Delete Item in Document Libarary using Client Object Model?

ClientContext clientContext = new ClientContext("http://sharepoint:6666");
            Uri uri = new Uri(filePath);
            List spList = clientContext.Web.Lists.GetByTitle("Shared Documents");
            Microsoft.SharePoint.Client.CamlQuery query = new Microsoft.SharePoint.Client.CamlQuery();
            query.ViewXml = "<View>"
               + "<Query>"
               + "<Where><Eq><FieldRef Name='FileLeafRef'/><Value Type='File'>" + filename + "</Value></Eq></Where>"
               + "</Query>"
               + "</View>";
            // execute the query                
            ListItemCollection listItems = spList.GetItems(query);
            clientContext.Load(listItems);
            clientContext.ExecuteQuery();
            foreach (ListItem listitem in listItems)
            {


                listitem.DeleteObject();
                clientContext.ExecuteQuery();
            }

FileLeafRef is internal column name of Name.

Added on a little to the answer. It works perfectly. Suggest passing the Main Site name int he sLoginUri and then the Folder Location as not everyone has a "Shared Documents".

    #region Delete a File

    //============================================================================== Delete a File from a Library
    public static bool DeleteAFile(string sFileName, string sFldrLoc, string sUserName, string sPassword, 
                                   string sLoginUri, ref String sError)
    {
        bool bRetVal = false;

        string sourceFolderName = "/" + sFldrLoc;
        string documentRelativePath = sLoginUri + sourceFolderName + "/" + sFileName;

        try
        {
            SP.ClientContext clientContext = new SP.ClientContext(sLoginUri);
            //NetworkCredential credential = System.Net.CredentialCache.DefaultNetworkCredentials;
            //clientContext.Credentials = credential;
            NetworkCredential credential = new NetworkCredential(sUserName, sPassword, "citgo");
            clientContext.Credentials = credential;

            Uri uri = new Uri(documentRelativePath);
            SP.List spList = clientContext.Web.Lists.GetByTitle(sFldrLoc);
            Microsoft.SharePoint.Client.CamlQuery query = new Microsoft.SharePoint.Client.CamlQuery();
            query.ViewXml = "<View>"
               + "<Query>"
               + "<Where><Eq><FieldRef Name='FileLeafRef'/><Value Type='File'>" + sFileName + "</Value></Eq></Where>"
               + "</Query>"
               + "</View>";
            // execute the query                
            SP.ListItemCollection listItems = spList.GetItems(query);
            clientContext.Load(listItems);
            clientContext.ExecuteQuery();
            foreach (SP.ListItem listitem in listItems)
            {
                listitem.DeleteObject();
                clientContext.ExecuteQuery();
                bRetVal = true;
            }
        }
        catch (Exception exc)
        {
            //Log Error Here
            sError = exc.Message;
        }

        return bRetVal;
    }

    #endregion