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

• Label: 144.4.i
• Level: $144$
• Weight: $4$
• Character orbit: 144.i
• Rep. character: $\chi_{144}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $34$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	156	38	118
Cusp forms	132	34	98
Eisenstein series	24	4	20

Trace form

\( 34 q + 2 q^{3} - q^{5} + q^{7} + 8 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.4.i.a	$144$	$4$	144.i	9.c	$3$	$2$	$1$	$8.496$	\(\Q(\sqrt{-3}) \)	None					18.4.c.a	$2$	$0$	\(0\)	\(0\)	\(9\)	\(-31\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-6\zeta_{6})q^{3}+9\zeta_{6}q^{5}+(-31+31\zeta_{6})q^{7}+\cdots\)
144.4.i.b	$144$	$4$	144.i	9.c	$3$	$4$	$2$	$8.496$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	None					18.4.c.b	$2$	$0$	\(0\)	\(-3\)	\(9\)	\(19\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(6+6\beta _{1}+3\beta _{3})q^{5}+\cdots\)
144.4.i.c	$144$	$4$	144.i	9.c	$3$	$4$	$2$	$8.496$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					9.4.c.a	$2$	$0$	\(0\)	\(3\)	\(-15\)	\(7\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-8+7\beta _{1}+\cdots)q^{5}+\cdots\)
144.4.i.d	$144$	$4$	144.i	9.c	$3$	$6$	$3$	$8.496$	6.0.6831243.2	None					36.4.e.a	$2$	$0$	\(0\)	\(3\)	\(6\)	\(6\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{3}+(-2+3\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
144.4.i.e	$144$	$4$	144.i	9.c	$3$	$8$	$4$	$8.496$	8.0.5206055409.1	None					72.4.i.a	$2$	$0$	\(0\)	\(3\)	\(-5\)	\(-3\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
144.4.i.f	$144$	$4$	144.i	9.c	$3$	$10$	$5$	$8.496$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None			✓		72.4.i.b	$2$	$0$	\(0\)	\(-4\)	\(-5\)	\(3\)	$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

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

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