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

• Label: 2020.1.z
• Level: $2020$
• Weight: $1$
• Character orbit: 2020.z
• Rep. character: $\chi_{2020}(219,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $306$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2020.z (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2020 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
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	32	32	0
Cusp forms	16	16	0
Eisenstein series	16	16	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

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

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.z.a	$2020$	$1$	2020.z	2020.z	$10$	$4$	$1$	$1.008$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}^{3}q^{5}+\cdots\)
2020.1.z.b	$2020$	$1$	2020.z	2020.z	$10$	$4$	$1$	$1.008$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{5}+\cdots\)
2020.1.z.c	$2020$	$1$	2020.z	2020.z	$10$	$8$	$2$	$1.008$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{20}^{3}q^{2}+(-\zeta_{20}^{5}-\zeta_{20}^{9})q^{3}+\cdots\)