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

• Label: 1023.1.ba
• Level: $1023$
• Weight: $1$
• Character orbit: 1023.ba
• Rep. character: $\chi_{1023}(263,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• 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.ba (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1023 \)
Character field:			\(\Q(\zeta_{10})\)
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	24	24	0
Cusp forms	8	8	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 2 q^{4} - 2 q^{9} + O(q^{10}) \)

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.ba.a	$1023$	$1$	1023.ba	1023.aa	$10$	$4$	$1$	$0.511$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{3}q^{4}+(-\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
1023.1.ba.b	$1023$	$1$	1023.ba	1023.aa	$10$	$4$	$1$	$0.511$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{10}^{4}q^{3}+\zeta_{10}^{3}q^{4}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)