Space of modular forms of level 144, weight 4, and Character 144.s

• Label: 144.4.s
• Level: $144$
• Weight: $4$
• Character orbit: 144.s
• Rep. character: $\chi_{144}(47,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(96\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(144, [\chi])\).

	Total	New	Old
Modular forms	156	36	120
Cusp forms	132	36	96
Eisenstein series	24	0	24

Trace form

\( 36 q - 30 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(144, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.4.s.a	$144$	$4$	144.s	36.h	$6$	$2$	$1$	$8.496$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-21\)	\(-15\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-3+6\zeta_{6})q^{3}+(-14+7\zeta_{6})q^{5}+\cdots\)
144.4.s.b	$144$	$4$	144.s	36.h	$6$	$2$	$1$	$8.496$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-21\)	\(15\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3-6\zeta_{6})q^{3}+(-14+7\zeta_{6})q^{5}+(5+\cdots)q^{7}+\cdots\)
144.4.s.c	$144$	$4$	144.s	36.h	$6$	$10$	$5$	$8.496$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(9\)	\(-33\)	$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\beta _{2}+\beta _{6})q^{3}+(1-\beta _{4}-\beta _{8}+\cdots)q^{5}+\cdots\)
144.4.s.d	$144$	$4$	144.s	36.h	$6$	$10$	$5$	$8.496$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(6\)	\(9\)	\(33\)	$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\beta _{2}-\beta _{6})q^{3}+(1-\beta _{4}-\beta _{8}+\cdots)q^{5}+\cdots\)
144.4.s.e	$144$	$4$	144.s	36.h	$6$	$12$	$6$	$8.496$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(24\)	\(0\)	$2^{8}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{4})q^{3}+(1-2\beta _{1}+\beta _{2}-\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)