Space of modular forms of level 3528, weight 1, and Character 3528.ba

• Label: 3528.1.ba
• Level: $3528$
• Weight: $1$
• Character orbit: 3528.ba
• Rep. character: $\chi_{3528}(67,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $672$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3528.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3528, [\chi])\).

	Total	New	Old
Modular forms	60	36	24
Cusp forms	28	20	8
Eisenstein series	32	16	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	4	0	0

Trace form

\( 20 q - 2 q^{3} - 6 q^{4} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3528, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3528.1.ba.a	$3528$	$1$	3528.ba	504.aa	$6$	$2$	$1$	$1.761$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{6}+q^{8}+\cdots\)
3528.1.ba.b	$3528$	$1$	3528.ba	504.aa	$6$	$2$	$1$	$1.761$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-1\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{6}+q^{8}+\cdots\)
3528.1.ba.c	$3528$	$1$	3528.ba	504.aa	$6$	$4$	$2$	$1.761$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3528.1.ba.d	$3528$	$1$	3528.ba	504.aa	$6$	$4$	$2$	$1.761$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
3528.1.ba.e	$3528$	$1$	3528.ba	504.aa	$6$	$8$	$4$	$1.761$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{8}q^{2}+\zeta_{24}^{9}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \)