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

• Label: 432.2.u
• Level: $432$
• Weight: $2$
• Character orbit: 432.u
• Rep. character: $\chi_{432}(49,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $102$
• Newform subspaces: $6$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

	Total	New	Old
Modular forms	468	114	354
Cusp forms	396	102	294
Eisenstein series	72	12	60

Trace form

\( 102 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.2.u.a	$432$	$2$	432.u	27.e	$9$	$6$	$1$	$3.450$	\(\Q(\zeta_{18})\)	None					54.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-2\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
432.2.u.b	$432$	$2$	432.u	27.e	$9$	$12$	$2$	$3.450$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					54.2.e.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{3}-\beta _{4}-\beta _{11})q^{3}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
432.2.u.c	$432$	$2$	432.u	27.e	$9$	$12$	$2$	$3.450$	12.0.\(\cdots\).1	None					27.2.e.a	$2$	$0$	\(0\)	\(6\)	\(-3\)	\(6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}+\beta _{6}+\beta _{7}-\beta _{9})q^{3}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
432.2.u.d	$432$	$2$	432.u	27.e	$9$	$18$	$3$	$3.450$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					108.2.i.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{12}q^{3}+(-1+\beta _{1}-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
432.2.u.e	$432$	$2$	432.u	27.e	$9$	$24$	$4$	$3.450$		None					216.2.q.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{9}]$
432.2.u.f	$432$	$2$	432.u	27.e	$9$	$30$	$5$	$3.450$		None			✓		216.2.q.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)