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

• Label: 140.2.s
• Level: $140$
• Weight: $2$
• Character orbit: 140.s
• Rep. character: $\chi_{140}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

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

Trace form

40 * q - 2 * q^4 - 6 * q^5 + 8 * q^9 - 12 * q^10 - 2 * q^14 + 2 * q^16 - 24 * q^21 - 24 * q^24 - 6 * q^25 - 18 * q^26 - 24 * q^29 - 6 * q^30 - 44 * q^36 + 42 * q^40 - 26 * q^44 - 24 * q^45 - 26 * q^46 - 8 * q^49 + 36 * q^50 + 84 * q^54 + 8 * q^56 + 4 * q^60 - 12 * q^61 + 100 * q^64 - 4 * q^65 - 24 * q^66 + 46 * q^70 + 14 * q^74 + 72 * q^80 + 56 * q^81 + 16 * q^84 + 20 * q^85 - 28 * q^86 - 72 * q^89 + 30 * q^94 + 12 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
140.2.s.a	$140$	$2$	140.s	140.s	$6$	$8$	$4$	$1.118$	8.0.3317760000.3	\(\Q(\sqrt{-5}) \)		✓			140.2.s.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{5})q^{3}-2\beta _{4}q^{4}-\beta _{7}q^{5}+\cdots\)
140.2.s.b	$140$	$2$	140.s	140.s	$6$	$32$	$16$	$1.118$		None		✓	✓		140.2.s.b	$8$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$