Space of modular forms of level 140, weight 10, and trivial character

• Label: 140.10.a
• Level: $140$
• Weight: $10$
• Character orbit: 140.a
• Rep. character: $\chi_{140}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	140.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(140))\).

	Total	New	Old
Modular forms	222	18	204
Cusp forms	210	18	192
Eisenstein series	12	0	12

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	Dim
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(8\)
Minus space			\(-\)	\(10\)

Trace form

\( 18 q + 292 q^{3} + 89510 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(140))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	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
140.10.a.a	$140$	$10$	140.a	1.a	$1$	$1$	$1$	$72.105$	\(\Q\)	None	✓	✓	140.10.a.a	$1$	$0$	\(0\)	\(-95\)	\(625\)	\(2401\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-95q^{3}+5^{4}q^{5}+7^{4}q^{7}-10658q^{9}+\cdots\)
140.10.a.b	$140$	$10$	140.a	1.a	$1$	$4$	$4$	$72.105$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	140.10.a.b	$1$	$1$	\(0\)	\(-59\)	\(2500\)	\(-9604\)		$-$	$-$	$+$	$+$	$2^{5}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-15+\beta _{1})q^{3}+5^{4}q^{5}-7^{4}q^{7}+\cdots\)
140.10.a.c	$140$	$10$	140.a	1.a	$1$	$4$	$4$	$72.105$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	140.10.a.c	$1$	$1$	\(0\)	\(43\)	\(-2500\)	\(9604\)		$-$	$+$	$-$	$+$	$2^{5}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(11+\beta _{1})q^{3}-5^{4}q^{5}+7^{4}q^{7}+(6743+\cdots)q^{9}+\cdots\)
140.10.a.d	$140$	$10$	140.a	1.a	$1$	$4$	$4$	$72.105$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	140.10.a.d	$1$	$0$	\(0\)	\(194\)	\(2500\)	\(9604\)		$-$	$-$	$-$	$-$	$2^{5}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+(7^{2}-\beta _{1})q^{3}+5^{4}q^{5}+7^{4}q^{7}+(11265+\cdots)q^{9}+\cdots\)
140.10.a.e	$140$	$10$	140.a	1.a	$1$	$5$	$5$	$72.105$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	140.10.a.e	$1$	$0$	\(0\)	\(209\)	\(-3125\)	\(-12005\)		$-$	$+$	$+$	$-$	$2^{9}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(42-\beta _{1})q^{3}-5^{4}q^{5}-7^{4}q^{7}+(-1828+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(140))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(140)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)