Space of modular forms of level 1620, weight 1, and Character 1620.f

• Label: 1620.1.f
• Level: $1620$
• Weight: $1$
• Character orbit: 1620.f
• Rep. character: $\chi_{1620}(1459,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $324$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1620.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(324\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1620, [\chi])\).

	Total	New	Old
Modular forms	46	16	30
Cusp forms	22	8	14
Eisenstein series	24	8	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1620, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1620.1.f.a	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1620.1.f.b	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$1$		\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1620.1.f.c	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1620.1.f.d	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1620.1.f.e	$1620$	$1$	1620.f	20.d	$2$	$4$	$4$	$0.808$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1620, [\chi]) \cong \)