Space of modular forms of level 728, weight 2, and Character 728.t

• Label: 728.2.t
• Level: $728$
• Weight: $2$
• Character orbit: 728.t
• Rep. character: $\chi_{728}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.t (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(728, [\chi])\).

	Total	New	Old
Modular forms	240	56	184
Cusp forms	208	56	152
Eisenstein series	32	0	32

Trace form

\( 56 q + 8 q^{3} - 4 q^{7} + 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(728, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
728.2.t.a	$728$	$2$	728.t	91.g	$3$	$2$	$1$	$5.813$	\(\Q(\sqrt{-3}) \)	None		✓			728.2.q.a	$2$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{3}+(-3+3\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
728.2.t.b	$728$	$2$	728.t	91.g	$3$	$6$	$3$	$5.813$	6.0.1156923.1	None		✓			728.2.q.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
728.2.t.c	$728$	$2$	728.t	91.g	$3$	$8$	$4$	$5.813$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			728.2.q.c	$2$	$0$	\(0\)	\(6\)	\(1\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(-3+\cdots)q^{7}+\cdots\)
728.2.t.d	$728$	$2$	728.t	91.g	$3$	$18$	$9$	$5.813$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			728.2.q.d	$2$	$0$	\(0\)	\(0\)	\(4\)	\(14\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+(-\beta _{4}-\beta _{12})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
728.2.t.e	$728$	$2$	728.t	91.g	$3$	$22$	$11$	$5.813$		None		✓	✓		728.2.q.e	$2$	$0$	\(0\)	\(4\)	\(-5\)	\(-3\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(728, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(728, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)