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

• Label: 140.2.i
• Level: $140$
• Weight: $2$
• Character orbit: 140.i
• Rep. character: $\chi_{140}(81,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
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	4	56
Cusp forms	36	4	32
Eisenstein series	24	0	24

Trace form

4 * q + 2 * q^3 + 2 * q^5 + 6 * q^7 - 4 * q^9 - 4 * q^11 - 8 * q^13 + 4 * q^15 + 4 * q^17 - 8 * q^19 + 14 * q^21 + 6 * q^23 - 2 * q^25 - 28 * q^27 + 12 * q^29 - 4 * q^31 - 12 * q^33 - 16 * q^37 - 20 * q^39 + 4 * q^41 + 12 * q^43 + 4 * q^45 - 8 * q^47 - 2 * q^49 + 12 * q^51 - 16 * q^53 - 8 * q^55 + 16 * q^57 + 8 * q^59 - 6 * q^61 + 32 * q^63 - 4 * q^65 + 10 * q^67 + 60 * q^69 + 16 * q^71 - 4 * q^73 + 2 * q^75 + 4 * q^77 - 10 * q^81 + 4 * q^83 + 8 * q^85 + 6 * q^87 - 10 * q^89 + 4 * q^91 + 4 * q^93 + 8 * q^95 - 40 * q^97 - 48 * q^99

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

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

\( S_{2}^{\mathrm{old}}(140, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)