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

• Label: 432.2.be
• Level: $432$
• Weight: $2$
• Character orbit: 432.be
• Rep. character: $\chi_{432}(47,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $108$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 108 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	468	108	360
Cusp forms	396	108	288
Eisenstein series	72	0	72

Trace form

\( 108 q + O(q^{10}) \)

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.be.a	$432$	$2$	432.be	108.l	$18$	$36$	$6$	$3.450$		None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
432.2.be.b	$432$	$2$	432.be	108.l	$18$	$36$	$6$	$3.450$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
432.2.be.c	$432$	$2$	432.be	108.l	$18$	$36$	$6$	$3.450$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)