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 + 6 * q^11 - 6 * q^15 + 8 * q^19 + 6 * q^21 - 2 * q^29 - 20 * q^31 - 2 * q^35 - 6 * q^39 + 30 * q^45 - 4 * q^49 - 30 * q^51 - 12 * q^55 + 28 * q^59 - 12 * q^61 + 14 * q^65 - 12 * q^69 + 24 * q^71 + 24 * q^75 + 22 * q^79 + 36 * q^81 - 26 * q^85 + 4 * q^89 + 10 * q^91 - 40 * q^95 - 36 * 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.e.a	$140$	$2$	140.e	5.b	$2$	$2$	$2$	$1.118$	\(\Q(\sqrt{-1}) \)	None		✓			140.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+(i-2)q^{5}-i q^{7}-6 q^{9}+\cdots\)
140.2.e.b	$140$	$2$	140.e	5.b	$2$	$2$	$2$	$1.118$	\(\Q(\sqrt{-1}) \)	None		✓			140.2.e.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2 i+1)q^{5}+i q^{7}+3 q^{9}-4 i q^{13}+\cdots\)

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

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