Space of modular forms of level 1728, weight 3, and Character 1728.t

• Label: 1728.3.t
• Level: $1728$
• Weight: $3$
• Character orbit: 1728.t
• Rep. character: $\chi_{1728}(415,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(864\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1728, [\chi])\).

	Total	New	Old
Modular forms	1224	96	1128
Cusp forms	1080	96	984
Eisenstein series	144	0	144

Trace form

\( 96 q + 240 q^{25} - 144 q^{41} + 336 q^{49} - 576 q^{89}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1728, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1728.3.t.a	$1728$	$3$	1728.t	72.p	$6$	$32$	$16$	$47.085$		None					576.3.t.a	$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1728.3.t.b	$1728$	$3$	1728.t	72.p	$6$	$32$	$16$	$47.085$		None					576.3.t.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1728.3.t.c	$1728$	$3$	1728.t	72.p	$6$	$32$	$16$	$47.085$		None					576.3.t.a	$4$	$0$	\(0\)	\(0\)	\(18\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1728, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)