Space of modular forms of level 144, weight 2, and Character 144.s

• Label: 144.2.s
• Level: $144$
• Weight: $2$
• Character orbit: 144.s
• Rep. character: $\chi_{144}(47,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

	Total	New	Old
Modular forms	60	12	48
Cusp forms	36	12	24
Eisenstein series	24	0	24

Trace form

\( 12 q + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.2.s.a	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
144.2.s.b	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-\zeta_{6})q^{7}+\cdots\)
144.2.s.c	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+\cdots\)
144.2.s.d	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
144.2.s.e	$144$	$2$	144.s	36.h	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{3}q^{3}+(1+\zeta_{12})q^{5}+(-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)