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

• Label: 2500.1.j
• Level: $2500$
• Weight: $1$
• Character orbit: 2500.j
• Rep. character: $\chi_{2500}(251,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $375$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 2500 = 2^{2} \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2500.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(375\)
Trace bound:			\(6\)

Dimensions

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

	Total	New	Old
Modular forms	164	72	92
Cusp forms	44	24	20
Eisenstein series	120	48	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 2 q^{4} + 2 q^{6} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2500.1.j.a	$2500$	$1$	2500.j	100.j	$10$	$4$	$1$	$1.248$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{8}+\zeta_{10}^{2}q^{9}+\cdots\)
2500.1.j.b	$2500$	$1$	2500.j	100.j	$10$	$4$	$1$	$1.248$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}^{4}q^{8}+\zeta_{10}^{2}q^{9}+\cdots\)
2500.1.j.c	$2500$	$1$	2500.j	100.j	$10$	$8$	$2$	$1.248$	\(\Q(\zeta_{20})\)	$D_{5}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{20}q^{2}+(\zeta_{20}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)
2500.1.j.d	$2500$	$1$	2500.j	100.j	$10$	$8$	$2$	$1.248$	\(\Q(\zeta_{20})\)	$D_{5}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{20}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2500, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)