Space of modular forms of level 2925, weight 1, and Character 2925.dj

• Label: 2925.1.dj
• Level: $2925$
• Weight: $1$
• Character orbit: 2925.dj
• Rep. character: $\chi_{2925}(499,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $420$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2925.dj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 585 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(420\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2925, [\chi])\).

	Total	New	Old
Modular forms	56	24	32
Cusp forms	8	8	0
Eisenstein series	48	16	32

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

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

Trace form

\( 8 q - 8 q^{9} + 4 q^{11} + 4 q^{16} + 8 q^{19} + 4 q^{29} + 4 q^{39} - 4 q^{41} - 8 q^{44} + 8 q^{71} + 4 q^{76} - 4 q^{79} + 8 q^{81} - 8 q^{89} - 4 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2925, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2925.1.dj.a	$2925$	$1$	2925.dj	585.cb	$12$	$4$	$1$	$1.460$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		✓			2925.1.dg.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)
2925.1.dj.b	$2925$	$1$	2925.dj	585.cb	$12$	$4$	$1$	$1.460$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		✓			2925.1.dg.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)