Space of modular forms of level 420, weight 1, and Character 420.o

• Label: 420.1.o
• Level: $420$
• Weight: $1$
• Character orbit: 420.o
• Rep. character: $\chi_{420}(419,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	420.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 420 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(420, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(420, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
420.1.o.a	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{105}) \)		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}-iq^{7}+\cdots\)
420.1.o.b	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{105}) \)		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}-iq^{7}+\cdots\)