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Multiple choice

The spherical harmonic

Y_\ell^m(\theta, \phi)

is a simultaneous eigenfunction of

L^2

and

L_z

. What are its eigenvalues?

$L^2$ gives $\hbar \ell$ and $L_z$ gives $\hbar m$
$L^2$ gives $\hbar^2 \ell^2$ and $L_z$ gives $\hbar m^2$
$L^2$ gives $\hbar^2 \ell(\ell+1)$ and $L_z$ gives $\hbar m$
$L^2$ gives $\hbar^2 m(m+1)$ and $L_z$ gives $\hbar \ell$