Space of modular forms of level 1023, weight 1, and Character 1023.u

• Label: 1023.1.u
• Level: $1023$
• Weight: $1$
• Character orbit: 1023.u
• Rep. character: $\chi_{1023}(626,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1023 = 3 \cdot 11 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1023.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1023 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1023, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	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

\( 4 q - 4 q^{4} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1023, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1023.1.u.a	$1023$	$1$	1023.u	1023.u	$6$	$2$	$1$	$0.511$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}-q^{4}+(-1+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)
1023.1.u.b	$1023$	$1$	1023.u	1023.u	$6$	$2$	$1$	$0.511$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(1\)	\(3\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-q^{4}+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)