Space of modular forms of level 432, weight 5, and Character 432.e

• Label: 432.5.e
• Level: $432$
• Weight: $5$
• Character orbit: 432.e
• Rep. character: $\chi_{432}(161,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $11$
• Sturm bound: $360$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	432.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(360\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(432, [\chi])\).

	Total	New	Old
Modular forms	306	32	274
Cusp forms	270	32	238
Eisenstein series	36	0	36

Trace form

\( 32 q + 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(432, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.5.e.a	$432$	$5$	432.e	3.b	$2$	$1$	$1$	$44.656$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-71\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-71q^{7}-337q^{13}+601q^{19}+5^{4}q^{25}+\cdots\)
432.5.e.b	$432$	$5$	432.e	3.b	$2$	$1$	$1$	$44.656$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-23\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-23q^{7}+191q^{13}-647q^{19}+5^{4}q^{25}+\cdots\)
432.5.e.c	$432$	$5$	432.e	3.b	$2$	$2$	$2$	$44.656$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-34\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-17q^{7}-11\beta q^{11}+95q^{13}+\cdots\)
432.5.e.d	$432$	$5$	432.e	3.b	$2$	$2$	$2$	$44.656$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-5q^{7}-13iq^{11}-34q^{13}+\cdots\)
432.5.e.e	$432$	$5$	432.e	3.b	$2$	$2$	$2$	$44.656$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(38\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+11iq^{5}+19q^{7}+41iq^{11}+302q^{13}+\cdots\)
432.5.e.f	$432$	$5$	432.e	3.b	$2$	$2$	$2$	$44.656$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(62\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+31q^{7}+5\beta q^{11}-241q^{13}+\cdots\)
432.5.e.g	$432$	$5$	432.e	3.b	$2$	$2$	$2$	$44.656$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(146\)	$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+73q^{7}-5\beta q^{11}+95q^{13}+\cdots\)
432.5.e.h	$432$	$5$	432.e	3.b	$2$	$4$	$4$	$44.656$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-68\)	$2^{3}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-17+\zeta_{8}^{3})q^{7}+\cdots\)
432.5.e.i	$432$	$5$	432.e	3.b	$2$	$4$	$4$	$44.656$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-60\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-15+\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
432.5.e.j	$432$	$5$	432.e	3.b	$2$	$4$	$4$	$44.656$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-36\)	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-9+\beta _{3})q^{7}+(3\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
432.5.e.k	$432$	$5$	432.e	3.b	$2$	$8$	$8$	$44.656$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(72\)	$2^{18}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(9+\beta _{2})q^{7}+(-\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)