Just on dividing your current take home pay by 5 and multiplying by 3, that does look too low. Added to that, on €360 per week you would be below the Health Levy threshold.
If your previous gross pay was €120 per day, and you worked 5 days, to take home €524.42 your tax credits must have been 99.35.
Using the same tax credits, and a weekly gross of €360, I calculate your take home pay would be €343.38 ( more if tax refunds are permitted).
In one of those little twists, you would take home slightly more if your gross weekly pay was only €352, as no employee Prsi would be payable.
You should check your tax credits, and ask the accountant for pay slips (previous and current).