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

• Label: 728.2.b
• Level: $728$
• Weight: $2$
• Character orbit: 728.b
• Rep. character: $\chi_{728}(363,\cdot)$
• Character field: $\Q$
• Dimension: $108$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 728 \)
Character field:			\(\Q\)
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	116	116	0
Cusp forms	108	108	0
Eisenstein series	8	8	0

Trace form

108 * q - 4 * q^4 - 108 * q^9 + 2 * q^14 + 12 * q^16 + 28 * q^22 - 100 * q^25 + 20 * q^30 + 16 * q^35 + 12 * q^36 - 30 * q^42 - 8 * q^43 + 12 * q^49 + 16 * q^51 - 22 * q^56 + 44 * q^64 + 16 * q^65 + 16 * q^74 - 40 * q^78 + 92 * q^81 + 4 * q^88 + 52 * q^91 + 4 * q^92

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.b.a	$728$	$2$	728.b	728.b	$2$	$12$	$12$	$5.813$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	\(\Q(\sqrt{-26}) \)		✓			728.2.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+2q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
728.2.b.b	$728$	$2$	728.b	728.b	$2$	$96$	$96$	$5.813$		None		✓	✓		728.2.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$