Space of modular forms of level 3969, weight 1, and Character 3969.k

• Label: 3969.1.k
• Level: $3969$
• Weight: $1$
• Character orbit: 3969.k
• Rep. character: $\chi_{3969}(460,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $504$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3969 = 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3969.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(504\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3969, [\chi])\).

	Total	New	Old
Modular forms	112	20	92
Cusp forms	16	12	4
Eisenstein series	96	8	88

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

\( 12 q - 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3969, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3969.1.k.a	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-q^{8}+q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.b	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{16}+q^{25}+\zeta_{6}q^{37}+\cdots\)
3969.1.k.c	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}q^{4}+(1+\zeta_{6})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.d	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}+q^{8}-q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.e	$3969$	$1$	3969.k	63.k	$6$	$4$	$2$	$1.981$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)