As Cloverjo states, there are two different ways of jointly owning a property. If you've not got a copy of the title register you can download one for £3 from the Land Registry (assuming that you're in England or Wales):
https://www.gov.uk/search-property-information-land-registry
If the title register shows that you were 'joint tenants' then it was your
partnership that owned the property and, as the surviving partner, you now own the property in its entirety. (Even if your mother had written a will, she couldn't have left her share of the house to anyone, as she never owned a share in her own right).
If the title register shows that you were 'tenants in common' then you and your mother each owned half of the property. If your mother had written a will she would have been free to leave her half to whomever she chose, irrespective of any family ties. (She could have left it to your local dogs' home if she'd wanted to). As she didn't write a will, the laws of intestacy apply and each of you three siblings receive one third of her share. (So you now own two thirds of it and each of your siblings owns one sixth).
If your mother left no significant estate (other than the house) you probably don't need to apply for 'letters of administration' (to enable you to distribute the estate) if you were 'joint tenants'. You simply need to fill in a Land Registry form, so that the title register is amended to show you as the sole owner.
However if you were 'tenants in common' you probably need to apply for letter of administration in order to transfer the one sixth shares to your siblings. (Contact your local Probate Office).
To return to your original question:
If you now own the house outright you can throw your siblings out unless they've acquird tenants' rights through paying you rent. (Even then, any such rights are likely to be very limited as, if they share the accommodation with you, they're effectively only 'lodgers').
If you only own two thirds of the house, one or both of your siblings can insist that you buy out their share of the property or, if you refuse, seek a court order to force its sale (so that they can get their share in cash).