Space of modular forms of level 36, weight 9, and Character 36.c

• Label: 36.9.c
• Level: $36$
• Weight: $9$
• Character orbit: 36.c
• Rep. character: $\chi_{36}(17,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	36.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(36, [\chi])\).

	Total	New	Old
Modular forms	54	2	52
Cusp forms	42	2	40
Eisenstein series	12	0	12

Trace form

2 * q + 616 * q^7 + 36928 * q^13 + 299104 * q^19 + 778334 * q^25 + 933064 * q^31 - 1929044 * q^37 - 4134320 * q^43 - 11339874 * q^49 - 711504 * q^55 - 7532780 * q^61 + 52447024 * q^67 + 1418272 * q^73 + 76931320 * q^79 - 9060012 * q^85 + 11373824 * q^91 - 222541376 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(36, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
36.9.c.a	$36$	$9$	36.c	3.b	$2$	$2$	$2$	$14.666$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	36.9.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(616\)	$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+308q^{7}+244\beta q^{11}+18464q^{13}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)