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

• Label: 1856.1.ca
• Level: $1856$
• Weight: $1$
• Character orbit: 1856.ca
• Rep. character: $\chi_{1856}(193,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $12$
• 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.ca (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{28})\)
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	180	36	144
Cusp forms	36	12	24
Eisenstein series	144	24	120

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 \(S_{1}^{\mathrm{new}}(1856, [\chi])\) 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.ca.a	$1856$	$1$	1856.ca	29.f	$28$	$12$	$1$	$0.926$	\(\Q(\zeta_{28})\)	$D_{28}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{28}^{4}-\zeta_{28}^{12})q^{5}-\zeta_{28}^{3}q^{9}+(-\zeta_{28}^{9}+\cdots)q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)