Space of modular forms of level 2520, weight 1, and Character 2520.eq

• Label: 2520.1.eq
• Level: $2520$
• Weight: $1$
• Character orbit: 2520.eq
• Rep. character: $\chi_{2520}(899,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2520.eq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 840 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2520, [\chi])\).

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

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

\( 16 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2520, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2520.1.eq.a	$2520$	$1$	2520.eq	840.bt	$6$	$8$	$4$	$1.258$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-10}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{4}q^{5}+\cdots\)
2520.1.eq.b	$2520$	$1$	2520.eq	840.bt	$6$	$8$	$4$	$1.258$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-10}) \)	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+\zeta_{24}^{4}q^{5}+\cdots\)