Space of modular forms of level 432, weight 8, and Character 432.i

• Label: 432.8.i
• Level: $432$
• Weight: $8$
• Character orbit: 432.i
• Rep. character: $\chi_{432}(145,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $82$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(432, [\chi])\).

	Total	New	Old
Modular forms	1044	86	958
Cusp forms	972	82	890
Eisenstein series	72	4	68

Trace form

82 * q + q^5 + q^7 + 7985 * q^11 - q^13 - 23968 * q^17 + 4 * q^19 - 73003 * q^23 - 578126 * q^25 - 64011 * q^29 + 161287 * q^31 - 872754 * q^35 - 4 * q^37 + 150303 * q^41 + 72079 * q^43 - 1531569 * q^47 - 4117716 * q^49 + 4 * q^53 - 156246 * q^55 + 5670407 * q^59 - q^61 - 2263697 * q^65 + q^67 + 19088296 * q^71 + 3202760 * q^73 - 4621701 * q^77 + q^79 + 12683635 * q^83 - 78126 * q^85 - 19738092 * q^89 + 11260346 * q^91 - 12417164 * q^95 + 5296361 * q^97

Decomposition of \(S_{8}^{\mathrm{new}}(432, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.8.i.a	$432$	$8$	432.i	9.c	$3$	$6$	$3$	$134.950$	6.0.\(\cdots\).1	None					18.8.c.a	$2$	$0$	\(0\)	\(0\)	\(-54\)	\(-210\)	$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-18+18\beta _{1}+3\beta _{2}-3\beta _{3}-2\beta _{5})q^{5}+\cdots\)
432.8.i.b	$432$	$8$	432.i	9.c	$3$	$8$	$4$	$134.950$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					18.8.c.b	$2$	$0$	\(0\)	\(0\)	\(-54\)	\(44\)	$2^{4}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-14+14\beta _{1}+\beta _{4})q^{5}+(-2+12\beta _{1}+\cdots)q^{7}+\cdots\)
432.8.i.c	$432$	$8$	432.i	9.c	$3$	$12$	$6$	$134.950$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					9.8.c.a	$2$	$0$	\(0\)	\(0\)	\(180\)	\(84\)	$2^{16}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(30+30\beta _{7}+\beta _{10})q^{5}+(-2\beta _{1}+3\beta _{4}+\cdots)q^{7}+\cdots\)
432.8.i.d	$432$	$8$	432.i	9.c	$3$	$14$	$7$	$134.950$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					36.8.e.a	$2$	$0$	\(0\)	\(0\)	\(-321\)	\(83\)	$2^{20}\cdot 3^{33}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(46\beta _{7}-\beta _{9})q^{5}+(12+\beta _{3}+12\beta _{7}+\cdots)q^{7}+\cdots\)
432.8.i.e	$432$	$8$	432.i	9.c	$3$	$20$	$10$	$134.950$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					72.8.i.a	$2$	$0$	\(0\)	\(0\)	\(125\)	\(-1245\)	$2^{48}\cdot 3^{45}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{10}+12\beta _{11})q^{5}+(-5^{3}+\cdots)q^{7}+\cdots\)
432.8.i.f	$432$	$8$	432.i	9.c	$3$	$22$	$11$	$134.950$		None			✓		72.8.i.b	$2$	$0$	\(0\)	\(0\)	\(125\)	\(1245\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

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