Space of modular forms of level 140, weight 5, and Character 140.h

• Label: 140.5.h
• Level: $140$
• Weight: $5$
• Character orbit: 140.h
• Rep. character: $\chi_{140}(69,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	140.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(140, [\chi])\).

	Total	New	Old
Modular forms	102	16	86
Cusp forms	90	16	74
Eisenstein series	12	0	12

Trace form

\( 16 q + 366 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
140.5.h.a	$140$	$5$	140.h	35.c	$2$	$2$	$2$	$14.472$	\(\Q(\sqrt{105}) \)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(-17\)	\(-50\)	\(-98\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-8-\beta )q^{3}-5^{2}q^{5}-7^{2}q^{7}+(9+\cdots)q^{9}+\cdots\)
140.5.h.b	$140$	$5$	140.h	35.c	$2$	$2$	$2$	$14.472$	\(\Q(\sqrt{105}) \)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(17\)	\(50\)	\(98\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(9-\beta )q^{3}+5^{2}q^{5}+7^{2}q^{7}+(26-17\beta )q^{9}+\cdots\)
140.5.h.c	$140$	$5$	140.h	35.c	$2$	$12$	$12$	$14.472$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{7})q^{5}+(-\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)