Space of modular forms of level 432, weight 1, and Character 432.e

• Label: 432.1.e
• Level: $432$
• Weight: $1$
• Character orbit: 432.e
• Rep. character: $\chi_{432}(161,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	432.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(432, [\chi])\).

	Total	New	Old
Modular forms	22	1	21
Cusp forms	4	1	3
Eisenstein series	18	0	18

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q + q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.1.e.a	$432$	$1$	432.e	3.b	$2$	$1$	$1$	$0.216$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{7}-q^{13}+q^{19}+q^{25}-2q^{31}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)