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

• Label: 2020.1.d
• Level: $2020$
• Weight: $1$
• Character orbit: 2020.d
• Rep. character: $\chi_{2020}(2019,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $306$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - 12 q^{4} - 6 q^{5} + 4 q^{6} - 16 q^{9} + O(q^{10}) \)

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.d.a	$2020$	$1$	2020.d	2020.d	$2$	$1$	$1$	$1.008$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-505}) \)	\(\Q(\sqrt{505}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots\)
2020.1.d.b	$2020$	$1$	2020.d	2020.d	$2$	$1$	$1$	$1.008$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-505}) \)	\(\Q(\sqrt{505}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots\)
2020.1.d.c	$2020$	$1$	2020.d	2020.d	$2$	$2$	$2$	$1.008$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-101}) \)	\(\Q(\sqrt{505}) \)		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+iq^{2}-iq^{3}-q^{4}-q^{5}+2q^{6}-iq^{7}+\cdots\)
2020.1.d.d	$2020$	$1$	2020.d	2020.d	$2$	$4$	$4$	$1.008$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{505}) \)		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
2020.1.d.e	$2020$	$1$	2020.d	2020.d	$2$	$12$	$12$	$1.008$	\(\Q(\zeta_{28})\)	$D_{14}$	\(\Q(\sqrt{-101}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+\zeta_{28}^{7}q^{2}+(-\zeta_{28}^{3}-\zeta_{28}^{11})q^{3}+\cdots\)