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

• Label: 144.4.c
• Level: $144$
• Weight: $4$
• Character orbit: 144.c
• Rep. character: $\chi_{144}(143,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	84	6	78
Cusp forms	60	6	54
Eisenstein series	24	0	24

Trace form

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

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.c.a	$144$	$4$	144.c	12.b	$2$	$2$	$2$	$8.496$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-92q^{13}+11\beta q^{17}-37q^{25}+\cdots\)
144.4.c.b	$144$	$4$	144.c	12.b	$2$	$4$	$4$	$8.496$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+28q^{13}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(144, [\chi]) \cong \)