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

• Label: 432.3.o
• Level: $432$
• Weight: $3$
• Character orbit: 432.o
• Rep. character: $\chi_{432}(127,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $216$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(216\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	324	24	300
Cusp forms	252	24	228
Eisenstein series	72	0	72

Trace form

\( 24 q + O(q^{10}) \)

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.o.a	$432$	$3$	432.o	36.f	$6$	$8$	$4$	$11.771$	8.0.856615824.2	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\beta _{6})q^{7}+\cdots\)
432.3.o.b	$432$	$3$	432.o	36.f	$6$	$8$	$4$	$11.771$	8.0.856615824.2	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{5})q^{5}+(-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
432.3.o.c	$432$	$3$	432.o	36.f	$6$	$8$	$4$	$11.771$	8.0.121550625.1	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\beta _{2}+\beta _{4}-\beta _{6})q^{5}-\beta _{3}q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)