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

• Label: 144.5.e
• Level: $144$
• Weight: $5$
• Character orbit: 144.e
• Rep. character: $\chi_{144}(17,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(7\)
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	8	100
Cusp forms	84	8	76
Eisenstein series	24	0	24

Trace form

\( 8 q - 32 q^{7} + O(q^{10}) \)

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.e.a	$144$	$5$	144.e	3.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-2}) \)	None					36.5.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-136\)	$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-68q^{7}-4\beta q^{11}-2^{4}q^{13}+\cdots\)
144.5.e.b	$144$	$5$	144.e	3.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-2}) \)	None					72.5.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-72\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}-6^{2}q^{7}-116\beta q^{11}+304q^{13}+\cdots\)
144.5.e.c	$144$	$5$	144.e	3.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-2}) \)	None					9.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(56\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+7\beta q^{5}+28q^{7}+4\beta q^{11}-112q^{13}+\cdots\)
144.5.e.d	$144$	$5$	144.e	3.b	$2$	$2$	$2$	$14.885$	\(\Q(\sqrt{-2}) \)	None					72.5.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(120\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+11\beta q^{5}+60q^{7}-44\beta q^{11}-176q^{13}+\cdots\)

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

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