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

• Label: 432.2.c
• Level: $432$
• Weight: $2$
• Character orbit: 432.c
• Rep. character: $\chi_{432}(431,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(13\)
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	90	8	82
Cusp forms	54	8	46
Eisenstein series	36	0	36

Trace form

\( 8 q + O(q^{10}) \)

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.c.a	$432$	$2$	432.c	12.b	$2$	$2$	$2$	$3.450$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{7}-5q^{13}-\zeta_{6}q^{19}+5q^{25}+\cdots\)
432.2.c.b	$432$	$2$	432.c	12.b	$2$	$2$	$2$	$3.450$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{7}+7q^{13}-5\zeta_{6}q^{19}+5q^{25}+\cdots\)
432.2.c.c	$432$	$2$	432.c	12.b	$2$	$4$	$4$	$3.450$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}-\zeta_{12}^{3}q^{11}+\cdots\)

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

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