Space of modular forms of level 140, weight 2, and trivial character

• Label: 140.2.a
• Level: $140$
• Weight: $2$
• Character orbit: 140.a
• Rep. character: $\chi_{140}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(140))\).

	Total	New	Old
Modular forms	30	2	28
Cusp forms	19	2	17
Eisenstein series	11	0	11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(5\)	\(0\)	\(5\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(6\)	\(0\)	\(6\)		\(4\)	\(0\)	\(4\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(12\)	\(0\)	\(12\)		\(7\)	\(0\)	\(7\)		\(5\)	\(0\)	\(5\)
Minus space			\(-\)		\(18\)	\(2\)	\(16\)		\(12\)	\(2\)	\(10\)		\(6\)	\(0\)	\(6\)

Trace form

2 * q + 4 * q^3 + 4 * q^9 - 2 * q^11 - 4 * q^13 - 2 * q^15 - 4 * q^17 + 8 * q^19 - 2 * q^21 + 2 * q^25 + 4 * q^27 - 18 * q^29 + 4 * q^31 - 12 * q^33 + 2 * q^35 - 8 * q^37 - 10 * q^39 - 4 * q^41 + 12 * q^43 - 8 * q^45 - 4 * q^47 + 2 * q^49 - 6 * q^51 + 4 * q^53 + 8 * q^55 + 20 * q^57 + 4 * q^59 - 8 * q^63 + 2 * q^65 + 20 * q^67 + 12 * q^69 + 8 * q^71 + 16 * q^73 + 4 * q^75 + 8 * q^77 + 18 * q^79 + 10 * q^81 - 16 * q^83 - 2 * q^85 - 36 * q^87 + 16 * q^89 + 2 * q^91 - 4 * q^93 - 4 * q^95 + 4 * q^97 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(140))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	7
140.2.a.a	$140$	$2$	140.a	1.a	$1$	$1$	$1$	$1.118$	\(\Q\)	None	✓	✓	✓	✓	140.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
140.2.a.b	$140$	$2$	140.a	1.a	$1$	$1$	$1$	$1.118$	\(\Q\)	None	✓	✓	✓	✓	140.2.a.b	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-q^{7}+6q^{9}-5q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(140)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)