Space of modular forms of level 432, weight 6, and Character 432.c

• Label: 432.6.c
• Level: $432$
• Weight: $6$
• Character orbit: 432.c
• Rep. character: $\chi_{432}(431,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $7$
• Sturm bound: $432$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	432.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(432, [\chi])\).

	Total	New	Old
Modular forms	378	40	338
Cusp forms	342	40	302
Eisenstein series	36	0	36

Trace form

\( 40 q + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(432, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.6.c.a	$432$	$6$	432.c	12.b	$2$	$2$	$2$	$69.286$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+149\zeta_{6}q^{7}+427q^{13}+1525\zeta_{6}q^{19}+\cdots\)
432.6.c.b	$432$	$6$	432.c	12.b	$2$	$2$	$2$	$69.286$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-29\zeta_{6}q^{7}+775q^{13}+31\zeta_{6}q^{19}+\cdots\)
432.6.c.c	$432$	$6$	432.c	12.b	$2$	$4$	$4$	$69.286$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-23\beta _{1}q^{7}-\beta _{3}q^{11}-629q^{13}+\cdots\)
432.6.c.d	$432$	$6$	432.c	12.b	$2$	$4$	$4$	$69.286$	\(\Q(\sqrt{-3}, \sqrt{-34})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+55\beta _{2}q^{7}-\beta _{3}q^{11}-185q^{13}+\cdots\)
432.6.c.e	$432$	$6$	432.c	12.b	$2$	$8$	$8$	$69.286$	8.0.\(\cdots\).21	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-7\beta _{1}-\beta _{7})q^{7}+(\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\)
432.6.c.f	$432$	$6$	432.c	12.b	$2$	$8$	$8$	$69.286$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{5}q^{11}+(226+\beta _{6}+\cdots)q^{13}+\cdots\)
432.6.c.g	$432$	$6$	432.c	12.b	$2$	$12$	$12$	$69.286$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{34}\cdot 3^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(3\beta _{1}-\beta _{8})q^{7}+(-\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(432, [\chi]) \cong \)