Space of modular forms of level 2020, weight 1, and Character 2020.cd

• Label: 2020.1.cd
• Level: $2020$
• Weight: $1$
• Character orbit: 2020.cd
• Rep. character: $\chi_{2020}(7,\cdot)$
• Character field: $\Q(\zeta_{100})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $306$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2020.cd (of order \(100\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2020 \)
Character field:			\(\Q(\zeta_{100})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(306\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2020, [\chi])\).

	Total	New	Old
Modular forms	200	200	0
Cusp forms	40	40	0
Eisenstein series	160	160	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	40	0	0	0

Trace form

\( 40 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2020, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2020.1.cd.a	$2020$	$1$	2020.cd	2020.bd	$100$	$40$	$1$	$1.008$	\(\Q(\zeta_{100})\)	$D_{100}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{100}^{41}q^{2}-\zeta_{100}^{32}q^{4}-\zeta_{100}^{21}q^{5}+\cdots\)