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

• Label: 432.4.s
• Level: $432$
• Weight: $4$
• Character orbit: 432.s
• Rep. character: $\chi_{432}(143,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	468	36	432
Cusp forms	396	36	360
Eisenstein series	72	0	72

Trace form

\( 36 q + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.4.s.a	$432$	$4$	432.s	36.h	$6$	$2$	$1$	$25.489$	\(\Q(\sqrt{-3}) \)	None					144.4.s.a	$2$	$0$	\(0\)	\(0\)	\(21\)	\(-15\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(14-7\zeta_{6})q^{5}+(-5-5\zeta_{6})q^{7}+(-39+\cdots)q^{11}+\cdots\)
432.4.s.b	$432$	$4$	432.s	36.h	$6$	$2$	$1$	$25.489$	\(\Q(\sqrt{-3}) \)	None					144.4.s.a	$2$	$0$	\(0\)	\(0\)	\(21\)	\(15\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(14-7\zeta_{6})q^{5}+(5+5\zeta_{6})q^{7}+(39+\cdots)q^{11}+\cdots\)
432.4.s.c	$432$	$4$	432.s	36.h	$6$	$10$	$5$	$25.489$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					144.4.s.c	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-33\)	$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{7})q^{5}+(-6+3\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
432.4.s.d	$432$	$4$	432.s	36.h	$6$	$10$	$5$	$25.489$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					144.4.s.c	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(33\)	$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{7})q^{5}+(6-3\beta _{1}-\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)
432.4.s.e	$432$	$4$	432.s	36.h	$6$	$12$	$6$	$25.489$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None			✓		144.4.s.e	$4$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)	$2^{8}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{5}-\beta _{7}q^{7}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)

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

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