Space of modular forms of level 143, weight 1, and Character 143.d

• Label: 143.1.d
• Level: $143$
• Weight: $1$
• Character orbit: 143.d
• Rep. character: $\chi_{143}(142,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	143.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 143 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(143, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	4	4	0
Eisenstein series	2	2	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

4 * q - 2 * q^3 + 2 * q^4 + 2 * q^9 - 6 * q^12 - 4 * q^14 - 2 * q^22 - 2 * q^23 + 4 * q^25 - 2 * q^26 - 4 * q^27 + 6 * q^36 + 6 * q^38 + 2 * q^42 + 2 * q^49 - 2 * q^53 + 2 * q^56 - 2 * q^64 + 6 * q^66 - 4 * q^69 - 2 * q^75 - 2 * q^77 + 6 * q^78 - 4 * q^82 - 4 * q^88 - 2 * q^91 + 4 * q^92

Decomposition of \(S_{1}^{\mathrm{new}}(143, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
143.1.d.a	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-143}) \)	None	✓	✓			143.1.d.a	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
143.1.d.b	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-143}) \)	None	✓	✓			143.1.d.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)