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

• Label: 2925.1.dp
• Level: $2925$
• Weight: $1$
• Character orbit: 2925.dp
• Rep. character: $\chi_{2925}(1801,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $420$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2925.dp (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(420\)
Trace bound:			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	104	20	84
Cusp forms	8	8	0
Eisenstein series	96	12	84

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

\( 8 q + 4 q^{16} + 4 q^{19} + 8 q^{31} + 12 q^{49} + 4 q^{76} + 4 q^{91}+O(q^{100}) \)

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.dp.a	$2925$	$1$	2925.dp	13.f	$12$	$4$	$1$	$1.460$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None		✓			2925.1.dp.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{12}^{5}q^{4}+(-1+\zeta_{12})q^{7}-\zeta_{12}^{3}q^{13}+\cdots\)
2925.1.dp.b	$2925$	$1$	2925.dp	13.f	$12$	$4$	$1$	$1.460$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None		✓			2925.1.dp.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{12}^{5}q^{4}+(1-\zeta_{12})q^{7}+\zeta_{12}^{3}q^{13}+\cdots\)