Slack variable in SDP

I have the following toy example of an SDP:

cvx_begin sdp
variable M(2,2) symmetric
variable s

subject to
s*eye(2) >= M;
4*M >=  s*eye(2);

M >= 0.1*eye(2);

minimize norm(M - [1 2; 3 4]);


I wonder if there is a way to formulate the two first LMI in CVX without the need to use the real slack variable s.

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