Space of modular forms of level 144, weight 5, and Character 144.g

• Label: 144.5.g
• Level: $144$
• Weight: $5$
• Character orbit: 144.g
• Rep. character: $\chi_{144}(127,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(144, [\chi])\).

	Total	New	Old
Modular forms	108	10	98
Cusp forms	84	10	74
Eisenstein series	24	0	24

Trace form

\( 10 q + 36 q^{5} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(144, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.5.g.a	$144$	$5$	144.g	4.b	$2$	$1$	$1$	$14.885$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓			144.5.g.a	$2$	$0$	\(0\)	\(0\)	\(-48\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-48q^{5}+238q^{13}+480q^{17}+1679q^{25}+\cdots\)
144.5.g.b	$144$	$5$	144.g	4.b	$2$	$1$	$1$	$14.885$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓			144.5.g.a	$2$	$0$	\(0\)	\(0\)	\(48\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+48q^{5}+238q^{13}-480q^{17}+1679q^{25}+\cdots\)
144.5.g.c	$144$	$5$	144.g	4.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-3}) \)	None					16.5.c.a	$2$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-18q^{5}+2\zeta_{6}q^{7}-9\zeta_{6}q^{11}+178q^{13}+\cdots\)
144.5.g.d	$144$	$5$	144.g	4.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-3}) \)	None					48.5.g.b	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-6q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{11}-86q^{13}+\cdots\)
144.5.g.e	$144$	$5$	144.g	4.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			144.5.g.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{7}-146q^{13}-26\zeta_{6}q^{19}-5^{4}q^{25}+\cdots\)
144.5.g.f	$144$	$5$	144.g	4.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-3}) \)	None					48.5.g.a	$2$	$0$	\(0\)	\(0\)	\(84\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+42q^{5}+11\zeta_{6}q^{7}+3\zeta_{6}q^{11}-182q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)