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 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

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	$4$	$0$	\(-20\)	\(0\)	\(0\)	\(-50\)		$\mathrm{SU}(2)[C_{50}]$