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

• Label: 728.2.ef
• Level: $728$
• Weight: $2$
• Character orbit: 728.ef
• Rep. character: $\chi_{728}(73,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $112$
• 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.ef (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
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	480	112	368
Cusp forms	416	112	304
Eisenstein series	64	0	64

Trace form

112 * q - 4 * q^7 + 56 * q^9 - 4 * q^11 - 16 * q^15 + 24 * q^19 + 8 * q^29 - 48 * q^31 + 24 * q^33 + 16 * q^35 - 4 * q^37 + 28 * q^39 + 36 * q^47 - 28 * q^53 - 56 * q^57 + 36 * q^61 + 12 * q^63 - 24 * q^65 + 20 * q^67 + 16 * q^71 + 36 * q^73 - 24 * q^81 - 64 * q^85 + 96 * q^87 - 4 * q^93 - 88 * 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.ef.a	$728$	$2$	728.ef	91.ab	$12$	$112$	$28$	$5.813$		None		✓	✓	✓	728.2.ef.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$

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

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