Space of modular forms of level 2000, weight 1, and Character 2000.z

• Label: 2000.1.z
• Level: $2000$
• Weight: $1$
• Character orbit: 2000.z
• Rep. character: $\chi_{2000}(351,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $300$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2000 = 2^{4} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2000.z (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(300\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2000, [\chi])\).

	Total	New	Old
Modular forms	164	8	156
Cusp forms	44	8	36
Eisenstein series	120	0	120

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2000, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2000.1.z.a	$2000$	$1$	2000.z	100.j	$10$	$8$	$2$	$0.998$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$		\(q+\zeta_{20}^{8}q^{9}+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{13}+(\zeta_{20}^{3}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2000, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 2}\)