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

• Label: 663.2.n
• Level: $663$
• Weight: $2$
• Character orbit: 663.n
• Rep. character: $\chi_{663}(86,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $152$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
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	152	24
Cusp forms	160	152	8
Eisenstein series	16	0	16

Trace form

\( 152 q + 12 q^{6} - 16 q^{7} + O(q^{10}) \)

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.n.a	$663$	$2$	663.n	39.f	$4$	$76$	$38$	$5.294$		None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$
663.2.n.b	$663$	$2$	663.n	39.f	$4$	$76$	$38$	$5.294$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$

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

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