Space of modular forms of level 2997, weight 1, and Character 2997.n

• Label: 2997.1.n
• Level: $2997$
• Weight: $1$
• Character orbit: 2997.n
• Rep. character: $\chi_{2997}(998,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $342$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 2997 = 3^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2997.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(342\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2997, [\chi])\).

	Total	New	Old
Modular forms	46	26	20
Cusp forms	22	22	0
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	22	0	0	0

Trace form

\( 22 q - 9 q^{4} + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2997, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2997.1.n.a	$2997$	$1$	2997.n	333.n	$6$	$2$	$1$	$1.496$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-111}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(1\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
2997.1.n.b	$2997$	$1$	2997.n	333.n	$6$	$2$	$1$	$1.496$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \)	\(\Q(\sqrt{37}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{25}+\cdots\)
2997.1.n.c	$2997$	$1$	2997.n	333.n	$6$	$2$	$1$	$1.496$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-111}) \)	None		$4$	$0$	\(2\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
2997.1.n.d	$2997$	$1$	2997.n	333.n	$6$	$4$	$2$	$1.496$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-111}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
2997.1.n.e	$2997$	$1$	2997.n	333.n	$6$	$4$	$2$	$1.496$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-111}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$		\(q-\zeta_{12}^{4}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{5}+\cdots\)
2997.1.n.f	$2997$	$1$	2997.n	333.n	$6$	$8$	$4$	$1.496$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-111}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$		\(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{8}q^{4}+(\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)