Space of modular forms of level 3200, weight 1, and Character 3200.bi

• Label: 3200.1.bi
• Level: $3200$
• Weight: $1$
• Character orbit: 3200.bi
• Rep. character: $\chi_{3200}(319,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3200 = 2^{7} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3200.bi (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3200, [\chi])\).

	Total	New	Old
Modular forms	72	8	64
Cusp forms	8	8	0
Eisenstein series	64	0	64

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

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

Trace form

\( 8 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3200, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3200.1.bi.a	$3200$	$1$	3200.bi	200.s	$10$	$4$	$1$	$1.597$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
3200.1.bi.b	$3200$	$1$	3200.bi	200.s	$10$	$4$	$1$	$1.597$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)