Space of modular forms of level 3584, weight 1, and Character 3584.h

• Label: 3584.1.h
• Level: $3584$
• Weight: $1$
• Character orbit: 3584.h
• Rep. character: $\chi_{3584}(769,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $512$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3584.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(512\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3584, [\chi])\).

	Total	New	Old
Modular forms	68	12	56
Cusp forms	36	12	24
Eisenstein series	32	0	32

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

\( 12 q + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3584, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3584.1.h.a	$3584$	$1$	3584.h	56.h	$2$	$4$	$4$	$1.789$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\beta _{3}q^{3}-\beta _{1}q^{5}-q^{7}+(1-\beta _{2})q^{9}+\cdots\)
3584.1.h.b	$3584$	$1$	3584.h	56.h	$2$	$4$	$4$	$1.789$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{14}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
3584.1.h.c	$3584$	$1$	3584.h	56.h	$2$	$4$	$4$	$1.789$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-14}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q+\beta _{3}q^{3}-\beta _{1}q^{5}+q^{7}+(1-\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)