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

• Label: 432.2.i
• Level: $432$
• Weight: $2$
• Character orbit: 432.i
• Rep. character: $\chi_{432}(145,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	180	14	166
Cusp forms	108	10	98
Eisenstein series	72	4	68

Trace form

10 * q + q^5 + q^7 - 7 * q^11 - q^13 + 8 * q^17 + 4 * q^19 + 5 * q^23 - 2 * q^25 - 3 * q^29 + 7 * q^31 + 30 * q^35 - 4 * q^37 + 3 * q^41 + 7 * q^43 + 15 * q^47 + 4 * q^53 - 6 * q^55 - 25 * q^59 - q^61 - 17 * q^65 + q^67 - 56 * q^71 - 16 * q^73 - 21 * q^77 + q^79 - 29 * q^83 - 6 * q^85 - 12 * q^89 - 22 * q^91 + 28 * q^95 + 5 * q^97

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.i.a	$432$	$2$	432.i	9.c	$3$	$2$	$1$	$3.450$	\(\Q(\sqrt{-3}) \)	None					72.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
432.2.i.b	$432$	$2$	432.i	9.c	$3$	$2$	$1$	$3.450$	\(\Q(\sqrt{-3}) \)	None					18.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots\)
432.2.i.c	$432$	$2$	432.i	9.c	$3$	$2$	$1$	$3.450$	\(\Q(\sqrt{-3}) \)	None					36.2.e.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
432.2.i.d	$432$	$2$	432.i	9.c	$3$	$4$	$2$	$3.450$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None			✓		72.2.i.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)

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

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