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

• Label: 1000.2.y
• Level: $1000$
• Weight: $2$
• Character orbit: 1000.y
• Rep. character: $\chi_{1000}(41,\cdot)$
• Character field: $\Q(\zeta_{25})$
• Dimension: $740$
• 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.y (of order \(25\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 125 \)
Character field:			\(\Q(\zeta_{25})\)
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	3080	740	2340
Cusp forms	2920	740	2180
Eisenstein series	160	0	160

Trace form

\( 740 q + O(q^{10}) \)

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.y.a	$1000$	$2$	1000.y	125.g	$25$	$360$	$18$	$7.985$		None		✓			1000.2.y.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{25}]$
1000.2.y.b	$1000$	$2$	1000.y	125.g	$25$	$380$	$19$	$7.985$		None		✓	✓		1000.2.y.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{25}]$

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

\( S_{2}^{\mathrm{old}}(1000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)