Why do I owe NY State tax? I can be claimed on another person's return and I'm a full time college student. Income: $4,830

If you are a dependent, New York will only give you a standard deduction of $3100.  Since your income is above that amount, you will pay tax on the $1730 of income that is above your standard deduction.  This website has additional information for you on this subject:  Please note this website:  https://www.tax.ny.gov/pit/file/residents.htm, where you will find the following information:  

If you are a New York State resident you must file Form IT-201, Resident Income Tax Return, if you meet any of the following conditions:

• You have to file a federal return.

• You did not have to file a federal return but your federal adjusted gross income1 plus New York additions2 was more than $4,000 ($3,100 if you are single1 and can be claimed as a dependent on another taxpayer's federal return). (Bolding for emphasis)

• You want to claim a refund of any New York State, New York City, or Yonkers income taxes withheld from your pay.

• You want to claim any of the refundable or carryover credits available.