant developments in other musical forms, such as nationalistic music and the exploration of new harmonic and structural techniques.