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

• Label: 1000.2.t
• Level: $1000$
• Weight: $2$
• Character orbit: 1000.t
• Rep. character: $\chi_{1000}(101,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $336$
• Newform subspaces: $2$
• Sturm bound: $300$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(300\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	640	384	256
Cusp forms	560	336	224
Eisenstein series	80	48	32

Trace form

\( 336 q + 3 q^{2} + 3 q^{4} - 5 q^{6} + 16 q^{7} + 12 q^{8} + 78 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1000.2.t.a	$1000$	$2$	1000.t	200.t	$10$	$112$	$28$	$7.985$		None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{10}]$
1000.2.t.b	$1000$	$2$	1000.t	200.t	$10$	$224$	$56$	$7.985$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1000, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)