Space of modular forms of level 441, weight 3, and Character 441.t

• Label: 441.3.t
• Level: $441$
• Weight: $3$
• Character orbit: 441.t
• Rep. character: $\chi_{441}(166,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $152$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(441, [\chi])\).

	Total	New	Old
Modular forms	240	168	72
Cusp forms	208	152	56
Eisenstein series	32	16	16

Trace form

\( 152 q + 2 q^{2} + 3 q^{3} + 290 q^{4} + 3 q^{5} + 12 q^{6} - 8 q^{8} + 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(441, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.3.t.a	$441$	$3$	441.t	63.t	$6$	$28$	$14$	$12.016$		None		$2$	$0$	\(-2\)	\(3\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
441.3.t.b	$441$	$3$	441.t	63.t	$6$	$28$	$14$	$12.016$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
441.3.t.c	$441$	$3$	441.t	63.t	$6$	$96$	$48$	$12.016$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)