Space of modular forms of level 432, weight 3, and Character 432.q

• Label: 432.3.q
• Level: $432$
• Weight: $3$
• Character orbit: 432.q
• Rep. character: $\chi_{432}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(432, [\chi])\).

	Total	New	Old
Modular forms	324	26	298
Cusp forms	252	22	230
Eisenstein series	72	4	68

Trace form

22 * q + 3 * q^5 + q^7 - 3 * q^11 - q^13 + 4 * q^19 - 3 * q^23 + 34 * q^25 + 75 * q^29 - 23 * q^31 - 4 * q^37 + 39 * q^41 + 49 * q^43 + 213 * q^47 - 36 * q^49 + 54 * q^55 + 213 * q^59 - q^61 + 147 * q^65 + q^67 - 28 * q^73 - 141 * q^77 + q^79 - 363 * q^83 + 24 * q^85 + 98 * q^91 - 726 * q^95 - 61 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(432, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.3.q.a	$432$	$3$	432.q	9.d	$6$	$2$	$1$	$11.771$	\(\Q(\sqrt{-3}) \)	None					9.3.d.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-4+2\zeta_{6})q^{5}+(2-2\zeta_{6})q^{7}+(-1+\cdots)q^{11}+\cdots\)
432.3.q.b	$432$	$3$	432.q	9.d	$6$	$4$	$2$	$11.771$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					36.3.g.a	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(1\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{2}-\beta _{3})q^{5}+(1-\beta _{1}+2\beta _{3})q^{7}+\cdots\)
432.3.q.c	$432$	$3$	432.q	9.d	$6$	$4$	$2$	$11.771$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					72.3.m.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\beta _{3})q^{7}+\cdots\)
432.3.q.d	$432$	$3$	432.q	9.d	$6$	$4$	$2$	$11.771$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					18.3.d.a	$2$	$0$	\(0\)	\(0\)	\(18\)	\(-2\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3+3\beta _{2})q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
432.3.q.e	$432$	$3$	432.q	9.d	$6$	$8$	$4$	$11.771$	8.0.\(\cdots\).9	None			✓		72.3.m.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

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