Space of modular forms of level 441, weight 2, and Character 441.bg

• Label: 441.2.bg
• Level: $441$
• Weight: $2$
• Character orbit: 441.bg
• Rep. character: $\chi_{441}(17,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

	Total	New	Old
Modular forms	720	216	504
Cusp forms	624	216	408
Eisenstein series	96	0	96

Trace form

\( 216 q - 16 q^{4} + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.2.bg.a	$441$	$2$	441.bg	147.o	$42$	$216$	$18$	$3.521$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{42}]$

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

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