Space of modular forms of level 432, weight 3, and Character 432.w

• Label: 432.3.w
• Level: $432$
• Weight: $3$
• Character orbit: 432.w
• Rep. character: $\chi_{432}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(432, [\chi])\).

	Total	New	Old
Modular forms	600	200	400
Cusp forms	552	184	368
Eisenstein series	48	16	32

Trace form

\( 184 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(432, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.3.w.a	$432$	$3$	432.w	144.v	$12$	$184$	$46$	$11.771$		None		$4$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)