Space of modular forms of level 144, weight 9, and Character 144.g

• Label: 144.9.g
• Level: $144$
• Weight: $9$
• Character orbit: 144.g
• Rep. character: $\chi_{144}(127,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $9$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	144.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(144, [\chi])\).

	Total	New	Old
Modular forms	204	20	184
Cusp forms	180	20	160
Eisenstein series	24	0	24

Trace form

\( 20 q - 504 q^{5} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(144, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.9.g.a	$144$	$9$	144.g	4.b	$2$	$1$	$1$	$58.663$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-672\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-672q^{5}+478q^{13}-154560q^{17}+\cdots\)
144.9.g.b	$144$	$9$	144.g	4.b	$2$	$1$	$1$	$58.663$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(672\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+672q^{5}+478q^{13}+154560q^{17}+\cdots\)
144.9.g.c	$144$	$9$	144.g	4.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1452\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-726q^{5}+7^{2}\zeta_{6}q^{7}+213\zeta_{6}q^{11}+\cdots\)
144.9.g.d	$144$	$9$	144.g	4.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-516\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-258q^{5}-238\zeta_{6}q^{7}+1671\zeta_{6}q^{11}+\cdots\)
144.9.g.e	$144$	$9$	144.g	4.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-47\zeta_{6}q^{7}+35806q^{13}-598\zeta_{6}q^{19}+\cdots\)
144.9.g.f	$144$	$9$	144.g	4.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(180\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+90q^{5}+133\zeta_{6}q^{7}-747\zeta_{6}q^{11}+\cdots\)
144.9.g.g	$144$	$9$	144.g	4.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-35}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1020\)	\(0\)	$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+510q^{5}-2\beta q^{7}-15\beta q^{11}-27710q^{13}+\cdots\)
144.9.g.h	$144$	$9$	144.g	4.b	$2$	$4$	$4$	$58.663$	\(\Q(\sqrt{-3}, \sqrt{355})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-119\beta _{2}q^{7}+\beta _{3}q^{11}-45986q^{13}+\cdots\)
144.9.g.i	$144$	$9$	144.g	4.b	$2$	$4$	$4$	$58.663$	\(\Q(\sqrt{-3}, \sqrt{1801})\)	None		$2$	$0$	\(0\)	\(0\)	\(264\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(66+\beta _{2})q^{5}+(-193\beta _{1}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)