Space of modular forms of level 432, weight 6, and Character 432.i

• Label: 432.6.i
• Level: $432$
• Weight: $6$
• Character orbit: 432.i
• Rep. character: $\chi_{432}(145,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $58$
• Newform subspaces: $6$
• Sturm bound: $432$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(432\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(432, [\chi])\).

	Total	New	Old
Modular forms	756	62	694
Cusp forms	684	58	626
Eisenstein series	72	4	68

Trace form

58 * q + q^5 + q^7 - 727 * q^11 - q^13 - 1000 * q^17 + 4 * q^19 + 3173 * q^23 - 15626 * q^25 + 3981 * q^29 - 1625 * q^31 + 35646 * q^35 - 4 * q^37 - 2901 * q^41 - 13865 * q^43 + 37935 * q^47 - 55224 * q^49 + 4 * q^53 - 6246 * q^55 - 55033 * q^59 - q^61 + 5743 * q^65 + q^67 - 23672 * q^71 - 53632 * q^73 - 24885 * q^77 + q^79 - 41693 * q^83 - 3126 * q^85 - 207948 * q^89 - 80758 * q^91 - 61748 * q^95 - 58147 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(432, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.6.i.a	$432$	$6$	432.i	9.c	$3$	$4$	$2$	$69.286$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					18.6.c.a	$2$	$0$	\(0\)	\(0\)	\(54\)	\(-74\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3^{3}\beta _{1}+2\beta _{2})q^{5}+(-37+37\beta _{1}+\cdots)q^{7}+\cdots\)
432.6.i.b	$432$	$6$	432.i	9.c	$3$	$6$	$3$	$69.286$	6.0.\(\cdots\).3	None					18.6.c.b	$2$	$0$	\(0\)	\(0\)	\(54\)	\(132\)	$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(18-18\beta _{1}-\beta _{5})q^{5}+(44\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
432.6.i.c	$432$	$6$	432.i	9.c	$3$	$8$	$4$	$69.286$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					9.6.c.a	$2$	$0$	\(0\)	\(0\)	\(-78\)	\(-28\)	$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-19\beta _{1}+\beta _{2}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
432.6.i.d	$432$	$6$	432.i	9.c	$3$	$10$	$5$	$69.286$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					36.6.e.a	$2$	$0$	\(0\)	\(0\)	\(21\)	\(-29\)	$2^{8}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\beta _{1}+\beta _{7})q^{5}+(-6\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
432.6.i.e	$432$	$6$	432.i	9.c	$3$	$14$	$7$	$69.286$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					72.6.i.a	$2$	$0$	\(0\)	\(0\)	\(-25\)	\(-93\)	$2^{20}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\beta _{1}-\beta _{3}+\beta _{6})q^{5}+(-13\beta _{1}+\cdots)q^{7}+\cdots\)
432.6.i.f	$432$	$6$	432.i	9.c	$3$	$16$	$8$	$69.286$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None			✓		72.6.i.b	$2$	$0$	\(0\)	\(0\)	\(-25\)	\(93\)	$2^{26}\cdot 3^{28}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3\beta _{8}-\beta _{10})q^{5}+(12-\beta _{2}-12\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

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