Space of modular forms of level 3456, weight 1, and Character 3456.j

• Label: 3456.1.j
• Level: $3456$
• Weight: $1$
• Character orbit: 3456.j
• Rep. character: $\chi_{3456}(161,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3456.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3456, [\chi])\).

	Total	New	Old
Modular forms	128	8	120
Cusp forms	32	8	24
Eisenstein series	96	0	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(3456, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3456.1.j.a	$3456$	$1$	3456.j	48.i	$4$	$4$	$2$	$1.725$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}q^{11}+(1+\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
3456.1.j.b	$3456$	$1$	3456.j	48.i	$4$	$4$	$2$	$1.725$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}q^{11}+(1+\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 3}\)