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

• Label: 728.2.ba
• Level: $728$
• Weight: $2$
• Character orbit: 728.ba
• Rep. character: $\chi_{728}(125,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.ba (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 728 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
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 - 4 * q^2 - 4 * q^7 - 4 * q^8 + 184 * q^9 + 12 * q^14 - 32 * q^15 - 8 * q^16 - 24 * q^18 - 8 * q^22 + 4 * q^28 + 16 * q^32 - 32 * q^39 - 20 * q^42 - 4 * q^44 - 56 * q^46 + 60 * q^50 - 64 * q^57 + 28 * q^58 - 44 * q^60 - 44 * q^63 - 8 * q^65 - 12 * q^70 - 72 * q^71 - 76 * q^72 - 64 * q^74 + 36 * q^78 - 16 * q^79 + 88 * q^81 + 44 * q^84 - 68 * q^86 + 56 * q^92 - 36 * q^98

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.ba.a	$728$	$2$	728.ba	728.aa	$4$	$4$	$2$	$5.813$	\(\Q(i, \sqrt{14})\)	None		✓			728.2.ba.a	$4$	$0$	\(-4\)	\(-4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}-q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
728.2.ba.b	$728$	$2$	728.ba	728.aa	$4$	$4$	$2$	$5.813$	\(\Q(i, \sqrt{14})\)	None		✓			728.2.ba.a	$4$	$0$	\(-4\)	\(4\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+q^{3}+2\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
728.2.ba.c	$728$	$2$	728.ba	728.aa	$4$	$8$	$4$	$5.813$	8.0.\(\cdots\).8	\(\Q(\sqrt{-14}) \)		✓			728.2.ba.c	$8$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-\beta _{3})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+2\beta _{3}q^{4}+\cdots\)
728.2.ba.d	$728$	$2$	728.ba	728.aa	$4$	$8$	$4$	$5.813$	8.0.\(\cdots\).8	\(\Q(\sqrt{-14}) \)		✓			728.2.ba.d	$8$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(1-\beta _{3})q^{2}+(-\beta _{4}-\beta _{6})q^{3}-2\beta _{3}q^{4}+\cdots\)
728.2.ba.e	$728$	$2$	728.ba	728.aa	$4$	$192$	$96$	$5.813$		None		✓	✓		728.2.ba.e	$8$	$0$	\(4\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$