Space of modular forms of level 2352, weight 1, and Character 2352.z

• Label: 2352.1.z
• Level: $2352$
• Weight: $1$
• Character orbit: 2352.z
• Rep. character: $\chi_{2352}(815,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $448$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2352.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(448\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2352, [\chi])\).

	Total	New	Old
Modular forms	112	8	104
Cusp forms	16	8	8
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	8	0	0	0

Trace form

\( 8 q - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2352, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2352.1.z.a	$2352$	$1$	2352.z	84.j	$6$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)
2352.1.z.b	$2352$	$1$	2352.z	84.j	$6$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)		$8$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}q^{19}-\zeta_{6}^{2}q^{25}+\cdots\)
2352.1.z.c	$2352$	$1$	2352.z	84.j	$6$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)		$8$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}q^{19}-\zeta_{6}^{2}q^{25}+\cdots\)
2352.1.z.d	$2352$	$1$	2352.z	84.j	$6$	$2$	$1$	$1.174$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2352, [\chi]) \cong \)