Contributions to IRA and 403(b) with only $6000 earned income

I have $6000 earned income.

 

Of the $6000, $4000 went into my traditional 403(b) plan at my employer, and $1000 to other before-tax deductions. The rest went to social security, medicare tax, withholding, and my bank account.

 

Can I also contribute $6000 to a traditional IRA (for conversion to a Roth IRA to accomplish a backdoor Roth)? Or can I only contribute a smaller amount to an IRA?