Space of modular forms of level 2979, weight 1, and Character 2979.c

• Label: 2979.1.c
• Level: $2979$
• Weight: $1$
• Character orbit: 2979.c
• Rep. character: $\chi_{2979}(2647,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $332$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2979 = 3^{2} \cdot 331 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2979.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 331 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(332\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2979, [\chi])\).

	Total	New	Old
Modular forms	21	9	12
Cusp forms	17	8	9
Eisenstein series	4	1	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	2	0

Trace form

\( 8 q - 2 q^{4} + 3 q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2979, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2979.1.c.a	$2979$	$1$	2979.c	331.b	$2$	$1$	$1$	$1.487$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-331}) \)	\(\Q(\sqrt{993}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{16}+2q^{19}-q^{25}-2q^{31}+\cdots\)
2979.1.c.b	$2979$	$1$	2979.c	331.b	$2$	$1$	$1$	$1.487$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-331}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{4}+q^{5}+q^{16}+q^{17}-q^{19}+q^{20}+\cdots\)
2979.1.c.c	$2979$	$1$	2979.c	331.b	$2$	$2$	$2$	$1.487$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{993}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
2979.1.c.d	$2979$	$1$	2979.c	331.b	$2$	$2$	$2$	$1.487$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta q^{2}-q^{4}+q^{5}-\beta q^{7}-\beta q^{10}+\cdots\)
2979.1.c.e	$2979$	$1$	2979.c	331.b	$2$	$2$	$2$	$1.487$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-331}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}-\beta q^{5}+q^{16}+\beta q^{17}-q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2979, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2979, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(331, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(993, [\chi])\)\(^{\oplus 2}\)