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

• Label: 441.3.bf
• Level: $441$
• Weight: $3$
• Character orbit: 441.bf
• Rep. character: $\chi_{441}(44,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $456$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.bf (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	1392	456	936
Cusp forms	1296	456	840
Eisenstein series	96	0	96

Trace form

\( 456 q - 80 q^{4} + 2 q^{7} + O(q^{10}) \)

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.bf.a	$441$	$3$	441.bf	147.n	$42$	$456$	$38$	$12.016$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{42}]$

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

\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)