Space of modular forms of level 140, weight 2, and Character 140.o

• Label: 140.2.o
• Level: $140$
• Weight: $2$
• Character orbit: 140.o
• Rep. character: $\chi_{140}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(140, [\chi])\).

	Total	New	Old
Modular forms	56	32	24
Cusp forms	40	32	8
Eisenstein series	16	0	16

Trace form

\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
140.2.o.a	$140$	$2$	140.o	28.f	$6$	$32$	$16$	$1.118$		None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)