Space of modular forms of level 800, weight 1, and Character 800.bh

• Label: 800.1.bh
• Level: $800$
• Weight: $1$
• Character orbit: 800.bh
• Rep. character: $\chi_{800}(31,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	800.bh (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(800, [\chi])\).

	Total	New	Old
Modular forms	56	8	48
Cusp forms	24	8	16
Eisenstein series	32	0	32

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

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

Trace form

\( 8 q - 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(800, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
800.1.bh.a	$800$	$1$	800.bh	100.j	$10$	$8$	$2$	$0.399$	\(\Q(\zeta_{20})\)	$A_{5}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{5}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)