Space of modular forms of level 2008, weight 1, and Character 2008.c

• Label: 2008.1.c
• Level: $2008$
• Weight: $1$
• Character orbit: 2008.c
• Rep. character: $\chi_{2008}(501,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2008 = 2^{3} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2008.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2008 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2008, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	6	6	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	6	0	0	0

Trace form

\( 6 q + 6 q^{4} - 2 q^{7} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2008, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2008.1.c.a	$2008$	$1$	2008.c	2008.c	$2$	$3$	$3$	$1.002$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-502}) \)	None	✓	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots\)
2008.1.c.b	$2008$	$1$	2008.c	2008.c	$2$	$3$	$3$	$1.002$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-502}) \)	None	✓	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots\)