Space of modular forms of level 144, weight 3, and Character 144.o

• Label: 144.3.o
• Level: $144$
• Weight: $3$
• Character orbit: 144.o
• Rep. character: $\chi_{144}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).

	Total	New	Old
Modular forms	108	24	84
Cusp forms	84	24	60
Eisenstein series	24	0	24

Trace form

\( 24 q - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.3.o.a	$144$	$3$	144.o	36.f	$6$	$8$	$4$	$3.924$	8.0.856615824.2	None		✓			144.3.o.a	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
144.3.o.b	$144$	$3$	144.o	36.f	$6$	$8$	$4$	$3.924$	8.0.121550625.1	None		✓			144.3.o.b	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{1}-\beta _{7})q^{5}+\cdots\)
144.3.o.c	$144$	$3$	144.o	36.f	$6$	$8$	$4$	$3.924$	8.0.856615824.2	None		✓			144.3.o.a	$2$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{4})q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

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