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**Additional resources for Dimension Formulae for the Vector Spaces of Siegel Cusp Forms of Degree Three**

**Example text**

Then M Let e2ir±/9 M is conjugate in (v = e 2iri/7 ) by e2jri/7 . be an element of Sp(3, R) Sp(3, Z) or order 7, to one of the following: 24 MINKING EIE [v, v 2 , v 3 ] , [v, v 2 , v 4 ] , [v, v 4 , v 5 ] , [v, v 3 , v 5 , 5 , v6,, v ] . r 2 [v2 , v 3 , v 4, ] , [v ,4v ,6, v 3r,4 [v 5 , v 6, , v r ]3 , [v r LEMMA 6. The number of conjugacy classes of regular elliptic elements of order X -fX -2X+1 , in Sp(3, Z) a, 3, y Suppose THEOREM 3. equation 7 is are distinct roots of the (or more precisely, 4TT 8 .

0 s, 0 53 's 1; ,1 0^ S X ] ~ [M2, -Uj_; 0, 0; S-% 0 0 0 s e z 19 [M2, -Ul5 20 [M2, -U2; 0, 0; 21 [M2, -U2; , 0; 22 s, € Z, s0 e Z - {0} ] , s ^ s 2 e Z - {0} . 0 s, s 0 0 s2i ] ~ [M2> -U2; 0, 0; s +% 0 '2J s1 0 0 0 ] ~ [M£, -Uj_; 0, 0; s+V 0 0 0 ], s e z 23 24 [M2, -Ux; [M|, -UL; [1' [o '1' [o ], s 9 e Z - {0} . , 0; [M2, -UL; ], s. s, 0 0; s. e z, l 1 S . ° l ° 1 ], s 2! "s 1' , 0; 1 s1 6 Z, s 2 e Z - {0} . ] ~ [M£, -Ux; 0, 0; ] 0 s+% 0 0 0 S G Z . 0 0. °. 0 Oj s e Z - {01 . ] - [M 2 , M 3 ; 0, 0; ] ~ [M 2 , M 3 ; 0 , 0; s-% 0 0 0 ] , s+% 0 0 0 ] , 0] s 0 0 0 ], s e Z - (0) .

X x J i=i i