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

• Label: 820.1.bp
• Level: $820$
• Weight: $1$
• Character orbit: 820.bp
• Rep. character: $\chi_{820}(39,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $126$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	820.bp (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 820 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(126\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	64	64	0
Cusp forms	32	32	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

32 * q + 4 * q^6 - 16 * q^14 - 8 * q^16 - 4 * q^24 + 8 * q^25 + 4 * q^26 - 20 * q^29 + 16 * q^30 - 16 * q^34 + 4 * q^41 - 8 * q^45 + 20 * q^54 - 4 * q^56 + 10 * q^65 + 8 * q^69 - 4 * q^70 - 40 * q^81 + 10 * q^85 + 8 * q^89 - 4 * q^94 + 4 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
820.1.bp.a	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	\(\Q(\zeta_{20})\)	$D_{20}$	\(\Q(\sqrt{-1}) \)	None		✓			820.1.bp.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
820.1.bp.b	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	\(\Q(\zeta_{20})\)	$D_{20}$	\(\Q(\sqrt{-5}) \)	None		✓			820.1.bp.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{20}q^{2}+(-\zeta_{20}^{2}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)
820.1.bp.c	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	\(\Q(\zeta_{20})\)	$D_{20}$	\(\Q(\sqrt{-5}) \)	None		✓			820.1.bp.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$1$		\(q-\zeta_{20}q^{2}+(\zeta_{20}^{2}+\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)
820.1.bp.d	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	\(\Q(\zeta_{20})\)	$D_{20}$	\(\Q(\sqrt{-1}) \)	None		✓			820.1.bp.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}-\zeta_{20}^{8}q^{8}+\cdots\)