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

• Label: 2020.1.bt
• Level: $2020$
• Weight: $1$
• Character orbit: 2020.bt
• Rep. character: $\chi_{2020}(279,\cdot)$
• Character field: $\Q(\zeta_{50})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $306$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2020.bt (of order \(50\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2020 \)
Character field:			\(\Q(\zeta_{50})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(306\)
Trace bound:			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	160	160	0
Cusp forms	80	80	0
Eisenstein series	80	80	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	80	0	0	0

Trace form

\( 80 q + 10 q^{9} + O(q^{10}) \)

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.bt.a	$2020$	$1$	2020.bt	2020.at	$50$	$20$	$1$	$1.008$	\(\Q(\zeta_{50})\)	$D_{50}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{50}^{8}q^{2}+\zeta_{50}^{16}q^{4}+\zeta_{50}^{11}q^{5}+\cdots\)
2020.1.bt.b	$2020$	$1$	2020.bt	2020.at	$50$	$20$	$1$	$1.008$	\(\Q(\zeta_{50})\)	$D_{50}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{50}^{8}q^{2}+\zeta_{50}^{16}q^{4}+\zeta_{50}^{23}q^{5}+\cdots\)
2020.1.bt.c	$2020$	$1$	2020.bt	2020.at	$50$	$40$	$2$	$1.008$	\(\Q(\zeta_{100})\)	$D_{50}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{100}q^{2}+(-\zeta_{100}^{15}-\zeta_{100}^{23})q^{3}+\cdots\)