Space of modular forms of level 2952, weight 1, and Character 2952.ds

• Label: 2952.1.ds
• Level: $2952$
• Weight: $1$
• Character orbit: 2952.ds
• Rep. character: $\chi_{2952}(187,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $504$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2952 = 2^{3} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2952.ds (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2952 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(504\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2952, [\chi])\).

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

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

16 * q - 2 * q^2 + 2 * q^4 - 5 * q^6 + 4 * q^8 + 2 * q^9 - 5 * q^11 + 2 * q^16 + 4 * q^18 - 10 * q^19 + 2 * q^25 + 8 * q^32 - q^33 - 3 * q^36 + q^41 - 3 * q^43 - 5 * q^48 - 2 * q^49 + 8 * q^50 + 6 * q^51 + 6 * q^57 + 2 * q^59 - 4 * q^64 + 5 * q^66 + 5 * q^67 + 3 * q^72 - 4 * q^73 - 5 * q^75 - 5 * q^76 + 2 * q^81 + 2 * q^82 + 4 * q^83 - 2 * q^86 - 4 * q^98

Decomposition of \(S_{1}^{\mathrm{new}}(2952, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2952.1.ds.a	$2952$	$1$	2952.ds	2952.cs	$30$	$8$	$1$	$1.473$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-2}) \)	None		✓			2952.1.ds.a	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{30}^{2}q^{2}-\zeta_{30}^{8}q^{3}+\zeta_{30}^{4}q^{4}+\cdots\)
2952.1.ds.b	$2952$	$1$	2952.ds	2952.cs	$30$	$8$	$1$	$1.473$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-2}) \)	None		✓			2952.1.ds.a	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{2}q^{3}+\zeta_{30}^{4}q^{4}+\cdots\)