Thought I recognized this. =====Discriminant ==Genus Size== 3 [ 1, 1, 32, 0, 0, 0 ] [ 2, 2, 9, 2, -2, 0 ] ---**----- end of spinor genus 1 -------- [ 1, 4, 9, -4, 0, 0 ] ---**----- end of spinor genus 2 -------- The loner is one of the very few spinor regular forms that are not regular. The following constitutes a proof that $\langle 1,4,9,4,0,0 \rangle$ does not lie in the same spinor genus as $\langle 1,1,32,0,0,0 \rangle:$ we have $$ x^2 + 4 y^2 + 9 z^2 + 4yz \neq 2 m^2, $$ where all prime factors $p$ of $m$ satisfy $p \equiv 1 \pmod 4.$