Space of modular forms of level 2025, weight 1, and Character 2025.j

• Label: 2025.1.j
• Level: $2025$
• Weight: $1$
• Character orbit: 2025.j
• Rep. character: $\chi_{2025}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $270$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2025 = 3^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2025.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(270\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2025, [\chi])\).

	Total	New	Old
Modular forms	80	14	66
Cusp forms	8	8	0
Eisenstein series	72	6	66

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2025, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2025.1.j.a	$2025$	$1$	2025.j	9.d	$6$	$2$	$1$	$1.011$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
2025.1.j.b	$2025$	$1$	2025.j	9.d	$6$	$2$	$1$	$1.011$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
2025.1.j.c	$2025$	$1$	2025.j	9.d	$6$	$4$	$2$	$1.011$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-15}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{8}-\zeta_{12}^{4}q^{16}+\cdots\)