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

• Label: 728.2.cl
• Level: $728$
• Weight: $2$
• Character orbit: 728.cl
• Rep. character: $\chi_{728}(451,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 728 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
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	232	232	0
Cusp forms	216	216	0
Eisenstein series	16	16	0

Trace form

216 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 12 * q^6 - 8 * q^8 + 102 * q^9 - 3 * q^10 + 2 * q^11 - 6 * q^12 - 10 * q^14 - 10 * q^16 - 9 * q^18 - 6 * q^19 + 24 * q^20 - 48 * q^24 - 96 * q^25 + 18 * q^26 + 31 * q^28 - 2 * q^30 - 22 * q^32 - 6 * q^33 + 18 * q^35 - 23 * q^36 - 36 * q^38 - 6 * q^40 - 9 * q^42 - 4 * q^43 - 6 * q^44 - 16 * q^46 - 18 * q^48 + 6 * q^49 - 4 * q^50 + 8 * q^51 + 9 * q^52 + 7 * q^56 - 36 * q^57 - 7 * q^58 - 21 * q^60 + 6 * q^62 - 8 * q^64 - 12 * q^65 - 45 * q^66 + 2 * q^67 + 24 * q^70 + 25 * q^72 - 36 * q^73 - 14 * q^74 - 24 * q^76 + 73 * q^78 + 108 * q^80 - 80 * q^81 - 90 * q^82 + 105 * q^84 - 10 * q^86 - 3 * q^88 + 42 * q^91 - 30 * q^92 - 48 * q^94 + 24 * q^96 + 80 * q^98 - 40 * q^99

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.cl.a	$728$	$2$	728.cl	728.bl	$6$	$4$	$2$	$5.813$	\(\Q(\zeta_{12})\)	None		✓			728.2.bf.a	$4$	$0$	\(-4\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots\)
728.2.cl.b	$728$	$2$	728.cl	728.bl	$6$	$212$	$106$	$5.813$		None		✓	✓		728.2.bf.b	$4$	$0$	\(2\)	\(-12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$