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

• Label: 1620.1.v
• Level: $1620$
• Weight: $1$
• Character orbit: 1620.v
• Rep. character: $\chi_{1620}(217,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $324$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1620.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(324\)
Trace bound:			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	152	8	144
Cusp forms	8	8	0
Eisenstein series	144	0	144

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

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

Trace form

\( 8 q + 4 q^{7} + O(q^{10}) \)

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.v.a	$1620$	$1$	1620.v	45.k	$12$	$4$	$1$	$0.808$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{11}+\cdots\)
1620.1.v.b	$1620$	$1$	1620.v	45.k	$12$	$4$	$1$	$0.808$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{4}q^{11}+\cdots\)