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

• Label: 144.9.e
• Level: $144$
• Weight: $9$
• Character orbit: 144.e
• Rep. character: $\chi_{144}(17,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $6$
• Sturm bound: $216$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	144.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(216\)
Trace bound:			\(13\)
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	16	188
Cusp forms	180	16	164
Eisenstein series	24	0	24

Trace form

\( 16 q + 3008 q^{7} + O(q^{10}) \)

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	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.9.e.a	$144$	$9$	144.e	3.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-2}) \)	None			9.9.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3304\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+233\beta q^{5}-1652q^{7}+5036\beta q^{11}+\cdots\)
144.9.e.b	$144$	$9$	144.e	3.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-2}) \)	None			18.9.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3304\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+215\beta q^{5}-1652q^{7}-3244\beta q^{11}+\cdots\)
144.9.e.c	$144$	$9$	144.e	3.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-2}) \)	None			36.9.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-616\)	$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-308q^{7}-244\beta q^{11}+18464q^{13}+\cdots\)
144.9.e.d	$144$	$9$	144.e	3.b	$2$	$2$	$2$	$58.663$	\(\Q(\sqrt{-2}) \)	None			18.9.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(7064\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+55\beta q^{5}+3532q^{7}+4756\beta q^{11}+\cdots\)
144.9.e.e	$144$	$9$	144.e	3.b	$2$	$4$	$4$	$58.663$	\(\Q(\sqrt{-2}, \sqrt{15})\)	None			72.9.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(816\)	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(85\beta _{1}-\beta _{2})q^{5}+(204-\beta _{3})q^{7}+(-34^{2}\beta _{1}+\cdots)q^{11}+\cdots\)
144.9.e.f	$144$	$9$	144.e	3.b	$2$	$4$	$4$	$58.663$	\(\Q(\sqrt{-2}, \sqrt{31})\)	None			72.9.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2352\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-43\beta _{1}+\beta _{2})q^{5}+(588-7\beta _{3})q^{7}+\cdots\)

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

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