Space of modular forms of level 432, weight 9, and Character 432.q

• Label: 432.9.q
• Level: $432$
• Weight: $9$
• Character orbit: 432.q
• Rep. character: $\chi_{432}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $94$
• Newform subspaces: $4$
• Sturm bound: $648$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	432.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(648\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(432, [\chi])\).

	Total	New	Old
Modular forms	1188	98	1090
Cusp forms	1116	94	1022
Eisenstein series	72	4	68

Trace form

94 * q + 3 * q^5 + q^7 - 3 * q^11 - q^13 + 4 * q^19 - 3 * q^23 + 3359374 * q^25 + 1897635 * q^29 + 214177 * q^31 - 4 * q^37 + 2063379 * q^41 + 3393985 * q^43 - 20714403 * q^47 - 33765264 * q^49 + 781254 * q^55 - 35302179 * q^59 - q^61 - 5224893 * q^65 + q^67 + 32396444 * q^73 + 35105475 * q^77 + q^79 - 105288483 * q^83 + 390624 * q^85 - 169039486 * q^91 - 476132550 * q^95 - 56298481 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(432, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.9.q.a	$432$	$9$	432.q	9.d	$6$	$14$	$7$	$175.988$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					9.9.d.a	$2$	$0$	\(0\)	\(0\)	\(-438\)	\(-922\)	$2^{14}\cdot 3^{30}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-21+21\beta _{1}+\beta _{9})q^{5}+(133\beta _{1}+\cdots)q^{7}+\cdots\)
432.9.q.b	$432$	$9$	432.q	9.d	$6$	$16$	$8$	$175.988$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					36.9.g.a	$2$	$0$	\(0\)	\(0\)	\(-441\)	\(-923\)	$2^{20}\cdot 3^{44}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-37-18\beta _{1}-\beta _{4})q^{5}+(-115+\cdots)q^{7}+\cdots\)
432.9.q.c	$432$	$9$	432.q	9.d	$6$	$16$	$8$	$175.988$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					18.9.d.a	$2$	$0$	\(0\)	\(0\)	\(882\)	\(1846\)	$2^{32}\cdot 3^{40}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(74+37\beta _{1}-\beta _{3})q^{5}+(230+230\beta _{1}+\cdots)q^{7}+\cdots\)
432.9.q.d	$432$	$9$	432.q	9.d	$6$	$48$	$24$	$175.988$		None			✓		72.9.m.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{9}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)