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

• Label: 1600.1.bd
• Level: $1600$
• Weight: $1$
• Character orbit: 1600.bd
• Rep. character: $\chi_{1600}(31,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1600.bd (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	64	16	48
Cusp forms	16	16	0
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	0	0	0	16

Trace form

\( 16 q + 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1600.1.bd.a	$1600$	$1$	1600.bd	200.n	$10$	$8$	$2$	$0.799$	\(\Q(\zeta_{20})\)	$A_{5}$	None	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$		\(q+(-1+\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}^{5}q^{7}+\cdots\)
1600.1.bd.b	$1600$	$1$	1600.bd	200.n	$10$	$8$	$2$	$0.799$	\(\Q(\zeta_{20})\)	$A_{5}$	None	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}-\zeta_{20}^{5}q^{7}+\cdots\)

Additional information

This is the first newspace containing multiple newforms with projective image $A_5$.