Lorentz covariance of the Noether charge The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int d^3\mathbf x\Theta^{0\nu}(x)$$But I cannot see explicitly how this quantity is a four-vector covariant under Lorentz transformation, since $d^3\mathbf x$ is part of the invariant $d^4x$, $\Theta^{0\nu}(x)$ is part of the covariant tensor $\Theta^{\mu\nu}(x)$, neither of which transforms covariantly.
So can someone show me how this becomes correct?
And generally, how to show that a Noether charge $Q$ corresponding to the Noether current $j^\mu$, $$Q=\int d^3\mathbf x j^0(x)$$ , is a Lorentz scalar?
 A: You may use the following notation for hypersurfaces in four dimensions :
$d\sigma_\mu = \epsilon_{\mu\alpha\beta\gamma}dx^\alpha dx^\beta dx^\gamma$
For instance $d\sigma_0= d^3x$
The expression of the momentum-energy is then : 
$P_\nu = \int d\sigma^\mu \Theta_{\mu\nu}$
The same kind of expression could be used with the charge : 
$Q = \int d\sigma^\mu j_{\mu}$
[EDIT]
How make the connection with the OP formulae ? 
One may adopt the following point of view, take for instance the formula for the charge $\tilde Q = \int d\sigma^\mu j_{\mu}$, this means : 
$ \tilde Q = \int d\sigma^0 j_{0} + \int  d\sigma^1 j_{1} + \int  d\sigma^2 j_{2}+ \int  d\sigma^3 j_{3} \\
=\int dx~ dy~ dz ~j_{0}+\int dy~ dz~ dt ~j_{1}+\int dz~ dt~ dx ~j_{2} + \int dt~ dx~ dy ~j_{3} \\=Q + \int dy~ dz~ dt ~j_{1}+\int dz~ dt~ dx ~j_{2} + \int dt~ dx~ dy ~j_{3}$
Now, take one of the residual integrals, for instance $I_1=\int dy~ dz~ dt ~j_{1}$, it is an integral at $x$ constant, and one may choose $x=\pm\infty$. At infinity, we may suppose that the current is zero : $j_1(\pm \infty)=0$. So, assuming a zero current $j_1$ at spatial $x$ infinity, we get $I_1=0$, and one may have the same demonstration for the other 2 integrals. 
So, finally , with the hypothesis of taking spatial slicing of the residual integrals at spatial infinity, and vanishing  currents at spatial infinity, we have $\tilde Q = Q$
