Space of modular forms of level 1020, weight 1, and Character 1020.o

• Label: 1020.1.o
• Level: $1020$
• Weight: $1$
• Character orbit: 1020.o
• Rep. character: $\chi_{1020}(509,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1020.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1020, [\chi])\).

	Total	New	Old
Modular forms	34	4	30
Cusp forms	22	4	18
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(1020, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1020.1.o.a	$1020$	$1$	1020.o	255.h	$2$	$4$	$4$	$0.509$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-51}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1020, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1020, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)