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

• Label: 3200.1.m
• Level: $3200$
• Weight: $1$
• Character orbit: 3200.m
• Rep. character: $\chi_{3200}(193,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $480$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 3200 = 2^{7} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3200.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(480\)
Trace bound:			\(41\)

Dimensions

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

	Total	New	Old
Modular forms	148	20	128
Cusp forms	52	20	32
Eisenstein series	96	0	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + O(q^{10}) \)

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.m.a	$3200$	$1$	3200.m	40.i	$4$	$2$	$1$	$1.597$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{9}+(-1-i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.b	$3200$	$1$	3200.m	40.i	$4$	$2$	$1$	$1.597$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{9}+(1+i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.c	$3200$	$1$	3200.m	40.i	$4$	$4$	$2$	$1.597$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{2}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\zeta_{8}q^{23}-q^{41}+\cdots\)
3200.1.m.d	$3200$	$1$	3200.m	40.i	$4$	$4$	$2$	$1.597$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{10}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q-\zeta_{8}^{3}q^{3}-3\zeta_{8}^{2}q^{9}+2\zeta_{8}q^{27}+q^{41}+\cdots\)
3200.1.m.e	$3200$	$1$	3200.m	40.i	$4$	$8$	$4$	$1.597$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$		\(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{4}-\zeta_{24}^{8})q^{11}+\cdots\)

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

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