Space of modular forms of level 32, weight 9, and Character 32.c

• Label: 32.9.c
• Level: $32$
• Weight: $9$
• Character orbit: 32.c
• Rep. character: $\chi_{32}(31,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	32.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(32, [\chi])\).

	Total	New	Old
Modular forms	36	8	28
Cusp forms	28	8	20
Eisenstein series	8	0	8

Trace form

\( 8 q + 336 q^{5} - 13688 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(32, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.9.c.a	$32$	$9$	32.c	4.b	$2$	$4$	$4$	$13.036$	\(\Q(i, \sqrt{39})\)	None		$2$	$0$	\(0\)	\(0\)	\(-728\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(-182+\beta _{2})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots\)
32.9.c.b	$32$	$9$	32.c	4.b	$2$	$4$	$4$	$13.036$	\(\Q(i, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(1064\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(266+3\beta _{2})q^{5}+(-7\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)