Space of modular forms of level 432, weight 2, and Character 432.bg

• Label: 432.2.bg
• Level: $432$
• Weight: $2$
• Character orbit: 432.bg
• Rep. character: $\chi_{432}(13,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $840$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.bg (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 432 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

	Total	New	Old
Modular forms	888	888	0
Cusp forms	840	840	0
Eisenstein series	48	48	0

Trace form

\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.2.bg.a	$432$	$2$	432.bg	432.ag	$36$	$840$	$70$	$3.450$		None		$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$