Space of modular forms of level 432, weight 4, and Character 432.c

• Label: 432.4.c
• Level: $432$
• Weight: $4$
• Character orbit: 432.c
• Rep. character: $\chi_{432}(431,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $8$
• Sturm bound: $288$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(432, [\chi])\).

	Total	New	Old
Modular forms	234	24	210
Cusp forms	198	24	174
Eisenstein series	36	0	36

Trace form

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

Decomposition of \(S_{4}^{\mathrm{new}}(432, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.4.c.a	$432$	$4$	432.c	12.b	$2$	$2$	$2$	$25.489$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-12\zeta_{6}q^{5}+17\zeta_{6}q^{7}-6^{2}q^{11}+19q^{13}+\cdots\)
432.4.c.b	$432$	$4$	432.c	12.b	$2$	$2$	$2$	$25.489$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+19\zeta_{6}q^{7}-89q^{13}-73\zeta_{6}q^{19}+\cdots\)
432.4.c.c	$432$	$4$	432.c	12.b	$2$	$2$	$2$	$25.489$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{7}+19q^{13}-17\zeta_{6}q^{19}+5^{3}q^{25}+\cdots\)
432.4.c.d	$432$	$4$	432.c	12.b	$2$	$2$	$2$	$25.489$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-12\zeta_{6}q^{5}-17\zeta_{6}q^{7}+6^{2}q^{11}+19q^{13}+\cdots\)
432.4.c.e	$432$	$4$	432.c	12.b	$2$	$4$	$4$	$25.489$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-6\zeta_{12}^{2})q^{5}+(-6\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
432.4.c.f	$432$	$4$	432.c	12.b	$2$	$4$	$4$	$25.489$	\(\Q(\sqrt{3}, \sqrt{-17})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}-2q^{13}+\cdots\)
432.4.c.g	$432$	$4$	432.c	12.b	$2$	$4$	$4$	$25.489$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{11}+\cdots\)
432.4.c.h	$432$	$4$	432.c	12.b	$2$	$4$	$4$	$25.489$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-6\zeta_{12}^{2})q^{5}+(6\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(432, [\chi]) \cong \)