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

• Label: 140.2.q
• Level: $140$
• Weight: $2$
• Character orbit: 140.q
• Rep. character: $\chi_{140}(9,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	60	8	52
Cusp forms	36	8	28
Eisenstein series	24	0	24

Trace form

\( 8 q - q^{5} + O(q^{10}) \)

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.q.a	$140$	$2$	140.q	35.j	$6$	$4$	$2$	$1.118$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(-6\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
140.2.q.b	$140$	$2$	140.q	35.j	$6$	$4$	$2$	$1.118$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(6\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)