Space of modular forms of level 820, weight 1, and Character 820.bz

• Label: 820.1.bz
• Level: $820$
• Weight: $1$
• Character orbit: 820.bz
• Rep. character: $\chi_{820}(7,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $126$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	820.bz (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 820 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(126\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(820, [\chi])\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	16	16	0
Eisenstein series	64	64	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(820, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
820.1.bz.a	$820$	$1$	820.bz	820.az	$40$	$16$	$1$	$0.409$	\(\Q(\zeta_{40})\)	$D_{40}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{40}^{8}q^{2}+\zeta_{40}^{16}q^{4}-\zeta_{40}^{9}q^{5}+\cdots\)