Most likely, no.  The California filing requirements for residents that are claimed as dependents is if your income exceeds your standard deduction.  For dependents, the minimum standard deduction if $1,050 while the highest is $4,044 if filing a single return.  This amount is based on your earned income up to the maximum deduction.

For California filing requirements, please see the link below.

https://www.ftb.ca.gov/forms/2015_California_Tax_Rates_and_Exemptions.shtml#ifr

For assistance calculating your standard deduction, please see the worksheet at the link below.

https://www.ftb.ca.gov/individuals/faq/net/902.shtml