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

• Label: 1620.1.bp
• Level: $1620$
• Weight: $1$
• Character orbit: 1620.bp
• Rep. character: $\chi_{1620}(79,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $324$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1620.bp (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1620 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(324\)
Trace bound:			\(23\)

Dimensions

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

	Total	New	Old
Modular forms	108	108	0
Cusp forms	36	36	0
Eisenstein series	72	72	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	36	0	0	0

Trace form

\( 36 q + O(q^{10}) \)

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.bp.a	$1620$	$1$	1620.bp	1620.ap	$54$	$18$	$1$	$0.808$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{54}^{25}q^{2}-\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots\)
1620.1.bp.b	$1620$	$1$	1620.bp	1620.ap	$54$	$18$	$1$	$0.808$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{54}^{25}q^{2}+\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots\)