Space of modular forms of level 1000, weight 2, and Character 1000.bd

• Label: 1000.2.bd
• Level: $1000$
• Weight: $2$
• Character orbit: 1000.bd
• Rep. character: $\chi_{1000}(29,\cdot)$
• Character field: $\Q(\zeta_{50})$
• Dimension: $2960$
• Newform subspaces: $1$
• Sturm bound: $300$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.bd (of order \(50\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1000 \)
Character field:			\(\Q(\zeta_{50})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(300\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1000, [\chi])\).

	Total	New	Old
Modular forms	3040	3040	0
Cusp forms	2960	2960	0
Eisenstein series	80	80	0

Trace form

\( 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1000, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1000.2.bd.a	$1000$	$2$	1000.bd	1000.ad	$50$	$2960$	$148$	$7.985$		None		✓	✓	✓	1000.2.bd.a	$4$	$0$	\(-20\)	\(0\)	\(0\)	\(-50\)		$\mathrm{SU}(2)[C_{50}]$