Space of modular forms of level 3072, weight 1, and Character 3072.h

• Label: 3072.1.h
• Level: $3072$
• Weight: $1$
• Character orbit: 3072.h
• Rep. character: $\chi_{3072}(2561,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $512$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3072 = 2^{10} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3072.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(512\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3072, [\chi])\).

	Total	New	Old
Modular forms	86	12	74
Cusp forms	38	4	34
Eisenstein series	48	8	40

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(3072, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3072.1.h.a	$3072$	$1$	3072.h	24.h	$2$	$4$	$4$	$1.533$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3072, [\chi]) \cong \)