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

• Label: 2020.1.k
• Level: $2020$
• Weight: $1$
• Character orbit: 2020.k
• Rep. character: $\chi_{2020}(1413,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• 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.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 505 \)
Character field:			\(\Q(i)\)
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	22	4	18
Cusp forms	10	4	6
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 2 q^{5} + 2 q^{13} - 2 q^{17} + 2 q^{23} - 2 q^{25} - 4 q^{37} + 4 q^{43} + 2 q^{47} + 2 q^{65} + 4 q^{71} - 4 q^{81} - 2 q^{85} - 4 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2020.1.k.a	$2020$	$1$	2020.k	505.h	$4$	$4$	$2$	$1.008$	\(\Q(\zeta_{12})\)	$D_{12}$	None	\(\Q(\sqrt{101}) \)		✓	✓	✓	2020.1.k.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{9}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2020, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2020, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(505, [\chi])\)\(^{\oplus 3}\)