Magnetic quantum number

The quantum number \[m_{\ell}\] refers, loosely, to the direction of the angular momentum vector. The magnetic quantum number \[m_{\ell}\] only affects the electron's energy if it is in a magnetic field because in the absence of one, all spherical harmonics corresponding to the different arbitrary values of \[m_{\ell}\] are equivalent. The magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field
Illustration of the effects of \[m_{\ell}\] on atomic orbitals: (Notation is in the form of \[n\ell_{m_{\ell}}\])

The values of \[m_{\ell}\] in an orbital with quantum number \[\ell\] range from \[m_{\ell}=-\ell,-\ell+1,-\ell+2,\dotso,\ell-2,\ell-1,\ell\]