Space of modular forms of level 1600, weight 1, and Character 1600.m

• Label: 1600.1.m
• Level: $1600$
• Weight: $1$
• Character orbit: 1600.m
• Rep. character: $\chi_{1600}(993,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1600.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1600, [\chi])\).

	Total	New	Old
Modular forms	84	12	72
Cusp forms	12	12	0
Eisenstein series	72	0	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1600, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1600.1.m.a	$1600$	$1$	1600.m	40.i	$4$	$2$	$1$	$0.799$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{5}) \)		✓			1600.1.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{9}-2 i q^{11}-2 q^{19}+2 q^{41}+\cdots\)
1600.1.m.b	$1600$	$1$	1600.m	40.i	$4$	$2$	$1$	$0.799$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{5}) \)		✓			1600.1.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{9}+2 i q^{11}+2 q^{19}+2 q^{41}+\cdots\)
1600.1.m.c	$1600$	$1$	1600.m	40.i	$4$	$4$	$2$	$0.799$	\(\Q(i, \sqrt{6})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		✓			1600.1.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+2\beta _{2}q^{9}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots\)
1600.1.m.d	$1600$	$1$	1600.m	40.i	$4$	$4$	$2$	$0.799$	\(\Q(i, \sqrt{6})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		✓			1600.1.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+2\beta _{2}q^{9}+\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots\)