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

• Label: 728.2.i
• Level: $728$
• Weight: $2$
• Character orbit: 728.i
• Rep. character: $\chi_{728}(701,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	116	84	32
Cusp forms	108	84	24
Eisenstein series	8	0	8

Trace form

84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

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.i.a	$728$	$2$	728.i	104.e	$2$	$84$	$84$	$5.813$		None		✓	✓	✓	728.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(728, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)