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

• Label: 432.3.e
• Level: $432$
• Weight: $3$
• Character orbit: 432.e
• Rep. character: $\chi_{432}(161,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $8$
• Sturm bound: $216$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(216\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	162	16	146
Cusp forms	126	16	110
Eisenstein series	36	0	36

Trace form

\( 16 q + 8 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.3.e.a	$432$	$3$	432.e	3.b	$2$	$1$	$1$	$11.771$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-11\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-11q^{7}+23q^{13}+37q^{19}+5^{2}q^{25}+\cdots\)
432.3.e.b	$432$	$3$	432.e	3.b	$2$	$1$	$1$	$11.771$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(13\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+13q^{7}-q^{13}-11q^{19}+5^{2}q^{25}+\cdots\)
432.3.e.c	$432$	$3$	432.e	3.b	$2$	$2$	$2$	$11.771$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-5q^{7}-5iq^{11}-10q^{13}+\cdots\)
432.3.e.d	$432$	$3$	432.e	3.b	$2$	$2$	$2$	$11.771$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-5q^{7}+\beta q^{11}-q^{13}-3\beta q^{17}+\cdots\)
432.3.e.e	$432$	$3$	432.e	3.b	$2$	$2$	$2$	$11.771$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-3q^{7}-\beta q^{11}-17q^{13}+5\beta q^{17}+\cdots\)
432.3.e.f	$432$	$3$	432.e	3.b	$2$	$2$	$2$	$11.771$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+3q^{7}-7\beta q^{11}+7q^{13}+5\beta q^{17}+\cdots\)
432.3.e.g	$432$	$3$	432.e	3.b	$2$	$2$	$2$	$11.771$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+7q^{7}-iq^{11}+14q^{13}+2iq^{17}+\cdots\)
432.3.e.h	$432$	$3$	432.e	3.b	$2$	$4$	$4$	$11.771$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{8}+\zeta_{8}^{2})q^{5}+(3-\zeta_{8}^{3})q^{7}+(-3\zeta_{8}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)