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

• Label: 140.2.e
• Level: $140$
• Weight: $2$
• Character orbit: 140.e
• Rep. character: $\chi_{140}(29,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	30	4	26
Cusp forms	18	4	14
Eisenstein series	12	0	12

Trace form

\( 4 q - 2 q^{5} - 6 q^{9} + O(q^{10}) \)

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.e.a	$140$	$2$	140.e	5.b	$2$	$2$	$2$	$1.118$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(-2+i)q^{5}-iq^{7}-6q^{9}+\cdots\)
140.2.e.b	$140$	$2$	140.e	5.b	$2$	$2$	$2$	$1.118$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+2i)q^{5}+iq^{7}+3q^{9}-4iq^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)