Space of modular forms of level 2839, weight 1, and Character 2839.c

• Label: 2839.1.c
• Level: $2839$
• Weight: $1$
• Character orbit: 2839.c
• Rep. character: $\chi_{2839}(2838,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2839 = 17 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2839.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2839 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2839, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	12	12	0
Eisenstein series	2	2	0

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

\( 12 q - 2 q^{2} + 10 q^{4} - 4 q^{8} + 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2839, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2839.1.c.a	$2839$	$1$	2839.c	2839.c	$2$	$6$	$6$	$1.417$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-2839}) \)	None	✓	✓	2839.1.c.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\beta _{4}q^{2}+(1-\beta _{5})q^{4}-\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2839.1.c.b	$2839$	$1$	2839.c	2839.c	$2$	$6$	$6$	$1.417$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-2839}) \)	None	✓	✓	2839.1.c.a	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\beta _{4}q^{2}+(1-\beta _{5})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)