Space of modular forms of level 432, weight 7, and Character 432.q

• Label: 432.7.q
• Level: $432$
• Weight: $7$
• Character orbit: 432.q
• Rep. character: $\chi_{432}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $70$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(504\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(432, [\chi])\).

	Total	New	Old
Modular forms	900	74	826
Cusp forms	828	70	758
Eisenstein series	72	4	68

Trace form

70 * q + 3 * q^5 + q^7 - 3 * q^11 - q^13 + 4 * q^19 - 3 * q^23 + 96874 * q^25 - 25701 * q^29 - 27719 * q^31 - 4 * q^37 + 15663 * q^41 - 65519 * q^43 + 62853 * q^47 - 487404 * q^49 + 31254 * q^55 - 605883 * q^59 - q^61 + 663987 * q^65 + q^67 - 356044 * q^73 - 1151277 * q^77 + q^79 + 2305797 * q^83 + 15624 * q^85 - 773854 * q^91 + 4430154 * q^95 + 34379 * q^97

Decomposition of \(S_{7}^{\mathrm{new}}(432, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.7.q.a	$432$	$7$	432.q	9.d	$6$	$10$	$5$	$99.383$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					9.7.d.a	$2$	$0$	\(0\)	\(0\)	\(219\)	\(121\)	$2^{6}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(15-\beta _{2}-15\beta _{3}+\beta _{5}-\beta _{7})q^{5}+\cdots\)
432.7.q.b	$432$	$7$	432.q	9.d	$6$	$12$	$6$	$99.383$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					18.7.d.a	$2$	$0$	\(0\)	\(0\)	\(-432\)	\(-240\)	$2^{12}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-48+24\beta _{2}+\beta _{7})q^{5}+(-40+40\beta _{2}+\cdots)q^{7}+\cdots\)
432.7.q.c	$432$	$7$	432.q	9.d	$6$	$12$	$6$	$99.383$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					36.7.g.a	$2$	$0$	\(0\)	\(0\)	\(216\)	\(120\)	$2^{12}\cdot 3^{24}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(12-12\beta _{1}-\beta _{3})q^{5}+(-20\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
432.7.q.d	$432$	$7$	432.q	9.d	$6$	$36$	$18$	$99.383$		None			✓		72.7.m.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{7}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)