work in a finite-dimensional truncated space ${\cal H}_{0}^{\rm tr}$ is spanned by (\[basis1\]), (\[basis2\]), (\[basis3\]) satisfying the following additional constraints \_[i=1]{}\^[p]{}|k\_i = \_[i=1]{}\^[q]{}k\_i n\_c , \_[i=1]{}\^[p]{}|n\_i = \_[i=1]{}\^[q]{}n\_i n\_c where $n_c$ is the integer that sets the level truncation[^5]. We choose the space ${\cal H}_{0}^{\rm tr}$ to contain only zero spin vectors that is relevant for identifying RG boundary states.

   $n_c$  dimension of truncated NS space   dimension of truncated R space   Total dimension of truncated space   Number of diagonal states
  ------- --------------------------------- -------------------------------- ------------------------------------ ---------------------------
     8    91                                97                               188                                  58
     9    141                               161                              302                                  76
    10    226                               261                              487                                  99
    11    354                               405                              759                                  127
    12    556                               630                              1186                                 162
    13    844                               954                              1798                                 204

  $n_c$                                  8     9    10    11     12     13     14     15     16     17     18
  ------------------------------------ ----- ----- ----- ----- ------ ------ ------ ------ ------ ------ -------
  dimension of truncated NS space       91    141   226   354   556    844    1296   1909   2838   4139  
  dimension of truncated R space        97    161   261   405   630    954    1438   2167   3191   4635   6751
  Total dimension of truncated space    188   302   487   759   1186   1798   2734   4076   6029   8774   12820
  Dimension of diagonal subspace        58    76    99    127   162    204    256    318    393    482     