Space of modular forms of level 1856, weight 1, and Character 1856.bh

• Label: 1856.1.bh
• Level: $1856$
• Weight: $1$
• Character orbit: 1856.bh
• Rep. character: $\chi_{1856}(255,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1856.bh (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1856, [\chi])\).

	Total	New	Old
Modular forms	108	18	90
Cusp forms	36	6	30
Eisenstein series	72	12	60

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 2 q^{5} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1856, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1856.1.bh.a	$1856$	$1$	1856.bh	116.j	$14$	$6$	$1$	$0.926$	\(\Q(\zeta_{14})\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-\zeta_{14}^{4}-\zeta_{14}^{6})q^{5}-\zeta_{14}q^{9}+(-\zeta_{14}^{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)