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

• Label: 3200.1.e
• Level: $3200$
• Weight: $1$
• Character orbit: 3200.e
• Rep. character: $\chi_{3200}(1599,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3200 = 2^{7} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3200.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	82	6	76
Cusp forms	34	6	28
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 6 q^{9} + O(q^{10}) \)

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.e.a	$3200$	$1$	3200.e	40.e	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+q^{9}-iq^{17}+q^{41}-q^{49}+iq^{73}+\cdots\)
3200.1.e.b	$3200$	$1$	3200.e	40.e	$2$	$4$	$4$	$1.597$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3200, [\chi]) \cong \)