Space of modular forms of level 2500, weight 1, and Character 2500.p

• Label: 2500.1.p
• Level: $2500$
• Weight: $1$
• Character orbit: 2500.p
• Rep. character: $\chi_{2500}(51,\cdot)$
• Character field: $\Q(\zeta_{50})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $375$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2500 = 2^{2} \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2500.p (of order \(50\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 500 \)
Character field:			\(\Q(\zeta_{50})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(375\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2500, [\chi])\).

	Total	New	Old
Modular forms	260	140	120
Cusp forms	60	20	40
Eisenstein series	200	120	80

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + 5 q^{18} + 5 q^{32} - 5 q^{34} + 5 q^{37} - 5 q^{49} + 5 q^{53} - 5 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2500, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2500.1.p.a	$2500$	$1$	2500.p	500.p	$50$	$20$	$1$	$1.248$	\(\Q(\zeta_{50})\)	$D_{25}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	500.1.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{50}^{3}q^{2}+\zeta_{50}^{6}q^{4}+\zeta_{50}^{9}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2500, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2500, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)