Space of modular forms of level 663, weight 2, and Character 663.bd

• Label: 663.2.bd
• Level: $663$
• Weight: $2$
• Character orbit: 663.bd
• Rep. character: $\chi_{663}(8,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $320$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.bd (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 663 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(663, [\chi])\).

	Total	New	Old
Modular forms	352	352	0
Cusp forms	320	320	0
Eisenstein series	32	32	0

Trace form

\( 320 q - 8 q^{3} - 304 q^{4} + 4 q^{6} - 8 q^{7} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(663, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
663.2.bd.a	$663$	$2$	663.bd	663.ad	$8$	$4$	$1$	$5.294$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
663.2.bd.b	$663$	$2$	663.bd	663.ad	$8$	$4$	$1$	$5.294$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
663.2.bd.c	$663$	$2$	663.bd	663.ad	$8$	$312$	$78$	$5.294$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$