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

• Label: 663.2.w
• Level: $663$
• Weight: $2$
• Character orbit: 663.w
• Rep. character: $\chi_{663}(16,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 221 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	176	88	88
Cusp forms	160	88	72
Eisenstein series	16	0	16

Trace form

\( 88 q + 4 q^{2} - 48 q^{4} - 24 q^{8} + 44 q^{9} + O(q^{10}) \)

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.w.a	$663$	$2$	663.w	221.l	$6$	$4$	$2$	$5.294$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
663.2.w.b	$663$	$2$	663.w	221.l	$6$	$8$	$4$	$5.294$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{7})q^{2}+\cdots\)
663.2.w.c	$663$	$2$	663.w	221.l	$6$	$76$	$38$	$5.294$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(663, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(663, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(221, [\chi])\)\(^{\oplus 2}\)